有界窄带激励下具有黏弹项的Duffing振子

讨论含线性黏弹项的Duffing振子对有界窄带随机激励的响应.用多尺度法分离了系统的稳态平均运动及随机摄动,讨论了系统的黏弹项对阻尼和刚度的效应,得到了系统随机均方响应的近似表达式.分析结果表明:在一定条件下,对应于同一解谐参数,系统有2个稳定的稳态平均运动,从而导致随机均方响应有2值解.数值模拟肯定了上述分析结果。     

谐和与窄带随机噪声联合作用下Duffing系统的参数主共振

研究了Ｄｕｆｉｎｇ振子在谐和与窄带随机噪声联合激励下的参数主共振响应和稳定性问题．用多尺度法分离了系统的快变项，并求出了系统的最大Ｌｙａｐｕｎｏｖ指数．本文还分析了失稳及跳跃现象，及系统的阻尼项、非线性项、随机项、确定性参激强度对系统响应的影响．数值模拟表明本文提出的方法是有效的．     

Visco-elastic systems under both deterministic and bound random parameteric excitation

The principal resonance of a visco-elastic systems under both deterministic and random parametric excitation was investigated. The method of multiple scales was used to determine the equations of modulation of amplitude and phase. The behavior, stability and bifurcation of steady state response were studied by means of qualitative analysis. The contributions from the visco-elastic force to both damping and stiffness can be taken into account. The effects of damping, detuning, bandwidth, and magnitudes of deterministic and random excitations were analyzed. The theoretical analysis is verified by numerical results. Foundation item: the National Natural Science Foundation of China (10072049) Biography: XU Wei (1957∼), Professor, Doctor (E-mail: weixu@nwpu.edu.cn)     

窄带噪声作用下二自由度非线性系统的响应

研究二自由度非线性系统在窄带随机噪声激励下的主共振响应,用多尺度法分离了系统的快变项,讨论了系统的阻尼项、随机项等对系统响应的影响。在一定条件下,系统具有两个均方响应值和跳跃现象,饱和现象也存在。数值模拟表明文中所提出的方法是有效的。     

参数激励与强迫激励联合作用下非线性振动系统的分叉

本文利用多尺度法研究了参数激励与强迫激励联合作用下非线性振动系统的分叉问题,给出了分叉集和八种分叉响应曲线。     

参数激励与强迫激励联合作用下非线性振动系统的余维2退化分叉

在本文里我们首先研究了具有Z_2-对称性的范式理论和退化向量场的普适开折理论。然后利用上述理论研究了参数激励与强迫激励联合作用下非线性振动系统的余维2退化分叉,从而解决了当解具有两个零特征值时解的稳定性问题。最后利用Melnikov方法求出了参数平面上的同宿分叉曲线,讨论了全局分叉的存在性。     

SEISMIC RANDOM RESPONSE ANALYSIS OF HYSTERETIC SYSTEMS WITH PSEUDO EXCITATION METHOD

The stationary random responses of nonlinear shear-type Multi-Degrees-of-Freedom (MDOF) hysteretic system are analyzed by using the Pseudo Excitation Method (PEM) combined with the Equivalent Linearization Method (ELM). The solution of the equivalent linear system is obtained by iteratively solving complex algebraic equations instead of the Lyapunov equations. The efficiency of this method is much higher for practical engineering systems with many degrees-of-freedom. Supported by NNSFC (Project No. 19772009), NKBRSF fund (No. G1999032805) and Doctoral Funding of State Education Ministry (No. 97014120).     

STOCHASTIC OPTIMAL CONTROL OF STRONGLY NONLINEAR SYSTEMS UNDER WIDE-BAND RANDOM EXCITATION WITH ACTUATOR SATURATION

A bounded optimal control strategy for strongly non-linear systems under non-white wide-band random excitation with actuator saturation is proposed. First, the stochastic averaging method is introduced for controlled strongly non-linear systems under wide-band random excitation using generalized harmonic functions. Then, the dynamical programming equation for the saturated control problem is formulated from the partially averaged Itō equation based on the dynamical programming principle. The optimal control consisting of the unbounded optimal control and the bounded bang-bang control is determined by solving the dynamical programming equation. Finally, the response of the optimally controlled system is predicted by solving the reduced Fokker-Planck-Kolmogorov （FPK） equation associated with the completed averaged Itō equation. An example is given to illustrate the proposed control strategy. Numerical results show that the proposed control strategy has high control effectiveness and efficiency and the chattering is reduced significantly comparing with the bang-bang control strategy.     

剪切型非线性滞迟系统随机地震响应的虚拟激励分析

运用虚拟激励法结合等效线性化法分析了剪切型多自由度滞迟系统的平稳随机地震响应.对于滞迟等效线性系统,对每一步迭代不需要求解高阶李亚谱诺夫方程,而只须求解一个低阶复系数代数方程即可;可以只计算所需要的方差向量,因而计算效率较高.特别是对于较多自由度的滞迟系统.     

参强联合作用非线性结构动力学实验建模

搭建以L 型梁为实验研究对象的参强联合作用多自由度非线性振动实验系统, 将增量谐波平衡非线性识别理论运用到实验建模方法中, 建立了L 型梁的动力学控制方程. 通过对不同激励频率和不同响应情况下的数值模拟与实验数据的比较, 验证了基于增量谐波平衡识别的实验建模方法对多自由度参强联合作用非线性动力学结构的有效性, 以及动力学控制方程的普适性.     

Invariant Measures and Lyapunov Exponents for Stochastic Mathieu System

The principal resonance of the stochastic Mathieu oscillator to randomparametric excitation is investigated. The method of multiple scales isused to determine the equations of modulation of amplitude and phase.The behavior, stability and bifurcation of steady state response arestudied by means of qualitative analyses. The effects of damping,detuning, bandwidth, and magnitudes of random excitation are analyzed.The explicit asymptotic formulas for the maximum Lyapunov exponent areobtained. The almost-sure stability or instability of the stochasticMathieu system depends on the sign of the maximum Lyapunov exponent.     

PRINCIPAL RESPONSE OF VAN DER POL-DUFFING OSCILLATOR UNDER COMBINED DETERMINISTIC AND RANDOM PARAMETRIC EXCITATION

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｓｔｕｄｙｏｆｒａｎｄｏｍｐａｒａｍｅｔｒｉｃｅｘｃｉｔｅｄｓｙｓｔｅｍｓａｒｅｍｏｒｅｉｍｐｏｒｔａｎｔｔｈａｎｔｈａｔｏｆｒａｎｄｏｍｅｘｔｅｒｎａｌｅｘｃｉｔｅｄｏｎｅｓ,ａｎｄａｒｅｔｈｅｏｒｅｔｉｃａｌｌｙｍｏｒｅｄｉｆｆｉｃｕｌｔｅｓｐｅｃｉａｌｌｙｗｈｅｎｔｈｅｅｘｃｉｔａｔｉｏｎｓａｒｅｎａｒｒｏｗ＿ｂａｎｄｒａｎｄｏｍｐｒｏｃｅｓｓｅｓ[1].Ｉｎｔｈｅｃａｓｅｗｈｅｎｔｈｅｓｙｓｔｅｍｓａｒｅｅｘｃｉｔｅｄｂｙｃｏｍｂｉｎｅｄｄｅｔｅｒｍｉｎｉｓｔｉ…     

NONLINEAR VIBRATION RESPONSE AND BIFURCATION OF CIRCULAR CYLINDRICAL SHELLS UNDER TRAVELING CONCENTRATED HARMONIC EXCITATION

The nonlinear vibration of a cantilever cylindrical shell under a concentrated harmonic excitation moving in a concentric circular path is proposed. Nonlinearities due to large-amplitude shell motion are considered, with account taken of the effect of viscous structure damping. The system is discretized by Galerkin's method. The method of averaging is developed to study the nonlinear traveling wave responses of the multi-degrees-of-freedom system. The bifurcation phenomenon of the model is investigated by means of the averaged system in detail. The results reveal the change process and nonlinear dynamic characteristics of the periodic solutions of averaged equations.     

窄带随机噪声激励下多自由度非线性系统的响应

在随机振动的研究中，研究较多的是系统在宽带噪声作用下的响应问题，对于非线性系统特别是多自由度非线性系统在窄带随机噪声作用下的响应问题则研究较少。本文研究了三自由度非线性系统在窄带随机噪声激励下的主共振响应和稳定性问题。用多尺度法分离了系统的快变项，给出了系统响应的振幅和相位角满足的方程。用摄动法讨论了系统随机项对系统响应的影响。当随机扰动较小时，在一定的参数范围内，对应于不同的初值，系统具有两个均方响应值，随机饱和现象也存在。当随机扰动增大时，系统可从一个大的响应突跳为一个小的响应，或从一个小的响应突跳为一个大的响应，即存在随机跳跃现象。数值模拟表明本文提出的方法是有效的。     

Response of nonlinear oscillator under narrow-band random excitation

IntroductionThestudyoftheresponseofnonlinearsystemstonarrow_bandrandomexcitationofconsiderableimportance.Forexample ,theexcitationofsecondarysystemwouldbeanarrow_bandrandomprocessiftheprimarysystemcouldbemodeledasasingle_degree_of_freedomsystemwithlightdampingsubjecttowide_bandexcitation .Inthetheoryofnonlinearrandomvibration ,mostresultsobtainedsofarareattributedtotheresponseofnonlinearoscillatorstowide_bandrandomexcitation .Incomparison ,resultsontheeffectofnarrow_bandexcitationonnonlinearos…     

Resonance and Bifurcation in a Nonlinear Duffing System with Cubic Coupled Terms

The dynamic behaviors of two-degree-of-freedom Duffing system with cubic coupled terms are studied. First, the steady-state responses in principal resonance and internal resonance of the system are analyzed by the multiple scales method. Then, the bifurcation structure is investigated as a function of the strength of the driving force F. In addition to the familiar routes to chaos already encountered in unidimensional Duffing oscillators, this model exhibits symmetry-breaking, period-doubling of both types and a great deal of highly periodic motion and Hopf bifurcation, many of which occur more than once. We explore the chaotic behaviors of our model using three indicators, namely the top Lyapunov exponent, Poincaré cross-section and phase portrait, which are plotted to show the manifestation of coexisting periodic and chaotic attractors.     

The method of matrices conjoint multiplication for the problem of circular arc corrugated diaphragm

The circular are corrugated diaphragins are taken in this paper and structures of several sections of the ring shells and a central cireular plale I matrices and link matrices are derived by using Prof. Chuen Hei-zang’s general the ring shell[1] and perturbation theory of the circular thin plates. Throngh the meined of matrices conjoint multiplication, the linear exact solution and nonlinear soluaen are obtained. The resutts agree with that of the experiments presented by W. A. Wildhack..     

Diffraction of elastic waves in the plane multiply-connected region and dynamic stress concentration

This paper deals with the problem of diffraction of elastic waves in the plane multiply-connected regions by the theory of complex functions. The complete function series which approach the solution of the problem and general expressions for boundary conditions are given.’ Then the problem is reduced to the solution to infinite series of algebraic equations and the solution can be directly obtained by using electronic computer. In particular, for the case of weak interaction, an asymptotic method is presented here, by which the problem ofp waves diffracted by a circular cavities is discussed in detail. Based on the solution of the diffracted wave field the general formulas for calculating dynamic stress concentration factor for a cavity of arbitrary shape in multiply-connected region are given.     

有界随机噪声激励下一类非线性系统的共振与饱和现象

研究了二自由度非线性系统在有界随机噪声激励下,系统响应的共振与随机饱和现象。用多尺度法分离了系统的快变项,用线性化方法求出了系统响应幅值的一、二阶矩,并给出了系统优化设计的一些建议。数值模拟表明本文提出的方法是有效的。     

多自由度强非线性耦合参激系统随机响应计算方法

本文采用非高斯矩闭合方法计算了一个含参数激振的二自由度强非线性耦合系统受随机激励的响应方差。用逐次消除法消除方程中的惯性耦合后推导出直到6阶的矩方程,采用中心累积量截断技术计算了白噪音激励下的响应方差,并与时域直接积分和数字模拟方法的结果进行比较,取得了一些有意义的结论。