虚拟激励法求解激励随机热传导问题
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摘要
为更有效地求解激励随机热传导问题,利用有限元技术和虚拟激励法,建立了激励随机热传导问题的数值求解模型,可考虑平稳与非平稳的随机激励。数值算例中的对比分析表明:通过虚拟激励技术,可有效计算真实响应的自/互功率谱密度和响应偏差。此外,对激励随机热传导逆问题进行了初步探讨。
Based on finite element and pseudo excitation methods,numerical model was developed for solving the heat conduction problem with stochastic excitations more effectively.The proposed model is applicable for both steady and unsteady excitations.Comparison of numerical examples indicates that the auto/cross power spectral density and the deviation of response can be calculated by utilizing the pseudo excitation skill effectively.Some preliminary investigation was carried out for the inverse heat conduction problem with stochastic excitation as well.
Based on finite element and pseudo excitation methods,numerical model was developed for solving the heat conduction problem with stochastic excitations more effectively.The proposed model is applicable for both steady and unsteady excitations.Comparison of numerical examples indicates that the auto/cross power spectral density and the deviation of response can be calculated by utilizing the pseudo excitation skill effectively.Some preliminary investigation was carried out for the inverse heat conduction problem with stochastic excitation as well.
引文
[1]胡亚才.随机热传导理论研究[D].杭州:浙江大学,1999.HU Ya-cai.Research on principle of stochastic heatconduction[D].Hangzhou:Zhejiang Univ.,1999.(in Chinese)
[2]沈季胜.活塞热冲击与随机传热过程的研究[D].杭州:浙江大学,2001.SHEN Ji-sheng.Study on the thermal shock andrandom heat transfer process of piston[D].Hangzhou:Zhejiang Univ.,2001.(in Chinese)
[3]MADERA A G.Simulation of stochastic heatconduction processes[J].Int J Heat MassTransfer,1994,37:2571-2577.
[4]SAMUELS J C.Heat conduction in solids withrandom external temperatures and/or randominternal heat generation[J].Int J Heat MassTransfer,1966,9:301-314.
[5]BECUS G A.Random generalized to the heatequation[J].J of Math Anal and Appl,1977,60(1):93-102.
[6]CAMPO A,YOSHIMURA T.Random heattransfer in flat channels with timewise variation ofambient temperature[J].Int J Heat MassTransfer,1979,22:5-12.
[7]KELLER J B.Wave Propagation in Random Media[J].Proc Symp Appl Math Soc Am,1962,13:33-45.
[8]AHMADI G.A perturbation method for studyingheat conduction in solid with random conductivity[J].J Appl Mech,1978,45(2):933-934.
[9]ZHOU D Y.Stochastic analysis of temperaturedistribution in a solid with random heat conductivity[J].Trans ASME J Heat Transfer,1988,110(1):23-29.
[10]ZHOU D Y.Stochastic modeling for contactproblems in heat conduction[J].Int J Heat MassTransfer,1989,32(5):913-921.
[11]GEORGIADIS J G.On the approximate solution ofnondeterministic heat and mass transport problems[J].Int J Heat Mass Transfer,1991,34:55-61.
[12]SUN T C.A finite element method for randomdifferential equations[C]//Bharucha-Reid A Ted.Approximate solution of random equations.Philadelphia,PA:Soc.for Ind.and Appl.Math.,1979.
[13]PADOVAN J,GUO Y H.Solution of non-deterministic finite difference heat conductionsimulations[J].Numer Heat Transfer,1989,15(3):383-398.
[14]MADERA A G.Numerical methods for analyzingthe stochastic stationary heat conduction equationwith random coefficients[J].J Eng Phys,1992,62:192-205.
[15]NICOLAI B M,BAERDEMAEKER J D.Avariance propagation algorithm for the computationof heat conduction under stochastic conditions[J].Int J Heat Mass Transfer,1999,31:1513-1520.
[16]EMERY A F.Solving stochastic heat transferproblems[J].Eng Anal with Boundary Elements,2004,28:279-291.
[17]CHANTASIRIWA S.Error and variance ofsolution to the stochastic heat conduction problemby multiquadric collocation method[J].IntCommun in Heat and Mass Transfer,2006,33:342-349.
[18]XIU D B,KARNIADAKIS G E.A new stochasticapproach to transient hea tconduction modeling withuncertainty[J].Int J of Heat and MassTransfer,2003,46:4681-4693.
[19]MALEKNEJAD K,MIRZAEE F.Numericalsolution of stochastic linear heat conduction problemby using new algorithms[J].Appl Math andComput,2005,163:97-106.
[20]于国安,邓智泉,彭兆行.基于随机过程的盘式制动器闸瓦温升研究[J].东北大学学报:自然科学版,1997,18(2):128-132.YU Guo-an,DENG Zhi-quan,PENG Zao-xing.Temperature analysis of disk brake shoe based onstochastic process[J].J of Northeastern Univ:Natural Sci,1997,18(2):128-132.(in Chinese)
[21]刘宁,刘光廷.大体积混凝土结构温度场的随机有限元算法[J].清华大学学报:自然科学版,1996(1):41-47.LIU Ning,LIU Guang-ting.Random temperaturefield of mass concrete structure solved by stochasticfinite element method[J].J of Tsinghua Univ:Sciand Tech,1996(1):41-47.(in Chinese)
[22]刘长虹,陈虬.在模糊随机因素影响下的多层圆筒结构的稳态热传导问题的区间数解法[J].应用数学和力学,2005,10:1191-1197.LIU Chang-hong,Chen Qiu.Interval analysis ofthe fuzzy-random heat conduction in the compositetubes[J].Appl Math and Mech,2005,10:1191-1197.(in Chinese)
[23]康健,赵明鹏,梁冰.随机固-热耦合模型与岩石热破裂数值试验研究[J].岩土力学,2005,26(1):135-139.KANG Jian,ZHAO Ming-pen,LIANG Bing.Random solid-head coupled model and numericaltests on hot cracking of rocks[J].Rock and SoilMech,2005,26(1):135-139.(in Chinese)
[24]林家浩,张亚辉.随机振动的虚拟激励法[M].北京:科学出版社,2004.LIN Jia-hao,Zhang Ya-hui.Pseudo-excitationmethod for random vibration[M].Beijing:Sci.Press,2004.(in Chinese)
[25]林家浩.随机地震响应的确定性算法[J].地震工程与工程振动,1985,5(1):89-93.LIN Jia-hao.A deterministic method for thecomputation of stochastic earthquake response[J].Earthquake Eng and Eng Vibration,1985,5(1):89-93.(in Chinese)
[26]林家浩.随机地震响应功率谱快速算法[J].地震工程与工程振动,1990,10(4):38-46.LIN Jia-hao.A fast algorithm for power spectra ofrandom seismic responses[J].Earthquake Eng andEng Vibration,1990,10(4):38-46.(in Chinese)
[27]刘元芳,林家浩.考虑流体和土壤耦合效应的桩基平台非线性随机地震响应分析[J].计算结构力学及其应用,1991,8(1):42-50.LIU Yuan-fang,LIN Jia-hao.Random seismicanalysis of nonlinear platform-fluid-soil-pilesystems[J].Chinese J of Comput Mech,1991,8(1):42-50.(in Chinese)
[28]林家浩.多相位输入结构随机响应[J].振动工程学报,1992,5(1):73-77.LIN Jia-hao.Structural random responses to multiphase excitations[J].J of Vibration Eng,1992,5(1):73-77.(in Chinese)
[29]LIN J H,SHEN W P,WILLIAMS F W.A highprecision direct integration scheme for structuressubjected to transient dynamic loading[J].Computand Struct,1995,56(1):113-120.
[30]智浩.平稳随机振动载荷功率谱识别研究[D].大连:大连理工大学,1998.ZHI Hao.Excitation spectrum identification ofstationary random vibration[D].Dalian:DalianUniv.of Tech.,1998.(in Chinese)
[31]林家浩,智浩,郭杏林.平稳随机振动荷载识别的逆虚拟激励法(一)[J].计算力学学报,1998,15(2):12-136.LIN Jia-hao,ZHI Hao,GUO Xing-lin.Inversepseudo excitation method for loading identificationof stationary random vibration(1)[J].Chinese Jof Comput Mech,1998,15(2):12-136.(inChinese)
[32]智浩,郭杏林,林家浩.平稳随机振动荷载识别的逆虚拟激励法(二)[J].计算力学学报,1998,15(4):395-428.ZHI Hao,GUO Xing-lin,LIN Jia-hao.Inversepseudo excitation method for loading identificationof stationary random vibration(2)[J].Chinese Jof Comput Mech,1998,15(4):395-428.(inChinese)
[33]ZHI H,LIN J H.Random loading identification ofmulti-input-multi-output structure[J].Struct Engand Mech,2000,10(4):359-369.
[34]LIN J H,GUO X L,ZHI H,et al.Computersimulation of structural random loadingidentification[J].Comput&Struct,2001,79(4):375-387.
[35]LEWIS R W,MORGAN K,THOMAS H R,et al.The finite element method in heat transferanalysis[M].Chichester:Wiley,1996
[2]沈季胜.活塞热冲击与随机传热过程的研究[D].杭州:浙江大学,2001.SHEN Ji-sheng.Study on the thermal shock andrandom heat transfer process of piston[D].Hangzhou:Zhejiang Univ.,2001.(in Chinese)
[3]MADERA A G.Simulation of stochastic heatconduction processes[J].Int J Heat MassTransfer,1994,37:2571-2577.
[4]SAMUELS J C.Heat conduction in solids withrandom external temperatures and/or randominternal heat generation[J].Int J Heat MassTransfer,1966,9:301-314.
[5]BECUS G A.Random generalized to the heatequation[J].J of Math Anal and Appl,1977,60(1):93-102.
[6]CAMPO A,YOSHIMURA T.Random heattransfer in flat channels with timewise variation ofambient temperature[J].Int J Heat MassTransfer,1979,22:5-12.
[7]KELLER J B.Wave Propagation in Random Media[J].Proc Symp Appl Math Soc Am,1962,13:33-45.
[8]AHMADI G.A perturbation method for studyingheat conduction in solid with random conductivity[J].J Appl Mech,1978,45(2):933-934.
[9]ZHOU D Y.Stochastic analysis of temperaturedistribution in a solid with random heat conductivity[J].Trans ASME J Heat Transfer,1988,110(1):23-29.
[10]ZHOU D Y.Stochastic modeling for contactproblems in heat conduction[J].Int J Heat MassTransfer,1989,32(5):913-921.
[11]GEORGIADIS J G.On the approximate solution ofnondeterministic heat and mass transport problems[J].Int J Heat Mass Transfer,1991,34:55-61.
[12]SUN T C.A finite element method for randomdifferential equations[C]//Bharucha-Reid A Ted.Approximate solution of random equations.Philadelphia,PA:Soc.for Ind.and Appl.Math.,1979.
[13]PADOVAN J,GUO Y H.Solution of non-deterministic finite difference heat conductionsimulations[J].Numer Heat Transfer,1989,15(3):383-398.
[14]MADERA A G.Numerical methods for analyzingthe stochastic stationary heat conduction equationwith random coefficients[J].J Eng Phys,1992,62:192-205.
[15]NICOLAI B M,BAERDEMAEKER J D.Avariance propagation algorithm for the computationof heat conduction under stochastic conditions[J].Int J Heat Mass Transfer,1999,31:1513-1520.
[16]EMERY A F.Solving stochastic heat transferproblems[J].Eng Anal with Boundary Elements,2004,28:279-291.
[17]CHANTASIRIWA S.Error and variance ofsolution to the stochastic heat conduction problemby multiquadric collocation method[J].IntCommun in Heat and Mass Transfer,2006,33:342-349.
[18]XIU D B,KARNIADAKIS G E.A new stochasticapproach to transient hea tconduction modeling withuncertainty[J].Int J of Heat and MassTransfer,2003,46:4681-4693.
[19]MALEKNEJAD K,MIRZAEE F.Numericalsolution of stochastic linear heat conduction problemby using new algorithms[J].Appl Math andComput,2005,163:97-106.
[20]于国安,邓智泉,彭兆行.基于随机过程的盘式制动器闸瓦温升研究[J].东北大学学报:自然科学版,1997,18(2):128-132.YU Guo-an,DENG Zhi-quan,PENG Zao-xing.Temperature analysis of disk brake shoe based onstochastic process[J].J of Northeastern Univ:Natural Sci,1997,18(2):128-132.(in Chinese)
[21]刘宁,刘光廷.大体积混凝土结构温度场的随机有限元算法[J].清华大学学报:自然科学版,1996(1):41-47.LIU Ning,LIU Guang-ting.Random temperaturefield of mass concrete structure solved by stochasticfinite element method[J].J of Tsinghua Univ:Sciand Tech,1996(1):41-47.(in Chinese)
[22]刘长虹,陈虬.在模糊随机因素影响下的多层圆筒结构的稳态热传导问题的区间数解法[J].应用数学和力学,2005,10:1191-1197.LIU Chang-hong,Chen Qiu.Interval analysis ofthe fuzzy-random heat conduction in the compositetubes[J].Appl Math and Mech,2005,10:1191-1197.(in Chinese)
[23]康健,赵明鹏,梁冰.随机固-热耦合模型与岩石热破裂数值试验研究[J].岩土力学,2005,26(1):135-139.KANG Jian,ZHAO Ming-pen,LIANG Bing.Random solid-head coupled model and numericaltests on hot cracking of rocks[J].Rock and SoilMech,2005,26(1):135-139.(in Chinese)
[24]林家浩,张亚辉.随机振动的虚拟激励法[M].北京:科学出版社,2004.LIN Jia-hao,Zhang Ya-hui.Pseudo-excitationmethod for random vibration[M].Beijing:Sci.Press,2004.(in Chinese)
[25]林家浩.随机地震响应的确定性算法[J].地震工程与工程振动,1985,5(1):89-93.LIN Jia-hao.A deterministic method for thecomputation of stochastic earthquake response[J].Earthquake Eng and Eng Vibration,1985,5(1):89-93.(in Chinese)
[26]林家浩.随机地震响应功率谱快速算法[J].地震工程与工程振动,1990,10(4):38-46.LIN Jia-hao.A fast algorithm for power spectra ofrandom seismic responses[J].Earthquake Eng andEng Vibration,1990,10(4):38-46.(in Chinese)
[27]刘元芳,林家浩.考虑流体和土壤耦合效应的桩基平台非线性随机地震响应分析[J].计算结构力学及其应用,1991,8(1):42-50.LIU Yuan-fang,LIN Jia-hao.Random seismicanalysis of nonlinear platform-fluid-soil-pilesystems[J].Chinese J of Comput Mech,1991,8(1):42-50.(in Chinese)
[28]林家浩.多相位输入结构随机响应[J].振动工程学报,1992,5(1):73-77.LIN Jia-hao.Structural random responses to multiphase excitations[J].J of Vibration Eng,1992,5(1):73-77.(in Chinese)
[29]LIN J H,SHEN W P,WILLIAMS F W.A highprecision direct integration scheme for structuressubjected to transient dynamic loading[J].Computand Struct,1995,56(1):113-120.
[30]智浩.平稳随机振动载荷功率谱识别研究[D].大连:大连理工大学,1998.ZHI Hao.Excitation spectrum identification ofstationary random vibration[D].Dalian:DalianUniv.of Tech.,1998.(in Chinese)
[31]林家浩,智浩,郭杏林.平稳随机振动荷载识别的逆虚拟激励法(一)[J].计算力学学报,1998,15(2):12-136.LIN Jia-hao,ZHI Hao,GUO Xing-lin.Inversepseudo excitation method for loading identificationof stationary random vibration(1)[J].Chinese Jof Comput Mech,1998,15(2):12-136.(inChinese)
[32]智浩,郭杏林,林家浩.平稳随机振动荷载识别的逆虚拟激励法(二)[J].计算力学学报,1998,15(4):395-428.ZHI Hao,GUO Xing-lin,LIN Jia-hao.Inversepseudo excitation method for loading identificationof stationary random vibration(2)[J].Chinese Jof Comput Mech,1998,15(4):395-428.(inChinese)
[33]ZHI H,LIN J H.Random loading identification ofmulti-input-multi-output structure[J].Struct Engand Mech,2000,10(4):359-369.
[34]LIN J H,GUO X L,ZHI H,et al.Computersimulation of structural random loadingidentification[J].Comput&Struct,2001,79(4):375-387.
[35]LEWIS R W,MORGAN K,THOMAS H R,et al.The finite element method in heat transferanalysis[M].Chichester:Wiley,1996
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