分数导数粘弹性模型的矩形板的振动分析  

Vibration Analysis of Rectangular Plates with Fractional Derivative Viscoelastic Model

作　　者：张亚鹏[1,2] 高峰[1,2] 

机构地区：[1]中国矿业大学深部岩土力学与地下工程国家重点实验室,江苏徐州221006 [2]中国矿业大学力学与建筑学院,江苏徐州221006

出　　处：《噪声与振动控制》2012年第3期34-36,81,共4页Noise and Vibration Control

基　　金：国家重点基础研究发展计划(973)项目(NO.:96578452);国家自然基金项目(50974125;50909093)

摘　　要：利用分数阶Kevin粘弹性模型,建立矩形薄板的动力学方程,并利用拉普拉斯变换及其逆变换给出四边简支粘弹性薄板的解析解,并着重分析在常值荷载作用下,分数阶Kevin粘弹性模型的分数阶参数、粘性参数和模量参数对挠度的影响。结果表明,随着粘性参数和分数阶参数的增大,粘弹性板的挠度变小;随着模量参数增大,粘弹性板的挠度变大。Dynamic equations of rectangular thin plates based on fractional-order Kevin viscoelastic model were established. The analytical solution of the dynamic equations for a viscoelastic plate with four edges simply supported was obtained by using Laplace transform and inverter Laplace transform. The influences of the fractional order parameter, viscosity parameters and modulus parameters on the deflection of the fractional-order Kevin viscoelastic model with constant load were analyzed. The results show that the deflection of the viscoelastic plates decreases with the increasing of the viscosity parameters, while the deflection of the viscoelastic plates increases with the increasing of the modulus parameters.

关 键 词：振动与波 分数阶Kevin模型 拉普拉斯变换 粘弹性板 参数影响 

分 类 号：O327[理学—一般力学与力学基础]