弹性半空间地基上正交异性矩形薄板稳态振动通解

General solutions to the steady vibration of orthotropic rectangular plates on the semi-infinite elastic foundation

先对边界任意约束的正交各向异性矩形薄板,构造了四次逐项可导的带有补充项的双重正弦傅里叶级数通解.该解析解既不需要叠加,对不同的物性参数又不需要分类,而且待定系数少又具有明确的物理含义,这使得正交各向异性矩形薄板的振动问题求解统一化、简单化、规律化.然后将该通解与弹性半空间受任意竖向稳态荷载作用下的动力位移积分变换解相结合,得出弹性半空间地基上边界任意约束的正交各向异性矩形板,在任意竖向稳态荷载作用下的稳态振动解析解.最后还给出了算例分析,其结果与文献吻合良好,证明本文的方法是切实可行的.

General solution to the steady vibration which was constructed by double trigonometrically sine series with supplementary terms was introduced for the vibration analysis of orthotropic rectangular thin plates loaded with arbitrary steady vertical force on the semi-infinite elastic foundation.This general solution is four-order derivative,and has less undetermined coefficients which has definite physical meaning.The solution can be used to sethe the problem of orthotropic rectangular plates on the semi-infinite elastic foundation with neither a dassification by different property parameter nor a superimposition.Such a solution has resulted in vibration analysis of orthotropic rectangular plates loaded with vertical steady force on the semi-infinite elastic foundation,unionization,simplification and systematization.The analytic vibration solution to orthotropic rectangular plates loaded with vertical steady force on the semi-infinite elastic foundation was given by combining the general solution of double trigonometrically sine series with supplementary terms with the dynamic integral representations for displacements of the semi-infinite elastic foundation loaded with arbitrary vertical steady force.The agreement is found satisfactory in proving the validity of the method in solving the problem.This new method would be feasible in practical applications.