一般边界条件下任意三角形薄板弯曲振动分析

Bending Vibration Analysis of Arbitrary Triangle Thin Plate under General Boundary Conditions

采用改进傅里叶级数法分析任意三角形薄板在多种边界条件下的弯曲振动特性。首先将三角域转换为单位正方形域,同时引入人工虚拟弹簧技术来模拟各种边界约束;为消除边界上的跳跃或不连续问题,使用一种改进傅里叶级数来表示薄板的容许位移函数;根据经典薄板理论建立薄板的能量方程,最后采用Rayleigh-Ritz法求解。通过将数值结果与有限元法的结果进行对比,表明该方法具有稳定性好、精度高、收敛速度快的特点。该方法可以很容易地得到任意三角形薄板在多种边界条件下的弯曲振动特性,包括固有频率和模态形状。

Bend vibration characteristics of arbitrary triangle thin plate under various boundary conditions is analyzed by improved Fourier series method(IFSM).The triangular domain is transformed into unit square region,and artificial virtual springs technology are introduced to simulate various boundary constraints.In order to remove the jumps or discontinuities problem on the boundary,an IFSM is used to express all allowable displacement functions of thin plate.The energy equations of thin plate are established by classical thin plate theory.Then Rayleigh-Ritz method is used to solve the problem.By comparing numerical results with those of the finite element method,it is shown that the current method has high stability,accuracy and rapid convergence.The method can easily obtain the bend vibration characteristics of arbitrary triangle thin plate under various boundary conditions,including its natural frequencies and modal shapes.