梁横向振动方程的特征值估计

本文考虑了一类常微分方程的特征值估计的上界。

梁横向振动方程的离散谱估计

考虑梁横向振动方程的离散谱估计 ,获得了用前n个离散谱来估计第n + 1个离散谱的上界的不等式的结果 ,估计系数与区间的几何度量无关 。

梁横向振动方程解的Ritz方法

考虑计算梁横向振动方程解的Ritz方法。主要结果的证明运用变分法。首先,证明变分问题(2)与问题(1)等价;其次,采用坐标函数系来构造适当的近似解;最后,将问题(1)的解的近似计算问题离散化为线性方程组解的计算问题,获得了计算问题(1)解的近似值的Ritz方法,而且可以用第n次近似值来估计第n-1次的近似值的精确度。随着n的增大,解的精确度逐步提高,只要适当选取n,就可以求得所要精确度解的近似值,这个算法具有广泛的实用价值和理论价值。

梁横向振动方程的第二特征值的上界

设（ａ，ｂ）Ｒ是一个有界开区间，对源自梁横向振动方程的如下特征值问题Ｄ２（Ｐ（ｘ）Ｄ２ｙ）＝－λＤ２ｙｙ（ａ）＝ｙ（ｂ）＝０，Ｄｙ（ａ）＝Ｄｙ（ｂ）＝０｛（其中Ｐ（ｘ）是关于ｘ的函数），建立了第二特征值λ２的上界用第一特征值λ１来估计的不等式。

升降工装切割作业振动故障特性分析

切割设备在大进给,大切深的作业工况下易出现切割片断裂飞崩的情况,会降低切割效率并且造成人员危险。通过提取作业时的振动加速度信号从时域和频域两个方面进行分析,利用小波包变换的方法对振动信号进行逐层分解,得到了不同进给速度下升降工装切割作业的振动特性。建立切割片横向振动方程研究振动的产生机理并分析切割故障时信号特征的产生原因及影响,最后提出合适的减振策略。研究方法对延长切割片使用寿命及减少切割作业故障产生的频率具有重要意义。

弹炮运动方程的建立及应用

本文给出了弹丸膛内运动方程和身管横向振动方程,对弹丸前定心部与膛壁的碰撞及前定心部紧贴膛壁时弹丸的运动特征作了深入的研究。给出了弹炮相互作用模型——耦合模型的计算方法,并对某弹炮系统进行了分析计算得到了一系列结论。

基于离散小波变换的接触网横向风振响应研究

接触网在风载作用下发生横向偏移及振动影响接触网系统的动力稳定性。本文采用适合接触网随机风场计算与高度无关的Davenport功率谱,运用小波分析法数值模拟水平方向脉动风速时程。基于铁路接触网结构模型,建立了接触网悬索横向振动微分方程。在此基础上,将随机风场、平均风载及最大风载施加于接触网,分析了直线区段接触网横向风振响应;研究了不同参数对接触网横向风偏的影响。仿真结果表明:随机风场引起接触网的横向振动,脉动风使接触网发生微幅振动,而静态风决定接触网横向风偏均值,是引起接触网横向偏移的主要因素。接触网跨距,风速的大小,风偏角等参数影响接触网的稳定性。

Modal analysis on transverse vibration of axially moving roller chain coupled with lumped mass

The modal characteristics of the transverse vibration of an axially moving roller chain coupled with lumped mass were analyzed.The chain system was modeled by using the multi-body dynamics theory and the governing equations were derived by means of Lagrange's equations.The effects of the parameters,such as the axially moving velocity of the chain,the tension force,the weight of lumped mass and its time-variable assign position in chain span,on the modal characteristics of transverse vibration for roller chain were investigated.The numerical examples were given.It is found that the natural frequencies and the corresponding mode shapes of the transverse vibration for roller chain coupled with lumped mass change significantly when the variations of above parameters are considered.With the movement of the chain strand,the natural frequencies present a fluctuating phenomenon,which is different from the uniform chain.The higher the order of mode is,the greater the fluctuating magnitude and frequency are.

Variational Approach of Timoshenko Beams with Internal Elastic Restraints

An exact approach for free transverse vibrations of a Timoshenko beam with ends elastically restrained against rotation and translation and arbitrarily located internal restraints is presented. The calculus of variations is used to obtain the equations of motion, the boundary conditions and the transitions conditions which correspond to the described mechanical system. The derived differential equations are solved individually for each segment of the beam with the corresponding boundary and transitions conditions. The derived mathematical formulation generates as particular cases, and several mathematical models are used to simulate the presence of cracks. Some cases available in the literature and the presence of some errors are discussed. New results are presented for different end conditions and restraint conditions in the intermediate elastic constraints with their corresponding modal shapes.

Transverse vibration of pre-tensioned nonlocal nanobeams with precise internal axial loads

This paper investigates the transverse vibration of a simply supported nanobeam with an initial axial tension based on the nonlocal stress field theory with a nonlocal size parameter. Considering an axial elongation due to transverse vibration, the internal axial tension is not precisely equal to the external initial tension. A sixth-order nonlinear partial differential equation that governs the transverse vibration for such nonlocal nanobeam is derived. Using a perturbation method, the relation between natural frequency and nonlocal nanoscale parameter is derived and the transverse vibration mode is solved. The external axial tension and nonlocal nanoscale parameter are proven to play significant roles in the nonlinear vibration behavior of nonlocal nanobeams. Such effects enhance the natural frequency and stiffness as compared to the predictions of the classical continuum mechanics models. Additionally, the frequency is higher if the precise internal axial load is considered with respect to that when only the approximate internal axial tension is assumed.

ON THE NONLINEARTIMOSHENKO-KIRCHHOFF BEAM EQUATION

When an elastic string with fixed ends is subjected to transverse vibrations, its length varies with the time: this introduces changes of the tension in the string. This induced Kirchhoff to propose a nonlinear correction of the classical D’Alembert equation. Later on, WoinowskyKrieger (Nash & Modeer) incorporated this correction in the classical Euler-Bernoulli equation for the beam (plate) with hinged ends.Here a new equation for the small transverse vibrations of a simply supported beam is proposed. Such equation takes into account Kirchhoff’s correction, as well as the correction for rotary inertia of the cross section Of the beam and the influence of shearing strains, already present in the Timoshenko beam equation (of the Mindlin-Timoshenko equation for the plate).The model is inspired by a remark of Rayleigh, and by a joint paper with Panizzi & Paoli. It looks more complicated than the one proposed by Sapir & Reiss, but as a matter of fact it is easier to study if a suitable change of variables is performed.The author proves the local well-posedness of the initial-boundary value problem in Sobolev spaces of order ≥2.5. The technique is abstract, i.e. the equation is rewritten as a fourth order evolution equation in Hilbert space (thus the results could be applied also to the formally analogous equation for the plate).