弹性地基上四边自由矩形薄板振动分析有限积分变换法

Vibration of a thin plate on Winkler foundation with completely free boundary by finite cosine integral transform method

将弹性地基以W ink ler模型模拟,利用双重有限余弦积分变换的方法推导出了弹性地基上四边自由矩形薄板的固有频率和振型的解析解表达式.由于在求解过程中不需要事先人为地选取挠度函数,而是从弹性地基上薄板的基本振动方程出发,直接利用数学的方法求解,使得问题的求解更加合理化.计算实例验证了所采用的方法以及所推导出的公式的正确性.

The theoretical solution of eigenfrequencies and vibration models of rectangular thin plate on foundation with completely free boundary was derived by the double finite cosine integral transform method. In the analytical process, the elastic foundation was regarded as Winkler foundation model. Due to the basic dynamic elasticity equations of the thin plate on elastic foundation were only used and it does not need to select in advance the deflection function arbitrarily, therefore, the solution obtained directly by mathematic method is reasonable and theoretical. The correctness of formulations and method is proved by a numerical example.