为了研究Mindlin矩形板在任意弹性边界条件下的自由振动特性，采用改进傅里叶级数的方法，将板的横向振动位移和转角位移函数表示为标准的二维傅里叶余弦级数和辅助级数的线性组合。结合Hamilton原理建立求解方程，得到Mindlin矩形板振动控制方程的矩阵表达式。通过辅助级数的引入，解决了位移函数和转角函数的导数在边界不连续的问题，从而使此法适用于任意的弹性边界条件。边界条件通过均匀布置的线性位移弹簧、旋转弹簧和扭转弹簧来模拟，通过改变3种类型弹簧的刚度值来实现不同的边界条件。最后给出了数值仿真算例，并对计算结果进行了分析。通过与已有文献的计算结果进行比较，本方法与文献中的结果间的偏差不超过5‰，验证了本方法的准确性。%In order to research the free vibrations of Mindlin rectangular plates with general elastic boundary sup-port, an improved Fourier series method was employed, in which the function on a transverse vibration displace-ment and rotational displacements was expressed as the linear combination of a standard two-dimensional Fourier co-sine series and an auxiliary series. In combination with Hamilton's principle, a solution equation was established and the matrix expression of the vibration control equation of the Mindlin rectangular plates was attained. By the use of the auxiliary series, the discontinuity at the boundary which was encountered by the derivative of a displacement function and rotation functions was solved, making the method applicable for arbitrary elastic boundary conditions. The boundary conditions were physically simulated by the linear-displacement spring, rotation spring and torsion spring with an even arrangement. By changing the stiffness of the three types of springs, different boundary condi-tions may be directly obtained. Finally, in this paper, a calculation example of the numerical simulation was given and the results were analyzed. By comparing the results in the existing literature, it was found that the deviation was less than 5 percent. Therefore, the accuracy of this method was demonstrated.
展开▼
