粘-弹层合悬臂板瞬态响应的近似解析解

采用双向梁函数组合级数逼近的方法构造粘-弹层合悬臂板的横向位移函数,用里兹法得悬臂板在集中力作用下的弯曲变形。用拉格朗日方程求出了板自由振动的频率和结构损耗因子;给出粘-弹层合悬臂板在集中力突然撤去以后瞬态响应的近似解析解。另外,分析了阻尼层损耗因子、弹性模量及厚度对响应的影响。

Approximate analytical solutions for transient response of visco-elastic laminated cantilever plate

The series composed by two-dimension beam mode function is used to approximate the transverse displacement function of visco-elastic cantilevered plate, and the transverse deformation of the plate on which a concentrated force is acted is calculated by using Ritz’s method. By solving Lagrange’s equation, the frequencies and model loss factors of free vibration of the plate are obtained, then transient response of visco-elastic cantilevered plate, when the concentrated force is withdrew suddenly, is obtained by using the method of mode superposition. Also the effects of loss factor, module and thickness of viscoelastic layer on the response are analyzed.