基于连续体的圆形三角和各向同性板的自由振动。
Continuum-based free vibration of circular trigonal and isotropic plates.
机构信息
Department of Civil and Environmental Engineering, Colorado State University, Fort Collins, Colorado 80523, USA.
出版信息
J Acoust Soc Am. 2013 Aug;134(2):1039-48. doi: 10.1121/1.4812261.
The free vibration behavior of completely unrestrained elastic circular plates with trigonal and isotropic material symmetry is studied with an approach involving approximate continuum solutions to the three-dimensional theory of linear elasticity. Of primary interest are (1) the influence of trigonal material symmetry on the modes of free vibration and (2) the accuracy of thin plate theory relative to the more exact three-dimensional theory. Resonant frequencies are calculated from the weak form of the equations of motion for the plate through the use of approximation functions and the Ritz method formulated in cylindrical coordinates. This approach enables the resulting eigenvalue problem to be split through group-theoretical symmetry analysis. Representative examples are given and quantitative limits are discussed.
本文采用涉及线性弹性三维理论的近似连续体解的方法研究了具有三角和各向同性材料对称性的完全无约束弹性圆板的自由振动行为。主要关注的是：（1）三角材料对称性对自由振动模态的影响；（2）与更精确的三维理论相比，薄板理论的准确性。通过在圆柱坐标系中使用近似函数和里兹方法，从板的运动方程的弱形式计算出共振频率。该方法使所得到的特征值问题能够通过群论对称性分析进行分割。给出了代表性的例子，并讨论了定量限制。
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