阶梯圆形和环形薄板的大幅度基础振动

利用修正迭代法求出了具有多个阶梯厚度圆形和环形薄板轴对称大幅度自由振动的一种新的解析解，导出了振幅和非线性振动基频的解析关系式，给出了较完善的数值计算结果，所得结果可供工程设计时参考。     

变截面耦合微悬臂双梁的基本振动特性

本文研究了连接部件的几何参数对变截面耦合微悬臂双梁振动特性的影响．首先，利用集总参数法建立了等效的两自由度系统耦合振动的解析模型；其次，利用分离变量法获得了耦合双梁自由振动的固有频率、振幅比和强迫振动的反共振频率；最后，通过比对解析解、有限元数值结果和实验数据，验证了解析预测的可靠性．研究结果表明，连接部件的宽度和初始偏转角的变化会对耦合双梁振动的特性产生较大的影响．     

用MATLAB进行单自由度系统机械振动试验

 分析单自由度阻尼系统受迫机械振动特性，建立数学模型，利用MATLAB对其进行仿真试验， 进行定量分析，试验结果得出振动方程解析解，并用几何方式描述了振动方程和幅频特性.     

点支承四边自由各向异性平行四边形板自由振动、屈曲和弯曲分析

一个精确的重富立叶级数解析解用于分析四边形自由的点支横观各向异性平行四边形板的自由振动、屈曲和弯曲。解析解用叠加法得到,此解收敛迅速。与现有结果的比较证实了由本法得到的解析解的精确性。文后用图表给出高精度的自由振动、屈曲和弯曲计算结果。     

多自由度分段光滑非线性系统的近似解——-中华文物龙洗的自激振动

建立了由干摩擦引起的两个弹性体之间自激振动的数学模型. 利用平均法 求出了由干摩擦引起的多自由度分段光滑非线性动力系统的近似解析解，分析了搓动速度、 振动频率与振幅的关系曲线，相位角与搓动速度的关系曲线，分析结果与数值解基本吻合. 为研究多自由度分段光滑非线性系统提供了一种有效的近似解析分析方法.     

桩侧扰动分区饱和土中桩竖向振动特性研究

考虑沉桩过程中桩周土受到扰动产生软化或硬化的现象,建立了饱和土中径向分区桩竖向振动简化模型,通过分离变量方法,得到了桩竖向振动频域解析解和时域半解析解。分析了分区土对桩竖向振动特性的影响,数值计算结果表明,土层模量比、分区半径和桩底支承系数对桩竖向振动有较明显的影响。研究结果还表明,在较强的振动作用下,由于分区软化或强...     

两自由度振动系统的斜碰撞分析

研究斜碰撞振动系统动力学的一个关键问题是对系统在碰撞前后的状态进行合理描述和正确计算．针对两弹性体斜碰撞问题，基于瞬间碰撞假设，提出了采用步进冲量来分析和求解斜碰撞前后的状态关系；并以弹簧摆和振子组成的两自由度斜碰撞振动系统为例，具体介绍了该算法如何实现．用解析方法讨论了该系统在斜碰撞过程中可能出现的各种力学现象，将冲量步进算法得到的数值解与解析结果进行对比，取得了完全一致的结果．该数值方法能适应多种斜碰撞问题的计算．     

单自由度振动系统特性的数学仿真实验

根据单自由度振动系统数学模型,设计了单自由度振动系统特性的数学仿真实验,实验结果给出振动方程解析解的表达式,并用几何方式定量描述振动过程及其幅频特性.     

多体系统传递矩阵法在火炮动力学中的应用

基于作者提出的多体系统传递矩阵法，研究了其在火炮动力学中的应用，求得了某类火炮系统固有振动的频率方程振型函数的精确解析式，并给出了电算结果。     

单自由度振动系数特性的数学仿真实验

根据单自由度振动系统数学模型,设计了单自由度振动系统特性的数学仿真实验,实验结果给出振动方程解析解的表达式,并用几何方式定量描述振动过程及其幅频特性。     

Non-linear argumental oscillators: Stability criterion and approximate implicit analytic solution

The behaviour of a space-modulated, so-called “argumental” oscillator, is studied. The oscillator is submitted to an external harmonic force, which is amplitude-modulated by the oscillator's position in space. An analytic expression of a stability criterion is given. Using the averaging method, an integrating factor and a Van der Pol representation in the (amplitude, phase)-space, an exact implicit analytic solution is given when there is no damping, and an approximate implicit analytic solution is given when there is damping, allowing the plotting of the separatrix curve. An attractor is identified.     

Large amplitude vibration of thin annular plates

A pure analytic solution of the axisymmetric large amplitude free vibration of thinannular plates is presented in this paper:By using the modified iteration method,we derivean analytic relation for the amplitudes vs.frequencies of vibrations.The present papershows the great potentiality of this method to tackle the large amplitude vibration problemsof plates.     

弹性地基上圆底扁球壳的非线性动力问题

本文从Krmn非线性基本微分方程出发,提出了将修正迭代法和伽辽金法联合运用,分析了弹性地基上圆底扁球壳在均布荷载作用下周边固定边界条件的非线性动力响应问题,给出了中心振幅与时间t之间关系的二次近似解析表达式;同时还讨论了Winkler地基参数K对中心最大振幅的影响。此外将本文的部分结果和已有文献结果作了比较,二者吻合较好。     

Large amplitude vibration of circular sandwich plates

In this paper, fundamental equations of the axisymmetric large amplitude free vibration for circular sandwich plates are derived by means of Hamilton principle. In most cases, the sandwich plates are composed of very thin faces, then the preceding fundamental equations are simplified considerably. For an illustrative example, a circular sandwich plate with edge clamped but free to slip is considered, and then we got a pure analytic solution of the axisymmetric large amplitude free vibration with the aid of the modified iteration method, and derived an analytic relation for the amplitude-frequency response.     

LARGE AMPLITUDE VIBRATION OF CIRCULAR SANDWICH PLATE

ＬＡＲＧＥＡＭＰＬＩＴＵＤＥＶＩＢＲＡＴＩＯＮＯＦＣＩＲＣＵＬＡＲＳＡＮＤＷＩＣＨＰＬＡＴＥＳＤｕＧｕｏ－ｊｕｎ（杜国君）（ＮｏｒｉｈｅａｓｉＩｎｓｔｉｔｕｔｅｏｆＨｅａｖｙＭａｃｈｉｎｅｒｙ,Ｑｉｑｉｈａｒ）（ＲｅｃｅｉｖｅｄＪａｎ．２,１９９２,...     

An analytic approximate technique for free oscillations of positively damped systems with algebraically decaying amplitude

The currently developed analytic technique known as the homotopy analysis method is employed to propose a new approach for free oscillations of positively damped systems with algebraically decaying amplitude. In contrast to perturbation techniques, this approach is valid even for damped systems without any small/large parameters. Besides, unlike other analytic techniques, this approach itself provides us with a convenient way to adjust and control convergence of approximation series. Some typical examples are employed to illustrate its validity, effectiveness and flexibility.     

Nonlinear vibration of circular sandwich plate under the uniformed load

ＩｎｔｒｏｄｕｃｔｉｏｎＳｏｆａｒ,ｏｎｌｙａｆｅｗｐｅｏｐｌｅｈａｖｅｓｔｕｄｉｅｄｔｈｅｌａｒｇｅｄｅｆｌｅｃｔｉｏｎｐｒｏｂｌｅｍｓｏｆｓａｎｄｗｉｃｈｐｌａｔｅｓａｎｄｓｈｅｌｌｓｂｅｃａｕｓｅｏｆｔｈｅｄｉｆｆｉｃｕｌｔｙｏｆｎｏｎｌｉｎｅａｒｍａｔｈｅｍａｔｉｃｓ.ＬｉｕＲｅｎｈｕａｉｈａｓｄｏｎｅｍｕｃｈｔｏｆｉｎｄａｓｅｒｉｅｓｏｆｒｅｓｕｌｔｓｗｉｔｈｔｈｅｖａｌｕｅｏｆａｐｐｌｉｃａｔｉｏｎｉｎｅｎｇｉｎｅｅｒｉｎｇｐｒａｃｔｉｃｅ[1～5].Ａｕｔｈｏｒ[6,7]ｈａｄｔｈｅｉｎｉｔｉ…     

KAM for Reversible Derivative Wave Equations

We prove the existence of Cantor families of small amplitude, analytic, linearly stable quasi-periodic solutions of reversible derivative wave equations.     

Explicit analytical approximation to large-amplitude non-linear oscillations of a uniform cantilever beam carrying an intermediate lumped mass and rotary inertia

This paper is concerned with analytical treatment of non-linear oscillations of planar, flexural large amplitude free vibrations of a slender, inextensible cantilever beam carrying a lumped mass with rotary inertia at an intermediate position along its span. An analytic approximate technique, namely Optimal Homotopy Asymptotic Method (OHAM) is employed for this purpose. It is proved that OHAM provide accurate solutions for large amplitudes and large modal constants in the considered nonlinear equations, when other classical methods fail. Our procedure provides us with a convenient way to optimally control the convergence of solution, such that the accuracy is always guaranteed. An excellent agreement of the approximate frequencies and periodic solutions with the numerical results and published results has been demonstrated. Two examples are given and the results reveal that this procedure is very effective, simple and accurate. This paper demonstrates the general validity and the great potential of the OHAM for solving strongly nonlinear problems.     

Nonlinear resonance interaction between three capillary-gravity waves on the plane charged fluid surface

Three-wave interaction between capillary-gravity waves on a uniformly charged free fluid surface is analyzed using second-order analytic calculations. The time evolution of the wave amplitudes in the state of nonlinear resonance is studied. It is shown that the number of three-wave resonances is infinite and their exact locations for waves of finite amplitude depend on the initial conditions.