【作者】 马建青；

【导师】 杜国君；

【作者基本信息】 燕山大学 ， 工程力学， 2005， 硕士

【摘要】 本文主要研究受均布载荷和周边面内压力作用下夹层圆板的非线性振动、屈曲问题。首先,给出了周边面内压力作用下夹层圆板静平衡问题的控制方程和静力问题的精确解,在此基础上,导出了周边面内压力作用下夹层圆板非线性振动的基本方程,同时采用修正迭代法对该问题进行求解,当周边压力使夹层圆板的最低固有频率为零时,就可得到分支解的临界点(即临界载荷)和相应的屈曲波型。然后,对于受均布载荷和周边面内压力联合作用的夹层圆板,给出了静力问题的精确解,在此基础上导出了受均布载荷和周边面内压力联合作用的夹层圆板非线性振动的基本方程,文中基于时间模态假设和变分法,将挠度和应力函数设为时间和空间函数的分离形式,时间函数取谐函数,空间函数未知。所假设的振动模态包含两个未知的内禀量,即振频和一个由于静变形而使板具有不对称刚度特性的非线性振子的“漂移”的小量,这两个量均与载荷、边界条件和振幅有关。将假定的模态函数代入本问题的变分方程,导出空间模态的控制方程和求解“漂移”的代数方程,采用修正迭代法求出了该问题的近似解析解,分别对均布载荷和周边载荷对频率的影响以及振幅对频率的影响进行了分析。更多还原

【Abstract】 The nonlinear bend and the large amplitude free vibration for circular sandwich plate under uniformed loading and circumjacent loading is researched firstly. First of all, exact solution of static loading of sandwich plate under circumjacent loading is given firstly. Based on the studies above , the nonlinear vibration fundmental equation of sandwich under circumjacent loading is established. At the same time, modified iteration method is employed to solve this problem and the influence of static loading on nonlinear vibration frequency is discussed. Consequently, for the sandwich plate under uniformed loading and circumjacent loading, exact solution of static loading is given, on this based the nonlinear vibration fundmental equation of sandwich under uniformed loading and circumjacent loading is established. During this course, based on time mode hypothesis, the deflection and stress function are assumed as the separation form of time and space function, the time function employs the simple harmonic, the space function is unknown. The vibration mode assumed includes two unknown natural values, that is, the amplitude frequency and one small value of “drift” of nonlinear vibrator that made the plate asymmetrical rigidity property caused by the static reflection. Both of them are related with load, boundary conditions and amplitude. Substituting the assumed mode functions to the calculus equations, then the control equation of the space mode and the algebra equation is derived. The approximate analytical solution of this problem under these boundary conditions is provided in this paper by the modified iteration method, based on which, the nonlinear vibration of the circular sandwich plates under uniformed load and circumjacent load in plate uniform pressure at the outer edges is made research on.更多还原