Boundary Controllability and Observability of a One-Dimensional Nonuniform SCOLE System

A hybrid system, composed of an elastic beam governed by an Euler-Bernoulli beam equation with variable coefficients and a linked rigid body governed by an ordinary differential equation, is considered. Various controllability/observability properties of the system under bounday control/observation are studied. It is shown that an open-loop smooth/singular controller of either torque control or force control is sufficient to make the system exactly controllable in arbitrarily short time duration. The work was carried out with the support of the National Natural Science Foundation of China and the Russian Foundation for Fundamental Researches, Grant 02-01-00554.     

弹性地基无限长梁动力问题的一般解

本文从Euler-Bernoulli梁出发,对弹性地基采用Winkler假定,建立了问题的数学模型.然后对空间变量和时间变量分别进行Fourier变换和Laplace变换,利用逆变换褶积积分,得到了弹性地基无限长梁一般动力问题的解析解.最后对自由振动,脉冲激励和运动载荷情况分别进行了讨论.     

一种裂纹梁振动响应分析的近似方法

本文以线弹簧模型为基础提出了一种近似分析裂纹梁振动响应的方法．把该方法同EulerBernoulli梁理论、模态分析方法以及断裂力学原理等结合起来运用，导出裂纹梁振动的特征方程．作为应用实例，本文考核了简支裂纹梁和悬臂裂纹梁的固有频率响应．结果表明，本文所获得的解与现有文献中的解或实验结果取得很好的一致．     

中心刚体-外Timoshenko梁系统的建模与分岔特性研究

对于中心刚体固结悬臂梁系统,当不考虑梁剪应力（ 即Ｅｕｌｅｒ＿Ｂｅｒｎｏｕｌｌｉ 梁） 影响时,匀速转动梁的平凡解是稳定的·　而对于深梁,有必要考虑剪应力（ 即Ｔｉｍｏｓｈｅｎｋｏ 梁） 的影响,此时其匀速转动平凡解将出现拉伸屈曲·　为此采用广义Ｈａｍｉｌｔｏｎ 变分原理建立了中心刚体固结Ｔｉｍｏｓｈｅｎｋｏ 梁这类刚＿柔耦合系统的非线性动力学模型,应用数值方法研究了匀速转动Ｔｉｍｏｓｈｅｎｋｏ 梁非线性系统的分岔特性,以及失稳的临界转速     

Nonlinear analysis of a parametrically excited beam with intermediate support by using Multi-dimensional incremental harmonic balance method

In this paper, a nonlinear Euler-Bernoulli beam under a concentrated harmonic excitation with intermediate nonlinear support is investigated. Continuous expression for the kinetic energy, potential energy and dissipation function are constructed. An energy method based on the Lagrange equation combined with the Galerkin truncation is used for discretizing the governing equation. The Multi-dimensional incremental harmonic balance method (MIHBM) is derived, and the comparisons between the numerical results and the approximate analytical solutions based on the MIHBM verify the excellent accuracy of the MIHBM. The steady state dynamic of the beam is investigated by MIHBM. In order to investigate the energy transmission and understand the vibration response of the Euler-Bernoulli beam, the effects of the key parameters on the dynamic behaviors are studied and discussed, individually. The results show that the amplitude-frequency curves exhibits softening nonlinear behavior in the super-harmonic resonance region, and near resonant region the hardening nonlinear behavior is observed depending on the different parameters. Nonlinear dynamic analysis, such as bifurcation, 3-D frequency spectrum, waveform, frequency spectrum, phase diagram and Poincaré map, are also presented in order to study the influences of the key parameters on the vibration behaviors for the beam in a more accurate manner. In addition, the path to chaotic motion is observed to be through a sequence of the periodic motion and quasi-periodic motion.     

Forced Vibration Analysis of Euler-Bernoulli Double-Beam Systems by Means of Green’s Functions北大核心CSCD

Double-curved-beam (DCB) systems are usually seen in many engineering fields. Compared to straight double-beam systems, DCB systems are more efficient in noise and vibration control problems. To obtain closed-form solutions of steady-state forced vibrations of DCB systems, the classical Euler-Bernoulli curved beam (ECB) model was employed to model vibration equations for the DCB systems. Green’s functions and the Laplace transform methods were used to get the closed-form solutions to the vibration equations for the DCB systems. These solutions apply to arbitrary boundary conditions. Numerical tests were conducted to verify the present solutions with related results from previous literatures. Effects of some important geometric and physical parameters on vibration responses and the interaction between the elastic layer stiffness and the DCB system, were discussed. The results show that, the DCB system will degenerate to a straight double-beam system when the 2 radii approach infinity, moreover, the DCB system can be simplified as one comprising a straight beam and a curved beam. © 2023 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

Existence and Exponential Stability for a Euler-Bernoulli Beam Equation with Memory and Boundary Output Feedback Control Term

In this paper, we consider the Euler-Bernoulli beam equation with memory and boundary output feedback control term. We prove the existence of solutions using the Galerkin method and then investigate the exponential stability of solutions by using multiplier technique. This work was supported by grant number KRF-2005-202-C00030 from the Korea Research Foundation. This work was supported by National Institute for Mathematical Sciences.     

Dynamic analysis of functionally graded nanocomposite beams reinforced by randomly oriented carbon nanotube under the action of moving load

This work deals with a study of the vibrational properties of functionally graded nanocomposite beams reinforced by randomly oriented straight single-walled carbon nanotubes (SWCNTs) under the actions of moving load. Timoshenko and Euler-Bernoulli beam theories are used to evaluate dynamic characteristics of the beam. The Eshelby-Mori-Tanaka approach based on an equivalent fiber is used to investigate the material properties of the beam. An embedded carbon nanotube in a polymer matrix and its surrounding inter-phase is replaced with an equivalent fiber for predicting the mechanical properties of the carbon nanotube/polymer composite. The primary contribution of the present work deals with the global elastic properties of nano-structured composite beams. The system of equations of motion is derived by using Hamilton’s principle under the assumptions of the Timoshenko beam theory. The finite element method is employed to discretize the model and obtain a numerical approximation of the motion equation. In order to evaluate time response of the system, Newmark method is also used. Numerical results are presented in both tabular and graphical forms to figure out the effects of various material distributions, carbon nanotube orientations, velocity of the moving load, shear deformation, slenderness ratios and boundary conditions on the dynamic characteristics of the beam. The results show that the above mentioned effects play very important role on the dynamic behavior of the beam and it is believed that new results are presented for dynamics of FG nano-structure beams under moving loads which are of interest to the scientific and engineering community in the area of FGM nano-structures.     

Periodic Solutions for a Damped Rayleigh Beam Model with Time Delay

Vibrations of a beam can be described as an Euler-Bernoulli beam,or as a Rayleigh beam or as a Timoshenko beam. In this paper, we establish the existence of periodic solutions in time for a damped Rayleigh beam model with time delay, which is treated as a bifurcation parameter. The main proof is based on a Lyapunov-Schmidt reduction together with the classical implicit function theorem. Moreover, we give a sufficient condition for a direction of bifurcation.     

非均质Euler-Bernoulli梁的边界反馈镇定问题

基于频域乘子方法，讨论非均质Euler-Bernoulli梁边界反馈镇定问题，利用黄发伦关于C0-半群指数稳定的判据和指数乘子技巧，证明了只用力或力矩反馈，由Euler-Bernoulli梁所决定的闭环系统可以指数稳定。