Control of table grape storage rots by pre-harvest applications of salts

Postharvest Biology and Technology 42(2006)

142–149

Control of table grape storage rots by pre-harvest applications of salts

Franco Nigro ?,Leonardo Schena,Angela Ligorio,Isabella Pentimone,

Antonio Ippolito,Mario G.Salerno

Dipartimento di Protezione delle Piante e Microbiologia Applicata,Universit`a degli Studi di Bari,

Via Amendola 165/A,70126Bari,Italy

Received 30November 2005;accepted 11June 2006

Abstract

The activity of 19inorganic and organic salts to control table grape storage rots was preliminarily assessed by in vitro and in vivo tests.Several salts reduced the growth of Botrytis cinerea Pers.on amended (0.1–2%,w/v)glucose–agar;however,only calcium chloride (CC),potassium carbonate (PC),sodium bicarbonate (SB)and sodium carbonate (SC)signi?cantly reduced the incidence of grey mould on small table grape bunches (cv.Italia).PC,SB and SC showed a similar effect in the in vitro (inhibition of mycelial growth and conidia germination of B.cinerea )and in vivo tests (reduction of incidence of grey mould on table grape),whereas CC was effective only in vivo .Ef?cacy of salts applied before harvest was extensively evaluated in small-scale tests (CC,PC,SB,and SC),and in large-scale tests (CC,SB,SC).In both,small-and large-scale tests,?eld applications of salts resulted in a signi?cant reduction of botrytis storage rots.Field rots (mainly sour rot)were signi?cantly reduced when vines were sprayed at least 21days before harvest.In large-scale tests,simulating the practical commercial conditions in Southern Italy,two salt applications (30and 90days before harvest)of CC,SC,or SB signi?cantly reduced postharvest grey mould from 63.8%among untreated controls to 22.5,31.2,and 29.5%,respectively.In the same conditions,?eld rots were 23.4%(untreated control),9.5%(CC),11.9%(SC)and 12.0%(SB).On the whole,salts showed an activity higher or similar to that of conventional chemical treatments.Finally,results from speci?c tests suggested that pH and inhibition of polygalacturonase activity of B.cinerea seem to play a role in the mode of action of SB,SC,PC and CC.?2006Elsevier B.V .All rights reserved.

Keywords:Botrytis cinerea ;Table grape;Inorganic salts;Grey mould;Sour rot;Control

1.Introduction

Grey mould,due to Botrytis cinerea Pers.,is one of the most important diseases of table grapes,because of the dam-age caused in the harvest season and during storage.Losses are severe,particularly in years when heavy rainfall dur-ing fruit ripening occurs.The pathogen can also develop at low temperature,shortening the duration of storage and marketing.Sour rot,a grape disease with an ambiguous and controversial aetiology (Guerzoni and Marchetti,1987),causes losses that exceed grey mould in Southern Italy.The disease,associated with Acetobacter spp.,and other bacte-ria and yeasts transmitted by the grape fruit?y (Drosophila melanogaster Mg.),is a serious problem in Apulia (South-?

Corresponding author.Tel.:+390805443055;fax:+390805442911.E-mail address:nigrof@agr.uniba.it (F.Nigro).

ern Italy)where table grapes bunches are left on vines under plastic coverings to delay the harvest.The control of botry-tis storage rot and sour rot is very dif?cult since postharvest treatments with synthetic fungicides or food additives are not allowed by European legislation (European Parliament and Council Directive 95/2/EC,1995).Pre-harvest fungi-cide applications are not always effective to control botrytis storage rot and ineffective against sour rot.Furthermore,the use of conventional chemicals is becoming increasingly restricted because of concerns for the environment and human health,as well as the cost of developing new fungicides to overcome resistance developed by the pathogens.Therefore,there is a need for alternative disease-management practices that can reduce rots without risks for consumers and work-ers.Many alternative means have been proposed to manage postharvest disease of fruit and vegetables.These include biocontrol agents (Janisiewicz and Korsten,2002),natural

0925-5214/$–see front matter ?2006Elsevier B.V .All rights reserved.doi:10.1016/j.postharvbio.2006.06.005

F.Nigro et al./Postharvest Biology and Technology42(2006)142–149143

substances(Ippolito and Nigro,2003),and physical treat-ments(Nigro et al.,1998).

In the search for biocompatible products,which could be de?ned as chemicals exhibiting low mammalian and envi-ronmental toxicity,many salts have been recently tested as alternative control means,either alone(Smilanick et al., 1999)or in combination with physical(Palou et al.,2001)and biological treatments(Ippolito et al.,2005;Karabulut et al., 2005).Salts are inexpensive,easily accepted by consumers, non-toxic,with minor environmental impact at the effective concentrations,and usually used in the food industry.

Several inorganic salts have been shown to be active antimicrobial agents against a range of phytopathogenic fungi.In particular,postharvest treatments with calcium chlo-ride(CC)and sodium bicarbonate(SB)have been proposed as safe and effective alternative means to control posthar-vest rots of fruit and vegetables.The activity of bicarbonate salts against fungal pathogens is well known(Hervieux et al.,2002)and recent postharvest applications reduced stor-age rots of melon(Aharoni et al.,1997),papaya(Sivakumar et al.,2002),citrus(Palou et al.,2002;Smilanick et al., 2005),banana(Alvindia et al.,2004),table grape(Mlikota Gabler and Smilanick,2001),and bell pepper(Fallik et al.,1997).Calcium,known for its ability to reduce or delay parasitic and/or physiological disorders in fruit and vegetables,also gave promising results in controlling stor-age rots when applied both as organic and inorganic salts (Punja and Grogan,1982;Biggs,1999;Conway et al., 1999).

Most of the research regarding the use of carbonates and calcium salts to control postharvest rots has involved posthar-vest applications;however,they are inappropriate for fruit such as strawberries and table grapes since the cosmetic appeal of these fruit can be seriously reduced by posthar-vest handling(Ippolito and Nigro,2000).There are only few reports about pre-harvest applications of salts to control stor-age rots.Application of SB24h before harvest signi?cantly reduced the incidence of botrytis storage rot on table grape (Karabulut et al.,2003).Field applications of CC increased the storage life of kiwifruit(Gerasopoulos et al.,1996)and reduced the incidence of russet on‘Golden Delicious’apples (Brown et al.,1996)and various rots on cactus pear(Schirra et al.,1999).Field applications of SB were effective for con-trolling Monilinia fructicola on organic apricots(McLaren and Fraser,2000).Similarly,pre-and postharvest applica-tion of CC on table grapes reduced the incidence of grey mould storage rot(Ippolito et al.,1997;Miceli et al.,1999).

The present work was performed to evaluate the effective-ness of a range of salts,mostly common food preservatives, for the control of pre and postharvest rots of table grapes.In this regard,we conducted small-and large-scale trials over a4-year period with different pre-harvest application sched-ules of these salts to obtain the most effective postharvest decay control ef?cacy.Investigation of some possible mech-anisms by which the most effective salts reduce rot incidence was also carried out.2.Materials and methods

2.1.In vitro and in vivo screening of salts

The effect of19salts(Table1)on the mycelial growth of B. cinerea was evaluated using1%glucose agar(GA).An aque-ous solution of the salts was sterilised by?ltration(0.45?m) and added to molten(45?C)GA,to achieve0.1,0.25,0.5,1, and2%(w/v)?nal concentration;GA without salts served as a control.GA-salt solutions,poured into100mm Petri dishes, were inoculated in the centre with a5mm mycelial plug taken from the edge of actively growing colony of B.cinerea and incubated for5days at22?C.Colony diameter was mea-sured as the average of the longest and the shortest diameter; the results were expressed as minimum inhibitory concentra-tion(MIC).Salts(Table2)were also tested for their activity against B.cinerea on table grape,cv.Italia,harvested at com-mercial maturity from groves located at Conversano,and Rutigliano(South-eastern Italy).Small bunches,of approxi-mately10berries,were sprayed with an aqueous salt solution (1%,w/v)or sterile distilled water(control)until dripping and left to dry.Before application the pH of all salt solu-tions was measured.The bunches were then sprayed with a conidial suspension of B.cinerea,prepared by removing the spores from a sporulating edge of the3-week-old culture with a sterile bacteriological loop and suspending them in sterile distilled water.The suspension was?ltered through three sterile cheesecloth layers and spore concentration was adjusted to5×105mL?1using a haemocytometer.Treated bunches were arranged in plastic trays,covered with plas-tic sheet,and stored at0?C(95–98%RH)for22days.The percentage of rotted berries was evaluated after7days shelf Table1

Minimum inhibitory concentration(MIC)of salts for Botrytis cinerea in a colony growth assay

Salt MIC(%,w/v) Sodium chloride(NaCl)>2.0 Sodium formate(HCOONa)>2.0 Calcium nitrate(Ca(NO3)2·4H2O)>2.0

Sodium phosphate monobasic(NaH2PO4·H2O)>2.0 Sodium nitrate(NaNO3)>2.0 Calcium chloride(CaCl2)>2.0 Ammonium chloride(NH4Cl)>2.0 Sodium acetate(CH3COONa·3H2O)>2.0 Potassium chloride(KCl)>2.0 Potassium phosphate dibasic(K2HPO4)>2.0 Ammonium sulphate((NH4)2SO4)>2.0 Sodium phosphate dibasic(Na2HPO4·12H2O) 2.0 Sodium sulphate(Na2SO4)0.5 Ammonium phosphate dibasic((NH4)2HPO4)0.5 Sodium bicarbonate(NaHCO3)0.5 Sodium silicate(Na2Ox2SiO2·2H2O)0.5 Potassium carbonate(K2CO3)0.5 Sodium carbonate(Na2CO3)0.25 Ammonium bicarbonate(NH4HCO3)0.25 Diameter of B.cinerea colonies was determined after5days incubation at 22?C on glucose agar amended with different salt concentrations(0.1,0.25, 0.5,1.0,and2%,w/v).

144F.Nigro et al./Postharvest Biology and Technology42(2006)142–149

Table2

pH values and effect of19aqueous salt solutions(1%,w/v)on the devel-opment of rots on small table grape bunches arti?cially inoculated with B. cinerea

Salts pH Rotted

berries(%) Sodium phosphate dibasic(Na2HPO4·12H2O)8.497.0a Ammonium chloride(NH4Cl) 5.580.0b Control(distilled water) 5.778.0bc Sodium nitrate(NaNO3) 5.978.0bc Ammonium sulphate((NH4)2SO4) 5.677.0bc Sodium sulphate(Na2SO4) 5.977.0bc Sodium chloride(NaCl) 5.976.0bc Sodium acetate(CH3COONa·3H2O)7.673.0bc Sodium formate(HCOONa)7.173.0bc Ammonium phosphate dibasic((NH4)2HPO4)8.172.0bc Monobasic sodium phosphate(NaH2PO4·H2O) 4.371.0bc Ammonium bicarbonate(NH4HCO3)8.164.0bcd Potassium chloride(KCl) 5.963.0bcd Calcium nitrate(Ca(NO3)2·4H2O) 5.762.0bcd Potassium phosphate dibasic(K2HPO4)9.062.0bcd Sodium silicate(Na2Ox2SiO2·2H2O)11.660.0cd Calcium chloride(CaCl2) 6.048.0de Sodium bicarbonate(NaHCO3)8.545.0de Sodium carbonate(Na2CO3)11.341.0e Potassium carbonate(K2CO3)11.336.0e Values marked with different letters are statistically different according to Fisher’s protected LSD test(P≤0.05).

life at20±1?C and90–95%RH.In both screening tests a completely randomized experimental design,including?ve replicates(Petri dishes or small bunches),was utilised.An arcsine transformation was applied to data percentage prior to analysis of variance(ANOV A)and the mean values were compared by using Fisher’s protected LSD test.

2.2.Small-and large-scale trials

Field trials were conducted over a4-year period in com-mercial orchards of table grapes(cv.Italia)located in South-eastern Italy,involving pre-harvest applications of salts and conventional fungicides(chemical controls)as described in Table3.In particular,aqueous salt solutions(1%,w/v)were sprayed twice(21and5days before harvest)in the?rst3 years of the trials;a treatment receiving only one salts appli-cation(5days before harvest)was also included in the second year.For each year,the spraying time was in the last week of October or the?rst week of November,depending on the harvest date.According to the control schedule used in the commercial grove which hosted the trials,in the fourth year salts were sprayed90days(end of August)and30days(end of October)before harvest,in order to test their effective-ness under the practical control conditions commonly used in Southern Italy.A motor-driven back sprayer(delivering approximately10hL ha?1)and a hydro-pneumatic sprayer (delivering approximately7hL ha?1)were used for small-and large-scale tests,respectively.Harvested bunches were placed in plastic crates,covered with plastic sheet to maintain high relative humidity(95–98%)and stored.The incidence Table3

Schematic representation of small-and large-scale?eld tests

Year Treatments Number of

applications

Timing a First

Untreated

CC221and5

SC

SB

PC

Procymidone121 Second b

Untreated

CC221and5

SC15

SB

PC

Procymidone121

Large-scale tests

Third

Untreated

CC221and5

SC

SB

Ciprodinil and

?udioxonil

121

Fourth

Untreated

CC290and30

SC

SB

Ciprodinil and

?udioxonil

Trials provided pre-harvest sprays with1%(w/v)aqueous solution of cal-cium chloride(CC),sodium bicarbonate(SB),sodium carbonate(SC),and potassium carbonate(PC).Untreated table grapes bunches and bunches treated with procymidone(Sumisclex?,50%a.i.)at0.75g L?1or a mix-ture of ciprodinil and?udioxonil(Switch?,37.5and25%a.i.,respectively) at0.8g L?1,were used as controls.

a Days before harvest.

b For each salt,treatments with two applications(21and5days before harvest)and one application(5days before harvest)were performed.

of naturally occurring decay(sour rot,grey mould,and sec-ondary rots)was evaluated on two different sets of bunches,in the?eld(5days before harvest)and after storage at0±1?C (1month)and shelf life(5–7days)at20±1?C,90–95%RH. Decay assessment was done by using an empirical scale with the following values:(0)bunch without rots;(1)1–5%of rot-ted berries;(2)6–10%of rotted berries;(3)11–25%of rotted berries;(4)26–50%of rotted berries;(5)51–75%of rotted berries;(6)more than76%of rotted berries.This empiri-cal scale made it possible to calculate the McKinney index (McKinney,1923),expressing the weighted average of the disease severity as actual percentage in terms of the maximum disease severity.The McKinney index(MI)was calculated by means of the following formula:MI=[

df/T n D]×100, where d is the degree of disease severity assessed on the bunch,f its frequency,T n the total number of the fruit exam-ined(healthy and diseased),and D the highest degree of disease intensity occurring on the empirical scale.

All trials were arranged in a completely randomised block design with four replicates.In small-scale tests each repli-cation contained three grape vines,from which15bunches

F.Nigro et al./Postharvest Biology and Technology42(2006)142–149145

were harvested;in large-scale tests each replication con-tained50grape vines,from which30bunches were randomly harvested.An arcsine transformation was applied to data per-centage prior to analysis of variance(ANOV A),and the mean values of treatments compared by using Fisher’s protected LSD test.

2.3.Effect of salts and pH on the germination of B. cinerea conidia

The ability of B.cinerea conidia to germinate was eval-uated in50mL of liquid medium containing2.4%potato dextrose broth(PDB)supplemented with1%of calcium chlo-ride(CC),potassium carbonate(PC),sodium bicarbonate (SB),or sodium carbonate(SC).PDB medium was utilised without modifying the pH determined by each salt or adjust-ing its value to pH6–10by means of NaOH,KOH or HCl. An equal set of PDB medium without salts was used as con-trol.Diluted conidial suspension of B.cinerea was added to the medium at a?nal concentration of104cells mL?1. The percentage of germinated conidia(length/width ratio≥2) was evaluated after6and24h incubation on a rotary shaker (100rpm),at21?C,in the dark.For each salt type,pH value and reading date,three separate replications of100conidia were evaluated.

2.4.Effect of salts on polygalacturonase activity of B. cinerea

To evaluate the effect of salts on polygalacturonase activity of B.cinerea,the pathogen was grown in a minimal salt(MS) medium(KH2PO4,13.6g/L;NH4NO3,4g;MgSO4·7H2O, 2.6g/L;FeSO4·7H2O,20mg/L;CuSO4·5H2O,0.07mg/L;

ZnSO4·7H2O,0.23mg/L;(NH4)2MoO4,0.18mg/L; MnSO4·4H2O,2mg/L;H3BO4, 3.1mg/L;pectin,5g/L; sodium polypectate,5g/L)containing CC,PC,SB,or SC at different concentrations(10,20,and40mM).MS medium without salts was used as a control.Two agar plugs (9mm in diameter)taken from the edge of actively growing mycelium of B.cinerea were used to inoculate50mL of medium.After7days incubation at25?C on a rotary shaker at120rpm,the media were collected by?ltration and the concentration of polygalacturonase(PG)assessed measuring the concentration of reducing sugars using the 2-cyanoacetamide method described by Gross(1982).Three replicate samples were utilised for each salt and for each concentration.

3.Results

3.1.Preliminary screening of salts

The in vitro tests showed a variable effect of salts on B. cinerea growth(Table1).After5days incubation at22?C most salts reduced the colony diameter of the pathogen.A complete inhibition was achieved by ammonium bicarbon-ate and SC at0.25%and by ammonium phosphate,PC,SB, sodium silicate,and sodium sulphate at0.5%.CC did not affect the growth of B.cinerea,whereas it was enhanced on GA amended with calcium nitrate,sodium chloride,and sodium nitrate,as compared to the control(Table1).

In the in vivo tests on small table grape bunches,salts showed a variable activity against B.cinerea(Table2).Aque-ous solutions(1%,w/v)of CC,SB,SC,and PC were the most effective,reducing the percentage of rotted berries by38.5, 42.3,47.4,and53.9,respectively,as compared to the water control.None of the salt solutions had a phytotoxic effect on the berries.The pH of salt solutions did not show any signif-icant correlation with the control activity(data not shown). High disease reductions were obtained with SC and PC for which the pH was11.3;however,a signi?cant disease reduc-tion was obtained also by using CC,with a pH of6.00.

3.2.Small-scale trials

In small-scale trials conducted in the?rst year,CC,PC, SB,and SC reduced the incidence of total rots on table grape bunches treated21and5days before harvest(Fig.1).In the?eld assessment(5days before harvest)all the salts sig-ni?cantly(P≤0.05)reduced rot incidence as compared to the untreated control,with reduction ranging from46.1to 64.6%(Fig.1).A signi?cant(P≤0.05)rot reduction was also achieved after30days of storage followed by5days of shelf life at20?C(Fig.1).CC,PC,SB,and SC reduced rot inci-dence from57.6to71.4%as compared to the untreated

con-Fig.1.Small-scale tests conducted in the?rst year investigation.Rot inci-dence among table grape bunches treated in the?eld21and5days before harvest with1%(w/v)aqueous solution of calcium chloride(CC),potas-sium carbonate(PC),sodium bicarbonate(SB),or sodium carbonate(SC). Untreated bunches and bunches treated with procymidone(Sumisclex?,50% a.i.)at0.75g L?1were used as controls.Rots were assessed in the?eld5 days before harvest(A)and after30days storage at0?C followed by5 days shelf life at20±1?C(B).For each assessment,columns marked with the same letters are not statistically different according to Fisher’s protected LSD test(P≤0.05).

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142–149

Fig.2.Small-scale tests conducted in the second year investigation.Inci-dence of postharvest rots among table grapes bunches treated in the?eld once(5days before harvest—A)or twice(21and5days before harvest—B) with calcium chloride(CC),potassium carbonate(PC),sodium bicarbonate (SB),or sodium carbonate(SC).Untreated bunches and bunches treated with procymidone(Sumisclex?,50%a.i.)at0.75g L?1were used as controls. Rots were assessed after30days storage at0?C followed by5days shelf life at20±1?C.Values followed by the same letters are not statistically different according to Fisher’s protected LSD test(P≤0.05).

trol;moreover,SB was signi?cantly(P≤0.05)more effective than the chemical control.

In the second year of trials,all salts reduced storage rots as compared to the untreated control(Fig.2).Two salt appli-cations(5and21days before harvest)allowed higher levels of protection compared to a single salt spray(5days before harvest),although the values were not statistically different. In particular,on the bunches treated21and5days before har-vest,storage rots were reduced by54.8%(CC),50.1%(PC), 50.7%(SB),and50.6%(SC),as compared to the untreated control(Fig.2).

In both years of trials,?eld rots were mainly ascribed to sour rot whereas storage rots were almost exclusively caused by B.cinerea(data not shown).

https://www.wendangku.net/doc/0613562123.html,rge-scale trials

In large-scale trials conducted in the third year of trials, salts applications21and5days before harvest signi?cantly reduced storage rots(Fig.3),but were ineffective in reducing the rot incidence in the?eld(data not shown).After1-month storage at0?C and5days at20±1?C,storage rot incidence was reduced by49.3%(CC),53.6%(SC),and37.2%(SB)as compared to the untreated control.Chemical control was the most effective treatment in reducing storage rots,although not statistically different from SC(Fig.3).

In the fourth year trials,the application of salts90and 30days before harvest resulted in a signi?cant reduction of rots compared to untreated controls(Fig.4).In the?eld assessment the three tested salts reduced sour rot incidence by 59.4%(CC),49.2%(SC),and48.6%(SB),whereas the chem-ical control was not statistically different from the

untreated https://www.wendangku.net/doc/0613562123.html,rge-scale trials conducted in the third year investigation.Stor-age rot incidence on table grapes bunches treated in the?eld21and5 days before harvest with calcium chloride(CC),potassium carbonate(PC), sodium bicarbonate(SB),or sodium carbonate(SC).Untreated bunches and bunches treated with a mixture of ciprodinil and?udioxonil(Switch?,37.5 and25%a.i.,respectively)at0.8g L?1were used as controls.Rot incidence was determined after30days storage at0?C followed by7days shelf life at 20±1?C.Columns marked with the same letter are not statistically different according to Fisher’s protected LSD test(P≤

0.05).

https://www.wendangku.net/doc/0613562123.html,rge-scale trials conducted in the fourth year investigation.Rot inci-dence among table grape bunches treated in the?eld30and90days before harvest with calcium chloride(CC),potassium carbonate(PC),sodium bicar-bonate(SB),or sodium carbonate(SC).Untreated bunches and bunches treated with a mixture of ciprodinil and?udioxonil(Switch?,37.5and25% a.i.,respectively)at0.8g L?1were used as controls.Rots were assessed in the?eld(A)and after30days storage at0?C followed by6days shelf life at20±1?C(B).For each assessment,columns marked with the same let-ters are not statistically different according to Fisher’s protected LSD test (P≤0.05).

F.Nigro et al./Postharvest Biology and Technology42(2006)142–149

147

Fig.5.Effect of different salt concentrations on the polygalacturonase activ-ity of https://www.wendangku.net/doc/0613562123.html,:calcium chloride;PC:potassium carbonate;SB: sodium bicarbonate;SC:sodium carbonate.Bars represent the standard error (n=3).

control.After1-month storage at0?C and5days shelf life, storage rots were reduced by64.7%(CC),51.1%(SC),53.8% (SB),and40.4%(chemical control),as compared to the untreated control(Fig.4).

In both years of trials?eld rots were mainly ascribed to sour rot,whereas storage rots were almost exclusively caused by B.cinerea,the incidence of secondary rots(due to Alternaria,Aspergillus,Cladosporium,Mucor,Penicillium, and Rhizopus spp.)being negligible(data not shown).

3.4.Effect of salts and pH on conidial germination and polygalacturonase activity of B.cinerea

The pH had a variable in?uence on germination of B. cinerea conidia for the different salts.After6h incubation,a concentration of1%of PC,SB,and SC prevented germina-tion of B.cinerea spores in PDB from pH6to10and at the native pH of each salt solution.Germination of the spores in 1%CC occurred from pH6to10and was similar to that of the control.

CC,PC,SB,and SC signi?cantly inhibited polygalac-turonase activity of B.cinerea at the tested concentrations (Fig.5).In particular,CC was the most effective at all the tested concentrations,whereas SB resulted in an increasing reduction with increasing concentrations(Fig.5).

4.Discussion

The objective of the present study was selection of salts effective in controlling sour rot and botrytis storage rot of table grapes by means of pre-harvest applications.In prelim-inary screenings,several salts showed in vitro and/or in vivo inhibitory activity against B.cinerea,although no correla-tion was found between the two activities.Indeed,ammo-nium bicarbonate,ammonium phosphate,sodium acetate,and sodium sulphate strongly reduced B.cinerea mycelial growth but displayed an inconsistent activity against grey mould on small bunches.In particular,sodium phosphate reduced the growth of the pathogen in vitro,but increased rot incidence on small table grape bunches.As reported for other phosphates(Palou et al.,2002),presumably this salt provided additional nutrients and/or enhanced environmental conditions for the development of the pathogen.In addition, CC showed almost no in vitro inhibitory activity but strongly reduced grey mould incidence on table grapes.Other salts such as PC,SB,and SC showed the same behaviour,with both in vitro and in vivo assays.Therefore,the present study suggests that in vitro tests are inappropriate to predict the potential of a salt in controlling grey mould of table grapes as already reported for silver scurf on potato tubers(Hervieux et al.,2002).The different in vitro and in vivo behaviour of salts suggests that speci?c salt–host tissue interactions may involve biochemical reactions,such as defense mechanisms contributing to the control of grey mould(Hervieux et al., 2002).Furthermore,the interaction between salt and agar medium(Biggs et al.,1997)as well as the interaction between salt and environment(Punja and Grogan,1982)may play an important role.

Results of the present work showed that pH of salt solu-tions has a minor role in the mode of action.High disease reductions were obtained with PC and SC(pH11.3),but also with SB(pH8.5),and CC(pH6.0).Furthermore,PC,SB,and SC completely inhibited the germination of B.cinerea inde-pendently of the pH,whereas in water and in CC solutions, conidial germination was reduced,but not completely inhib-ited by high pH.Although our results,in accordance with data reported by Palmer et al.(1997),demonstrate that pH alone cannot explain the inhibitory action of salts,it cannot be excluded that a change in pH value may affect the activity of salts(Punja and Grogan,1982;Mecteau et al.,2002).

In the present work,results from small-and large-scale tests demonstrated that pre-harvest applications of salts are an effective strategy to reduce the incidence of sour rot and botrytis storage rot of table grapes.Although with some dif-ferences,CC,PC,SB,and SC in small-scale tests and CC,SB, and SC in large-scale tests,provided similar or higher level of protection compared to conventional fungicides.Higher control levels were achieved with two applications(21and 5days before harvest)as compared to a single application made5days before harvest.Furthermore,early applications (90and30days before harvest)of calcium chloride provided better control of?eld rots,mainly sour rots.It is presumed that an early application of calcium chloride favoured the penetration of calcium through the skin and that a second application increased the calcium level inside the fruit,result-ing in higher levels of protection compared to treatments made just a few days before harvest.Our data are in accor-dance with previous reports on pre-harvest application of calcium chloride.Pre-harvest applications of calcium chlo-ride increased the Ca2+content of sweet cherries and apples (Brown et al.,1996),and table grape berries(Miceli et al.,

148F.Nigro et al./Postharvest Biology and Technology42(2006)142–149

1999).As demonstrated by the penetration of calcium chlo-ride via aqueous pores,exogenous Ca2+easily penetrates the fruit epidermis(Sch¨o nherr,2000).The mechanism by which calcium improves the resistance of plant tissues to pathogens is not completely understood.Most of the calcium,which penetrates into the fruit tissue,seems to accumulate in the middle lamella region of the cell wall where it exerts a stabil-ising effect,forming ionic bridges between and within pectic polysaccharides,thereby conferring rigidity to the cell wall. The formation of calcium cross-linkage between pectin poly-mers could make the cell wall more resistant to hydrolytic enzymes produced by decay causing organisms(Tobias et al.,1993).Furthermore,as assessed in the present work, calcium treatments affect pathogens directly,inhibiting the activity of polygalacturonase enzyme.A reduced virulence or a fungistatic activity of calcium has been already reported for Penicillium expansum and B.cinerea(Conway et al.,1999; Droby et al.,1997).Other studies have shown that calcium treatments preserve the membrane integrity of carrot shreds by delaying senescence-related membrane lipid changes and enhancing membrane-restructuring processes(Picchioni et al.,1996).Calcium also seems to increase the synthesis of phytoalexins and/or phenolic substances(Kohle et al., 1985).

Regarding other salts used in the present work(PC,SB, and SC),their mechanisms of action are not well understood; however,compared to CC the direct action of these salts on the pathogen seems be a major role.The activity of carbonates and bicarbonates in inhibiting spore germination,germ tube elongation,and production of pectinolytic enzymes in sev-eral pathogens is well recognized(Punja and Grogan,1982; Hervieux et al.,2002;Mills et al.,2004;Smilanick et al., 2005).These salts strongly inhibited mycelial growth and spore germination of B.cinerea as well as polygalacturonase activity.Considering that the proportion of CO32?ion is high at pH11.3(PC and SC)and that HCO3?is the predominant ion at pH8.4(SB),the results suggests that both the HCO3?and CO32?forms display an inhibitory activity on mycelial growth and spore germination(Palmer et al.,1997).Like calcium chloride,carbonate and bicarbonate salts were more effective when applied during the early phase of fruit devel-opment and when applied twice.Since the inhibitory action of carbonate and bicarbonates depends on the presence of salt residues within the wound infection site occupied by fungi, it is possible that earlier applications,especially when fol-lowed by a later one,provide a more effective action against pathogens and prevent the establishment of latent infections (Smilanick et al.,1999;Alvindia et al.,2004).However,other possible implications of earlier applications such as a major host resistance induction are also possible.

Control ef?cacy achieved with CC,SC,and SB seems to be remarkable since small and,in particular,large-scale trials were conducted simulating commercial practical con-ditions.Pre-harvest applications of salts are easy to achieve since they can be made using the same equipment used for conventional chemical applications and are appropriate for the reduction of postharvest water-based treatments that can reduce the appeal of table grape bunches(Ippolito and Nigro, 2000).Mlikota Gabler and Smilanick(2001)reported that dip treatments with sodium carbonate and potassium carbonate are very effective in the control of gray mold on grapes but they darkened the pedicels and caused dark brown spots on the berries.Such problems were completely avoided in the present work by applying salts before harvest.Other advan-tages of salts are the very low costs and the lack of legislative restrictions to their utilisation.However,several additional factors should be explored to optimise table grape disease control with salts.In the present work a1%solution of salts was utilised since they were effective and non-phytotoxic to the berries,though higher concentrations have been con-sidered necessary by other authors to achieve high levels of protection(Smilanick et al.,1999;Tian et al.,2002).Fur-thermore,although our data seem to indicate that salts are more effective when applied during the early phase of berry development and that more salt applications increase ef?cacy, additional research is still required to optimise time and num-ber of applications.

Acknowledgement

This work was partially supported by CRPV–Centro Ricerche Produzioni Vegetali Soc.Coop.,Diegaro di Cesena (FC),Italy-in the framework of the project:“Sviluppo di metodi innovativi di gestione dei frutti nella fase di post-raccolta”.

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系泊系统的设计和探究

赛区评阅编号（由赛区组委会填写）： 2016年高教社杯全国大学生数学建模竞赛 承诺书 我们仔细阅读了《全国大学生数学建模竞赛章程》和《全国大学生数学建模竞赛参赛规则》（以下简称为“竞赛章程和参赛规则”，可从全国大学生数学建模竞赛网站下载）。 料 我们的报名参赛队号（12位数字全国统一编号）： 参赛学校（完整的学校全称，不含院系名）： 参赛队员 (打印并签名) ：1. 2.

3. 指导教师或指导教师组负责人 (打印并签名)： （指导教师签名意味着对参赛队的行为和论文的真实性负责） 日期：年月日 送全国评阅统一编号（赛区组委会填写）： 全国评阅随机编号（全国组委会填写）： （请勿改动此页内容和格式。此编号专用页仅供赛区和全国评阅使用，参赛队打印后装订到纸质论文的第二页上。注意电子版论文中不得出现此页。）

系泊系统的设计和探究 摘要 本文利用牛顿力学定律，力矩平衡原理、非线性规划、循环遍历法等方法对系泊系统进行了设计与探究。通过对系泊系统各组件和浮标运用牛顿经典力学体系进行分析，得到了各个情况下的钢桶倾斜角度、锚链状态、浮标吃水深度和游动区域。 ?， 。当风 对于第二问，求解当海面风速为36m/s时，浮标的吃水深度和游动区域、钢桶以及钢管的倾斜角度和锚链形态。利用第一问中的力学方程和程序，求得钢桶的倾角为19.5951?和四节钢管的倾斜角度依次为19.756?、19.755?、19.916?、20.076?。浮标的游动区域为以锚在海面上的投影为圆心，半径为18.8828m的圆。由于部分数据与问题二中钢桶的倾斜角度不超过5?，锚链在锚点与海床的夹角不超过16?的要求不符，所以通过调节重物球的质量使钢桶的倾斜角度和锚链在锚点与海床的夹角处在要求的范围之内。借助MATLAB程序中的循环遍历法，可以求得重物球的质量3770kg。

2016数学建模A题系泊系统设计

系泊系统的设计 摘要 对于问题一，建立模型一，已知题目给出的锚链长度与其单位长度的质量，得到悬链共210环。对各节锚链，钢桶，四节钢管受力分析得出静力平衡方程，使用分段外推法，可以得到静力平衡下的迭代方程。其中锚对锚链的拉力大小方向为输入变量，迭代的输出变量为浮标的位置和对钢管的拉力，在给定的风速下，输入和输出满足关系2)2(25.1cos 水v h T -=α，αθcos cos 11T T =，通过多层搜索算法得出最符合的输入输出值，即可得到给定风速下浮标的吃水深度，浮标拉力、锚链与海床夹角。利用MATLAB 软件编程求解模型得到：风力12m/s 时，钢桶与竖直方向上的角度1.9863度，从下往上四节钢管与竖直方向夹角为1.9652度、1.9592度、1.9532度、1.9472度，浮标吃水0.7173m ，以锚为圆心浮标的游动区域16.5125m ，锚链末端切线与海床的夹角3.8268度。风力24m/s 时，锚链形状，钢桶与竖直方向上的夹角3.9835度，从下往上四节钢管与竖直方向夹角为3.9420度、3.9301度、3.9183度、3.9066度，浮标吃水0.7244m ，以锚为圆心浮标的游动区域18.3175m 。锚链末端切线与海床夹角15.9175度。 对于问题二的第一小问，使用模型一求解，当风速36m/s 时，锚链末端切线与海床夹角26.3339度，浮标吃水0.7482m ，浮标游动区域为以锚为圆心半径为18.9578m 的圆形区域，从下往上四节钢管与竖直方向倾斜角度为8.4463度、8.4225度、8.3989度、8.3753度，钢桶与竖直方向倾斜角度为8.5294度。为满足问题二的要求，在模型一的基础上把重物球质量作为变量，建立模型二，将钢桶倾斜角小于5度和锚链前端夹角小于16度当做两个约束条件，通过MATLAB 编程求解得到满足约束条件要求的重物球质量取值范围为3700kg 到5320kg 。 对于问题三，首先取不同水深、水速、风速三种情况，建立模型三，即在模型一的基础上增加水流对系统产生的影响。在三种情况下，找到合适的锚链型号、锚链长度，重物球质量，对吃水深度、游动区域、钢桶的倾斜角三个目标进行优化达到最小。通过MATLAB 编程实现该模型三得到结果：选用Ⅲ型锚链，锚链长度为27.24m ，重物球质量为2580kg 。 关键词：平面静力系分析 多层搜索算法 遗传算法 逐步外推法 多目标优化

系泊系统的设计和探究

系泊系统的设计和探究 This model paper was revised by the Standardization Office on December 10, 2020

赛区评阅编号（由赛区组委会填写）： 2016年高教社杯全国大学生数学建模竞赛 承诺书 我们仔细阅读了《全国大学生数学建模竞赛章程》和《全国大学生数学建模竞赛参赛规则》（以下简称为“竞赛章程和参赛规则”，可从全国大学生数学建模竞赛网站下载）。 我们完全明白，在竞赛开始后参赛队员不能以任何方式（包括电话、电子邮件、网上咨询等）与队外的任何人（包括指导教师）研究、讨论与赛题有关的问题。 我们知道，抄袭别人的成果是违反竞赛章程和参赛规则的，如果引用别人的成果或资料（包括网上资料），必须按照规定的参考文献的表述方式列出，并在正文引用处予以标注。在网上交流和下载他人的论文是严重违规违纪行为。 我们以中国大学生名誉和诚信郑重承诺，严格遵守竞赛章程和参赛规则，以保证竞赛的公正、公平性。如有违反竞赛章程和参赛规则的行为，我们将受到严肃处理。 我们授权全国大学生数学建模竞赛组委会，可将我们的论文以任何形式进行公开展示（包括进行网上公示，在书籍、期刊和其他媒体进行正式或非正式发表等）。 我们参赛选择的题号（从A/B/C/D中选择一项填写）： 我们的报名参赛队号（12位数字全国统一编号）： 参赛学校（完整的学校全称，不含院系名）： 参赛队员 (打印并签名) ：1.

2. 3. 指导教师或指导教师组负责人 (打印并签名)： （指导教师签名意味着对参赛队的行为和论文的真实性负责） 日期：年月日 （请勿改动此页内容和格式。此承诺书打印签名后作为纸质论文的封面，注意电子版论文中不得出现此页。以上内容请仔细核对，如填写错误，论文可能被取消评奖资格。） 赛区评阅编号（由赛区组委会填写）： 2016年高教社杯全国大学生数学建模竞赛 编号专用页 赛区评阅记录（可供赛区评阅时使用）： 送全国评阅统一编号（赛区组委会填写）： 全国评阅随机编号（全国组委会填写）：

数学建模a题系泊系统设计

摘要 本题要求观测近海观测网的组成，建立模型对其中系泊系统进行设计，在不同风速和水流的情况下确定锚链，重物球，钢管及浮标等的状态，从而使通讯设备的工作效果最佳。求解的具体流程如下： 针对问题一，分别对系统中的受力物体在水平方向和竖直方向上的力进行分析，找出锚链对锚无拉力时的临界风速，运用力矩平衡求出钢管与钢桶的倾斜角度。对于锚链，将其等效为悬链线模型，根据风速不同判断锚链的状态，从而求出结果。 ?时能够正常工针对问题二，需要调节重物球的质量，使通讯设备在36m m 作。为了确定重物球的质量，首先将实际风速与临界风速进行比较，判断此时系统中各物体的状态，与题目中已知数据进行比较。在钢桶倾斜角度达到临界角度时，计算锚链与海床的夹角并于题中数据进行比较，计算重物球的质量。在浮标完全没入海面时，计算相应条件下重物球的质量，从而确定满足条件的重物球的质量范围。 针对问题三，要求在不同条件下，求出系泊系统中各物体的状态。以型号I 锚链为例，当水流方向与风速方向相同时，系统条件最差，分析在不同水深条件下的系泊系统设计。由题中已知条件确定系统设计的限制条件，对系统各物体进行受力分析，以使整体结果最小，即可得出最优的系泊系统设计。 # 》 关键词：悬链线多目标非线性规划 @

一、问题重述 近浅海观测网的传输节点由浮标系统、系泊系统和水声通讯系统组成（如图1所示）。某型传输节点的浮标系统可简化为底面直径2m、高2m的圆柱体，浮标的质量为1000kg。系泊系统由钢管、钢桶、重物球、电焊锚链和特制的抗拖移锚组成。锚的质量为600kg，锚链选用无档普通链环，近浅海观测网的常用型号及其参数在附表中列出。钢管共4节，每节长度1m，直径为50mm，每节钢管的质量为10kg。要求锚链末端与锚的链接处的切线方向与海床的夹角不超过16度，否则锚会被拖行，致使节点移位丢失。水声通讯系统安装在一个长1m、外径30cm 的密封圆柱形钢桶内，设备和钢桶总质量为100kg。钢桶上接第4节钢管，下接电焊锚链。钢桶竖直时，水声通讯设备的工作效果最佳。若钢桶倾斜，则影响设备的工作效果。钢桶的倾斜角度（钢桶与竖直线的夹角）超过5度时，设备的工作效果较差。为了控制钢桶的倾斜角度，钢桶与电焊锚链链接处可悬挂重物球。 系泊系统的设计问题就是确定锚链的型号、长度和重物球的质量，使得浮标的吃水深度和游动区域及钢桶的倾斜角度尽可能小。 问题1某型传输节点选用II型电焊锚链，选用的重物球的质量为1200kg。现将该型传输节点布放在水深18m、海床平坦、海水密度为×103kg/m3的海域。若海水静止，分别计算海面风速为12m/s和24m/s时钢桶和各节钢管的倾斜角度、锚链形状、浮标的吃水深度和游动区域。 | 问题2在问题1的假设下，计算海面风速为36m/s时钢桶和各节钢管的倾斜角度、锚链形状和浮标的游动区域。请调节重物球的质量，使得钢桶的倾斜角度不超过5度，锚链在锚点与海床的夹角不超过16度。 问题3 由于潮汐等因素的影响，布放海域的实测水深介于16m~20m之间。布放点的海水速度最大可达到s、风速最大可达到36m/s。请给出考虑风力、水流力和水深情况下的系泊系统设计，分析不同情况下钢桶、钢管的倾斜角度、锚链形状、浮标的吃水深度和游动区域。 二、模型假设 1.不考虑流体对锚链的作用，忽略锚链本身的伸长，锚链沿长度均匀分布； 2.假设风是二维的，只存在平行于水平面的风速，不存在垂直方向上的分量；

数学建模A题系泊系统设计完整版

数学建模A题系泊系统 设计 HEN system office room 【HEN16H-HENS2AHENS8Q8-HENH1688】

系泊系统的设计 摘要 本题要求观测近海观测网的组成，建立模型对其中系泊系统进行设计，在不同风速和水流的情况下确定锚链，重物球，钢管及浮标等的状态，从而使通讯设备的工作效果最佳。求解的具体流程如下： 针对问题一，分别对系统中的受力物体在水平方向和竖直方向上的力进行分析，找出锚链对锚无拉力时的临界风速，运用力矩平衡求出钢管与钢桶的倾斜角度。对于锚链，将其等效为悬链线模型，根据风速不同判断锚链的状态，从而求出结果。 ?时能够正常工作。为针对问题二，需要调节重物球的质量，使通讯设备在36m m 了确定重物球的质量，首先将实际风速与临界风速进行比较，判断此时系统中各物体的状态，与题目中已知数据进行比较。在钢桶倾斜角度达到临界角度时，计算锚链与海床的夹角并于题中数据进行比较，计算重物球的质量。在浮标完全没入海面时，计算相应条件下重物球的质量，从而确定满足条件的重物球的质量范围。 针对问题三，要求在不同条件下，求出系泊系统中各物体的状态。以型号I锚链为例，当水流方向与风速方向相同时，系统条件最差，分析在不同水深条件下的系泊系统设计。由题中已知条件确定系统设计的限制条件，对系统各物体进行受力分析，以使整体结果最小，即可得出最优的系泊系统设计。 关键词：悬链线多目标非线性规划 一、问题重述 近浅海观测网的传输节点由浮标系统、系泊系统和水声通讯系统组成（如图1所示）。某型传输节点的浮标系统可简化为底面直径2m、高2m的圆柱体，浮标的质量为1000kg。系泊系统由钢管、钢桶、重物球、电焊锚链和特制的抗拖移锚组成。锚的质量为600kg，锚链选用无档普通链环，近浅海观测网的常用型号及其参数在附表中列出。钢管共4节，每节长度1m，直径为50mm，每节钢管的质量为10kg。要求锚链末端与锚的链接处的切线方向与海床的夹角不超过16度，否则锚会被拖行，致使节点移位丢失。水声通讯系统安装在一个长1m、外径30cm的密封圆柱形钢桶内，设备和钢桶总质量为100kg。钢桶上接第4节钢管，下接电焊锚链。钢桶竖直时，水声通讯设备的工作效果最佳。若钢桶倾斜，则影响设备的工作效果。钢桶的倾斜角度（钢桶与竖直线的夹角）超过5度时，设备的工作效果较差。为了控制钢桶的倾斜角度，钢桶与电焊锚链链接处可悬挂重物球。 系泊系统的设计问题就是确定锚链的型号、长度和重物球的质量，使得浮标的吃水深度和游动区域及钢桶的倾斜角度尽可能小。

系泊系统的研究设计

Internal Combustion Engine &Parts 0引言 近海系泊系统作为气象监控，海洋探测的主要载体工具，对工程的实际应用有一定的积极作用。为了开发海洋资源，促进经济的发展，满足日益增长的能源需求量，深海油气的开发已成为必然趋势，而系泊系统的设计是深海平台开发的关键问题之一，其设计的目的是保证选择的型号满足工作功能需求，建立相关的代数模型研究在不同情况下的设计方案。 1系泊系统模型 1.1系泊系统平衡模型 忽略作用在锚链上的流动力， 可以将整个锚链简化成悬链线的形式，浮标系统和系泊系统在经过持续海风时浮 标停止运动，系泊系统达到平衡，运用牛顿运动定律和平 行四边形状规则对系统内的各个物体进行受力分析，得到关系表达式为 第一钢管对浮标的拉力为T ，T 与竖直方向多的夹角为θ，浮标所受的浮力为F f ，所受海风荷载为F N ，浮标本身的重力为G ，浮标沉在水中的百分比为α，浮标的直径为d ，沉在水中的高度为h f ，海水的密度为ρ，风速为V ，根据海风荷载近似公式为 求。同时满足轮胎加防滑链极限包络大于 15mm 间隙要求。图3图4Z 向空间 >80mm 图5铆接设计图6铆接设计 ③翼子板下部设计。翼子板下部设计成台阶形。当下部长度>120mm ，需设计成双台阶形（图4），便于两个安装点安装。当翼子板下部刚度不足时，翼子板下部增加下部加强板。翼子板下部设计注意几点：1）翼子板下部加强板材料DC05，料厚为0.7-1.0。2）翼子板下部加强板与翼子板下部安装面打3-5焊点相连。④翼子板后部设计。翼子板后部由于前门总成运动包络影响，翼子板翻边向内小于45度，利于成型。通常安装面设计成台阶形或平 面。翼子板后部安装孔设计圆孔或开口U 形孔，U 形更利于装配。 ⑤翼子板上部设计。 翼子板上部通常安装点采有台阶设计。根据冲压工艺反馈，翻边高度设计为<40mm ，防止出现面品问题。 为满足行人保护要求，通常会从以下几种方式考虑。通常翼子板支架设计成几字形，并在支架两开孔落化（图4）。翼子板上部与边梁高度控制在80mm 以上（图4）。翼子板翻边在满足刚度前提下，尽量开豁口。随着新工艺的发展，翼子板结构，可以采铆接技术，具体设计如图5、6所示。 3制造过程控制 ①翼子板周边件产品要符合设计精度要求。②翼子板过涂装通常有两种方式，一种是在焊装装配 随车身一同电泳，另一种是单件单独电泳。建议采用第一 种，防止总装配出现难调整问题。③总装装配严格按工艺装配相关件。按装配顺序装配完成，再作微调。4结语总之保证翼子板品质，要从设计、制造过程着手。随着 铝合金翼子板、塑料翼子板应用，翼子板设计、制造过程有所变化，但总体设计理念不变。参考文献: [1]袁亮，秦信武，苗布和.汽车前翼子板的布置和结构设计[J].设计研究，2012，04，28. 系泊系统的研究设计 王莎莎;晏明莉 （河南师范大学，新乡453007） 摘要:本文所建立的近海系泊系统模型主要用于研究系泊系统在不同环境下的内在关系，进而给出适应不同情况的设计方案。影 响系泊系统的主要因素分别为锚链的型号，长度和重物球的质量，以及锚链的倾斜角度，浮标的吃水深度和游动区域，通过对系统中各个部分进行受力分析，建立相关的代数模型。该模型通过建立平衡方程组，采用最优控制策略、二分法收敛性和迭代判断，反复迭代计算求解。分别把锚链的型号，长度和重物球的质量作为自变量，把锚链的倾斜角度，浮标的吃水深度和游动区域作为因变量，建立模型进而得出不同环境下系泊系统的设计方案。 关键词:系泊系统设计；最优控制策略；二分法；平衡方程组；迭代计算

数学建模系泊系统的设计

系泊系统的设计 摘 要 近浅海观测网的传输节点由浮标系统、系泊系统和水声通讯系统组成，其中系泊系统由钢管、钢桶、重物球及锚链共同组成。此种系泊系统承受风、浪、流的作用及锚链的作用力，运动特性十分复杂。因此，针对海洋环境中水声通讯系统的要求，分析风浪中浮标的动力问题并设计出既安全又经济的系泊系统，对保证水声通讯系统的工作效果来说意义重大。 本文运用了两种方法对锚链进行了受力分析，首先对单一材质的锚链进行分析，从而得出了经典悬链方程，对不同段不同材质的锚链进行分段受力分析，得出了不同段不同材质的悬链方程，该方程的得出极大的方便了计算浮标锚泊系统的初始状态，为动力分析奠定基础；其次利用牛顿法对锚链受力问题进行了数值求解，得到当海面风速为12/m s 加大到24/m s 时，每节钢管的倾斜角度也随之变大，浮标的吃水深度也不断增大，浮标的游动区域增加的更为明显。当风速加大为36/m s 时，钢桶的倾斜角已超过5度，为使钢桶倾斜角小于5度，须将重物球的质量增加至1783kg 。 再考虑风力、水流力、潮汐（波浪）等动力因素时，可以将问题进行简化，即直接考虑在水深18m 的情况下由于波浪的作用（准确的说是2m 波浪的作用），可使整个浮标漂浮于水面上（20m 情形），也可使整个浮标沉于水面下（16m 情形）。最后通过对浮标的受力分析，可得到浮标的动力控制方程，采用数值方法，可以得到在风速为36/m s ，水流速度为1.5/m s 时，倾斜角、吃水深度的数值解。 关键词： 浮标；系统；设计；动力分析

一．问题重述 近浅海观测网的传输节点由浮标系统、系泊系统和水声通讯系统组成（如图1所示）。某型传输节点的浮标系统可简化为底面直径2m、高2m的圆柱体，浮标的质量为1000kg。系泊系统由钢管、钢桶、重物球、电焊锚链和特制的抗拖移锚组成。锚的质量为600kg，锚链选用无档普通链环，近浅海观测网的常用型号及其参数在附表中列出。钢管共4节，每节长度1m，直径为50mm，每节钢管的质量为10kg。要求锚链末端与锚的链接处的切线方向与海床的夹角不超过16度，否则锚会被拖行，致使节点移位丢失。水声通讯系统安装在一个长1m、外径30cm 的密封圆柱形钢桶内，设备和钢桶总质量为100kg。钢桶上接第4节钢管，下接电焊锚链。钢桶竖直时，水声通讯设备的工作效果最佳。若钢桶倾斜，则影响设备的工作效果。钢桶的倾斜角度（钢桶与竖直线的夹角）超过5度时，设备的工作效果较差。为了控制钢桶的倾斜角度，钢桶与电焊锚链链接处可悬挂重物球。系泊系统的设计问题就是确定锚链的型号、长度和重物球的质量，使得浮标的吃水深度和游动区域及钢桶的倾斜角度尽可能小。 问题1某型传输节点选用II型电焊锚链22.05m，选用的重物球的质量为1200kg。现将该型传输节点布放在水深18m、海床平坦、海水密度为1.025×103kg/m3的海域。若海水静止，分别计算海面风速为12m/s和24m/s时钢桶和各节钢管的倾斜角度、锚链形状、浮标的吃水深度和游动区域。 问题2在问题1的假设下，计算海面风速为36m/s时钢桶和各节钢管的倾斜角度、锚链形状和浮标的游动区域。请调节重物球的质量，使得钢桶的倾斜角度不超过5度，锚链在锚点与海床的夹角不超过16度。 问题3 由于潮汐等因素的影响，布放海域的实测水深介于16m20m之间。布放点的海水速度最大可达到1.5m/s、风速最大可达到36m/s。请给出考虑风力、水流力和水深情况下的系泊系统设计，分析不同情况下钢桶、钢管的倾斜角度、锚链形状、浮标的吃水深度和游动区域。 二．模型假设与符号说明 1.模型的假设 由于浮标在海洋受海风、气流、海浪等的作用，气象及水文条件多变，在此，我们对整个问题作适当假设，在下文中，当涉及到具体问题时，我们将有针对性地给出必要的补充。 （1）锚链重力远远大于锚链所受到的流体作用力； （2）海床平坦，无凹凸不平情况； （3）浮标始终是垂直于海平面的，无倾斜或跌倒现象； （4）海面风速均匀、恒定，且风向始终平行于海平面； （5）海水流速均匀（流速与水深无关），且方向恒定（海流无垂直分量）； （6）锚链在整个过程中是不可弹性形变。

数学建模a题系泊系统设计完整版

数学建模a题系泊系统 设计 集团标准化办公室：[VV986T-J682P28-JP266L8-68PNN]

系泊系统的设计 摘要 本题要求观测近海观测网的组成，建立模型对其中系泊系统进行设计，在不同风速和水流的情况下确定锚链，重物球，钢管及浮标等的状态，从而使通讯设备的工作效果最佳。求解的具体流程如下： 针对问题一，分别对系统中的受力物体在水平方向和竖直方向上的力进行分析，找出锚链对锚无拉力时的临界风速，运用力矩平衡求出钢管与钢桶的倾斜角度。对于锚链，将其等效为悬链线模型，根据风速不同判断锚链的状态，从而求出结果。 ?时能够正常工针对问题二，需要调节重物球的质量，使通讯设备在36m m 作。为了确定重物球的质量，首先将实际风速与临界风速进行比较，判断此时系统中各物体的状态，与题目中已知数据进行比较。在钢桶倾斜角度达到临界角度时，计算锚链与海床的夹角并于题中数据进行比较，计算重物球的质量。在浮标完全没入海面时，计算相应条件下重物球的质量，从而确定满足条件的重物球的质量范围。 针对问题三，要求在不同条件下，求出系泊系统中各物体的状态。以型号I 锚链为例，当水流方向与风速方向相同时，系统条件最差，分析在不同水深条件下的系泊系统设计。由题中已知条件确定系统设计的限制条件，对系统各物体进行受力分析，以使整体结果最小，即可得出最优的系泊系统设计。 关键词：悬链线多目标非线性规划 一、问题重述 近浅海观测网的传输节点由浮标系统、系泊系统和水声通讯系统组成（如图1所示）。某型传输节点的浮标系统可简化为底面直径2m、高2m的圆柱体，浮标的质量为1000kg。系泊系统由钢管、钢桶、重物球、电焊锚链和特制的抗拖移锚组成。锚的质量为600kg，锚链选用无档普通链环，近浅海观测网的常用型号及其参数在附表中列出。钢管共4节，每节长度1m，直径为50mm，每节钢管的质量为10kg。要求锚链末端与锚的链接处的切线方向与海床的夹角不超过16度，否则锚会被拖行，致使节点移位丢失。水声通讯系统安装在一个长1m、外径30cm的密封圆柱形钢桶内，设备和钢桶总质量为100kg。钢桶上接第4节钢管，下接电焊锚链。钢桶竖直时，水声通讯设备的工作效果最佳。若钢桶倾斜，则影响设备的工作效果。钢桶的倾斜角度（钢桶与竖直线的夹角）超过5度时，设备的工作效果较差。为了控制钢桶的倾斜角度，钢桶与电焊锚链链接处可悬挂重物球。

系泊系统的设计

系泊系统的设计 发表时间：2020-01-18T09:59:04.837Z 来源：《基层建设》2019年第28期作者：武佳雷宇张曼[导读] 摘要：系泊系统不论是在船舶航行，还是在海洋资源的综合利用与开发中，均得到了广泛应用，因而，系泊系统的设计问题十分具有现代意义。 华北理工大学数学建模实验室 063000摘要：系泊系统不论是在船舶航行，还是在海洋资源的综合利用与开发中，均得到了广泛应用，因而，系泊系统的设计问题十分具有现代意义。本文隔离系统各组成部分，逐一进行受力分析和力矩分析，构造相应的刚体力学方程组，并根据海水深度联系各参数最终建立系泊系统状态模型。 关键词：系泊系统状态模型；受力平衡；力矩平衡 0引言 当海面风速一定且海水静止时，系泊系统的状态，即钢桶和各节钢管的倾斜角度、锚链形状、浮标的吃水深度和游动区域与系泊系统各部分之间的受力平衡和力矩平衡以及海水深度的约束密切相关。因此，可以隔离该系统的各组成部分，逐一进行力学分析，并最终根据海水深度，联系各参数建立系泊系统状态模型。具体数值参考2016年高教社杯全国大学生数学建模竞赛A题。系泊系统可分为浮标、钢管、钢桶和重物球、锚链四个部分，由题中锚链长度和型号计算得锚链共有210个链环，为了方便表述，对系统内部由上到下的构件进行标记：表1 各构件编号 1力学方程与模型的建立 1.1对浮标的力学分析[1] 漂浮在水面上的浮标，受到来自水平方向的风力、海水对它的浮力、其余组件对它作用力以及自身的重力，与夹角为 。已知浮标的高为，质量为，直径为，海水的密度为，设浮标的吃水深度为，根据重力、浮力公式，以及近海风荷载的近似计 算公式，可得。此时，浮标受到速度为的海风作用在海面上达到平衡，受力分解后，其在水平方向和垂直方向的受力均平衡。于是整理可得关于浮标的完整的刚性力学方程组[2]。其中，其在竖直面的投影高度即为浮标的吃水深度。 1.2对钢管的力学分析没入水中的钢管，由于海水静止，因此忽略水流力水平方向的作用。以与浮标相接的第一节钢管为例，其受到浮标对它的反作用力 、其余组件对它的作用力、海水对它的浮力以及自身的重力。为保持力矩平衡，钢管不发生旋转的现象，浮标对它的反作用力应相对于它的中心轴更偏向竖直方向。 此时有相对于竖直方向的夹角与和的夹角相等，即：，根据牛顿第三定律：。此时，钢管在这些力的共同作用下保持平衡。已知每节钢管的长度为 ，直径为，质量为，根据受力平衡、力矩平衡和重力、浮力公式，可得到相应的刚性力学方程组。其中，其在竖直面的投影高度为。 对于余下的三节钢管，依次进行同样的力学分析。得到对应的完整的刚性力学方程组，以及各钢管在竖直面的投影高度为、 、。 1.3对钢桶和重物球的力学分析没入水中的钢桶和重物球，由于海水静止，则忽略水流力水平方向的作用。对于重物球，其受到钢桶对其的作用力、海水对它的浮 力以及自身的重力。对于钢桶，其受到重物球对其的作用力（方向竖直向下）、其余部件对它的作用力（与竖直方向夹角为 ）和（与夹角为）、海水对它的浮力以及自身的重力.根据牛顿第三定律有。此时，钢桶在这些力的共同作用下保持平衡。已知钢桶的长度为，重物球的质量，设备和钢桶的总质量为，且外径为，根据受力平衡、力矩平衡（注意判断力矩方向）、牛顿第三定律则和阿基米德定律可得到对应的完整的刚性力学方程组。 此时，其在竖直面的投影高度为。 1.4对锚链的力学分析选取编号为的链环，联系该链环以及其上的其余部件构成一个新的整体，对该整体进行受力平衡的分析，其受到海风给它的风力、余下部分给它的拉力、海水给它的浮力以及自身所受的总重力，与水平方向夹角为。通过对整体的分析，简化了作用力与反作用力不断迭代的过程，更加直观的得到受力平衡时的状态。锚链密度为，每节链环的长度和单位长度的质量，再根据前式得到整体所受的总重力，受到海水的总浮力，整理后，可得到关于这个整体的完整的刚性力学方程组。 此时，各链环与竖直方向的夹角即可描述出锚链的形状。各节链环在竖直面的投影高度分别为： 1.5建立系泊系统状态模型 已知水深为，则有