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Dynamics and response reshaping of nonlinear predator-prey system undergoing random abrupt disturbances

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Applied Mathematics and Mechanics(English Edition) 2021年第8期42卷 1123-1134页

作者： Lei XIA Jiaojiao SUN zuguang ying Ronghua HUAN weiqiu zhu Department of Mechanics Key Laboratory of Soft Machines and Smart Devices of Zhejiang ProvinceZhejiang UniversityHangzhou 310027China

An actual ecological predator-prey system often undergoes random environmental mutations owing to the impact of natural disasters and man-made destruction, which may destroy the balance between the species. In this paper,the stochastic dynamics of the nonlinear predator-prey system considering random environmental mutations is investigated, and a feedback control strategy is proposed to reshape the response of the predator-prey system against random abrupt environmental mutations. A delayed Markov jump system(MJS) is established to model such a predator-prey system. A novel first integral is constructed which leads to better approximation solutions of the ecosystem. Then, by applying the stochastic averaging method based on this novel first integral, the stochastic response of the predator-prey system is investigated, and an analytical feedback control is designed to reshape the response of the ecosystem from the disturbed state back to the undisturbed *** simulations finally illustrate the accuracy and effectiveness of the proposed procedure.

关键词： random excitation nonlinear dynamics reshaping control stationary probability density function(SPDF) predator-prey system

RESPONSE ANALYSIS OF PIEZOELECTRIC SHELLS IN PLANE STRAIN UNDER RANDOM EXCITATIONS

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Acta Mechanica Solida Sinica 2009年第2期22卷 152-160页

作者： zuguang ying Xinqun zhu Department of Mechanics School of Aeronautics and Astronautics Zhcjiang University Hangzhou 310027 China School of Engineering University of Western Sydney Penrith South DC NSW 1797 Australia

The random response of a piezoelectric thick shell in plane strain state under boundary random excitations is studied and illustrated with a piezoelectric cylindrical shell. The differential equation for electric potential is integrated radially to obtain the electric potential as a function of displacement. The random stress boundary conditions are converted into homogeneous ones by transformation,which yields the electrical and mechanical coupling differential equation for displacement under random excitations. Then this partial differential equation is converted into ordinary differential equations using the Galerkin method and the Legendre polynomials,which represent a random multi-degree-of-freedom system with asymmetric stiffness matrix due to the electrical and mechanical coupling and the transformed boundary conditions. The frequency-response function matrix and response power spectral density matrix of the system are derived based on the theory of random vibration. The mean-square displacement and electric potential of the piezoelectric shell are finally obtained,and the frequency-response characteristics and the electrical and mechanical coupling properties are explored.

关键词： piezoelectric shell random vibration boundary excitation random response

Asymptotic analysis of nonlinear micro-film buckling

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Science China(Technological Sciences) 2012年第7期55卷 1960-1963页

作者： ying zuguang WANG Yong zhu ZeFei Department of Engineering Mechanics School of Aeronautics and AstronauticsZhejiang UniversityHangzhou 310027China School of Mechanical Engineering Hangzhou Dianzi UniversityHangzhou 310018China

The buckling design of micro-films has various potential applications to *** substrate prestrain,interconnector buckling amplitude and critical strain are important parameters for the buckling *** the presented analysis,the buckled film shape was described approximately by a trigonometric function and the buckled film amplitude was obtained by minimizing the total strain ***,this method only generates the first-order approximate solution for the nonlinear *** the present paper,an asymptotic analysis based on the rigorous nonlinear differential equation for the buckled micro-film deformations is proposed to obtain more accurate relationship of the buckling amplitude and critical strain to *** obtained results reveal the nonlinear relation and are significant to accurate buckling design of micro-films.

关键词： buckling nonlinearity micro-film asymptotic solution critical strain

Stochastic optimal control of partially observable nonlinear quasi-integrable Hamiltonian systems

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Science China(Physics,Mechanics & Astronomy) 2010年第1期53卷 147-154页

作者： FENG Ju, zhu weiqiu & ying zuguang Department of Mechanics, State Key Laboratory of Fluid Power Transmission and Control, Zhejiang University, Hangzhou 310027, China 1. Department of Mechanics State Key Laboratory of Fluid Power Transmission and Control Zhejiang University Hangzhou 310027 China

The stochastic optimal control of partially observable nonlinear quasi-integrable Hamiltonian systems is investigated. First, the stochastic optimal control problem of a partially observable nonlinear quasi-integrable Hamiltonian system is converted into that of a completely observable linear system based on a theorem due to Charalambous and Elliot. Then, the converted stochastic optimal control problem is solved by applying the stochastic averaging method and the stochastic dynamical programming principle. The response of the controlled quasi Hamiltonian system is predicted by solving the averaged Fokker-Planck-Kolmogorov equation and the Riccati equation for the estimated error of system states. As an example to illustrate the procedure and effectiveness of the proposed method, the stochastic optimal control problem of a partially observable two-degree-of-freedom quasi-integrable Hamiltonian system is worked out in detail.

关键词： quasi-integrable Hamiltonian system partial observation stochastic optimal control

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不确定拟哈密顿系统的随机最优控制

动力学与控制学报 2017年第1期15卷 93-96页

作者：胡荣春应祖光朱位秋浙江大学航空航天学院力学系杭州310027

本文提出了不确定拟哈密顿系统、基于随机平均法、随机极大值原理和随机微分对策理论的一种随机极大极小最优控制策略.首先,运用拟哈密顿系统的随机平均法,将系统状态从速度和位移的快变量形式转化为能量的慢变量形式,得到部分平均的It... 详细信息

本文提出了不确定拟哈密顿系统、基于随机平均法、随机极大值原理和随机微分对策理论的一种随机极大极小最优控制策略.首先,运用拟哈密顿系统的随机平均法,将系统状态从速度和位移的快变量形式转化为能量的慢变量形式,得到部分平均的It随机微分方程;其次,给定控制性能指标,对于不确定拟哈密顿系统的随机最优控制,根据随机微分对策理论,将其转化为一个极小极大控制问题;再根据随机极大值原理,建立关于系统与伴随过程的前向-后向随机微分方程,随机最优控制表达为哈密顿控制函数的极大极小条件,由此得到最坏情形下的扰动参数与极大极小最优控制;然后,将最坏扰动参数与最优控制代入部分平均的It随机微分方程并完成平均,求解与完全平均的It随机微分方程相应的Fokker-Planck-Kolmogorov(FPK)方程,可得受控系统的响应量并计算控制效果;最后,将上述不确定拟哈密顿系统的随机最优控制策略应用于一个两自由度非线性系统,通过数值结果说明该随机极大极小控制策略的控制效果.

关键词：不确定性极大极小最优控制极大值原理随机平均法

能量包线随机平均法在双线性迟滞系统随机响应分析中的应用

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航空学报 1989年第1期10卷 A028-A034页

作者：朱位秋雷鹰浙江大学

本文将能量包线随机平均法应用于分析单自由度双线性迟滞系统对白噪声激励的随机响应,详细分析了位移、速度及总能量的平稳响应各统计量随系统粘性阻尼、次斜率及激励强度的变化。解析结果与数字模拟结果比较表明,该方法优于迄今为止用... 详细信息

本文将能量包线随机平均法应用于分析单自由度双线性迟滞系统对白噪声激励的随机响应,详细分析了位移、速度及总能量的平稳响应各统计量随系统粘性阻尼、次斜率及激励强度的变化。解析结果与数字模拟结果比较表明,该方法优于迄今为止用于双线性迟滞系统随机响应分析的其他近似方法。

关键词：随机激励迟滞线性能量包线

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股骨端部横向受力时的应力分布特征

科技通报 2018年第3期34卷 45-48页

作者：应祖光陈妍妤朱振康闵重函浙江大学航空航天学院力学系杭州310027 浙江中医大学附属嘉兴市中医医院浙江嘉兴314001

股骨是人体下肢承重的重要组成部分。当人体发生跌到或被撞击时,股骨受到的一个主要作用力是端部的横向力。当股骨颈开裂或折断后,要用人工假体替换损坏的股骨头部,因此需要研究替换前后股骨的应力分布情况。由于实验技术的限制和股骨... 详细信息

股骨是人体下肢承重的重要组成部分。当人体发生跌到或被撞击时,股骨受到的一个主要作用力是端部的横向力。当股骨颈开裂或折断后,要用人工假体替换损坏的股骨头部,因此需要研究替换前后股骨的应力分布情况。由于实验技术的限制和股骨构造的复杂性,通常采用三维有限元数值方法计算分析股骨的应力分布。本文基于股骨标本和假体植入股骨端部受横向力的多点应力测量结果,进行股骨模型的三维重构,通过有限元法的数值计算,得到全股骨的应力分布结果,说明其分布特征,并比较假体植入前后股骨的应力情况,说明假体植入对于股骨应力分布的影响。

关键词：股骨横向作用力应力分布有限元实验