含表面贯通裂纹粘弹性板的线性自由振动

基于各向同性线性粘弹性本构关系和板的几何线性理论,建立了含表面贯通裂纹粘弹性板的线性动力方程.根据相应的边界条件和裂纹处的位移与力的连续性条件,提出了一组满足所列边界条件和裂纹连续性条件的挠度形函数.在材料为标准线性固体的情况下,采用Galerk in法,对含裂纹四边简支矩形板问题进行了求解.在数值计算中,主要讨论了裂纹参数和材料粘弹性参数对板的固有频率的影响,并对有关的其它参数也进行了讨论.

Linear free vibration of a viscoelastic plate with an all-over part-through crack

Based on the plate geometric linear theory and the isotropic linear viscoelastic constitutive relation,the linear dynamic equations for a viscoelastic thin plate with an all-over part-through crack are developed.According to the corresponding boundary conditions and crack-continuity conditions,a set of suitable expressions of deflection shape functions that make satisfaction for all boundary and crack-continuity conditions are introduced.Provided that the materials of the plate are standard linear solid and with the use of Galerkin procedure,the problems of cracked rectangular viscoelastic plates are solved.In the numerical computations,the effects of viscoelastic parameters and crack parameters on the natural frequency of the plates are discussed,and other correlative parameters are also discussed.