Towards a new type of energy trap: Classical analog of quantum Landau-Zener tunneling

We present a novel type of an energy trap providing targeted energy transfer in a system of weakly coupled pendulums. Our approach is based on the analogy we revealed between the behavior of two weakly coupled classical parametric pendulums (in linear approximation) and the nonadiabatic Landau-Zener tunneling in a two-state quantum system. This analogy leads us to the prediction of an efficient irreversible transfer of vibration energy from one subsystem to another, when the eigenfrequency of at least one of them changes in time, so that the coupled subsystems pass through an internal resonance. The existence of such a phenomenon is not restricted to coupled pendulums, but is inherent to a wide class of both linear and nonlinear parametric oscillatory systems. This opens up the possibility of designing new types of energy traps and absorbers for the dynamic protection of various mechanical systems.     

多节摆的自由振动分析

利用拉格朗日方程,导出了多节摆系统的运动微分方程.根据三对角阵的性质,给出了振动系统的特征多项式和特征矢量的递推公式,并以三节摆为例,说明了结果的应用,用此方法验证了<力学与实践>2002年第24期<多自由度振动系统的简正坐标和简正振动模式>一文中的结果.     

Parametric Identification of a Base-Excited Single Pendulum

A harmonic balance based identification algorithm was applied to the simulated single pendulum with horizontal base-excitation. The purpose of this simulation was to examine the applicability of the algorithm on parametrically excited, whirling chaotic systems. Modifications were adopted to adapt to the whirling systems. The system was supposed to be unknown except only the excitation frequency. Linear interpolation functions and the Fourier series functions were tested to approximate unknown nonlinear functions in the governing differential equation. After extracting unstable periodic orbits, all of the parameters were simultaneously identified. By direct comparison, Poincaré section plots and reconstructed phase portrait techniques, it was shown that the identified system had similar dynamical characteristics to the original simulated pendulum, which implies the effectiveness of the examined algorithm.     

Synchronization and phase relations in the motion of two-pendulum system

The synchronization phenomenon in non-linear oscillating system is studied by means of examination of the coupled pendulums. Dependence of the phase shift between pendulum states on system parameters and initial conditions is studied both analytically and numerically. The harmonic linearization technique is applied for analytical examinations.     

失调耦合摆振动分析

利用拉格朗日方程建立了耦合摆的矩阵方程,对失调耦合摆振动进行了分析;研究了失调耦合摆的模态局部化现象,利用MAPLE9.0计算机绘图,作出了振幅比和固有频率随参数变化的三维曲线,得出固有频率随参数ε和β的增大而增大;失调耦合摆有模态局部化现象,第一阶模态振幅比随ε的增大而增大。     

Rotary motion of the parametric and planar pendulum under stochastic wave excitation

In this paper a rotary motion of a pendulum subjected to a parametric and planar excitation of its pivot mimicking random nature of sea waves has been studied. The vertical motion of the sea surface has been modelled and simulated as a stochastic process, based on the Shinozuka approach and using the spectral representation of the sea state proposed by Pierson–Moskowitz model. It has been investigated how the number of wave frequency components used in the simulation can be reduced without the loss of accuracy and how the model relates to the real data. The generated stochastic wave has been used as an excitation to the pendulum system in numerical and experimental studies. For the first time, the rotary response of a pendulum under stochastic wave excitation has been studied. The rotational number has been used for statistical analysis of the results in the numerical and experimental studies. It has been demonstrated how the forcing arrangement affects the probability of rotation of the parametric pendulum.     

A new class of vector spaces

Reciprocal vectors and reciprocal vector spaces are defined. The special case of symmetric vectors is considered. Reciprocal linear transformations and the symmetrical homomorphism are introduced and some properties presented.     

析物理学中的旋轮线（摆线）

用简单的数学方法证明旋轮线的一些重要性质,介绍在物理学中应用的一些重要实例。     

一般双线摆振动的渐近解

采用渐近法研究了一般双线摆的振动特性,利用该种方法可以精确地确定不规则棒体的转动惯量。     

On the nonlinear interactions and existence of breathers in a chain of coupled pendulums

The paper considers a chain of linearly coupled pendulums. Continues first order system equations are treated via time and space multiple scale method which lead to nonlinear Schrödinger equation. Further investigations on the nonlinear Schrödinger equation detects systems responses in the form of propagated nonlinear waves as functions of their envelope and phases. This provides information about localization of nonlinear waves and their directions in space and time.