摘要
基于三维Biot理论和弹性薄板理论,考虑多孔介质薄板骨架与流体的耦合作用,导出了多孔介质矩形薄板在谐激励作用下的一阶常微分矩阵方程。利用齐次扩容精细积分方法,对两对边简支矩形薄板在均布荷载和集中荷载两种情况下的弯曲振动问题进行了求解,对比经典算例,验证了所建模型的可行性和有效性。相对于数值方法,本文提出的方法适用于中高频段的分析计算。
Based on the three dimensional Biot theory and the elastic theory of thin plate, the first order differential equations of a thin rectangular porous plate under harmonic excitation were established by considering the coupling effect between the solid phase and the fluid phase. Employing the extended homogeneous capacity precision integration method, transverse vibrations problem of a thin rectangular porous plate was discussed with simply supported boundary condition in two opposite edges. In the numerical examples, both the uniform force and unit point force were taken into account. Comparisons with the classic example have verified the feasibility and effectiveness of the present model. The present model was high precision, which was derived rigorously and easy to conduct various boundary conditions. It can be applied in higher frequency range than the numerical method.
出处
《振动工程学报》
EI
CSCD
北大核心
2016年第6期1020-1027,共8页
Journal of Vibration Engineering
基金
国家自然科学基金资助项目(11162001
11502056)
广西自然科学基金资助项目(2015GXNSFBA139007)
关键词
多孔介质矩形薄板
吸声
BIOT理论
齐次扩容精细积分法
thin rectangular porous plate
absorption
Biot theory
extended homogeneous capacity high precision integration method
