Abstract

Accurate and profound comprehension of the dynamical behavior of viscoelastic plates is a key task in designing these structures, and also optimizing their mechanical/vibrational behavior. In the present research, the dynamic response of the annular sector plates under asymmetric impulsive and harmonic transverse loads is determined analytically. The boundary conditions for the radial edges are simply supported, but for the circular boundaries, different cases are investigated. By employing Hamilton’s principle, the governing equations of motion are derived based on the first-order shear deformation theory. The viscoelastic behavior of the polymer sector plate is considered as the standard linear solid in shear and elastic in bulk. An analytical method based on the perturbation technique and the Fourier series is adopted to solve the equations of motion which include a system of partial differential equations with variable coefficients. Moreover, in parallel, the classical plate theory is obtained in the same procedure to examine the influence of each theory. Then, the sensitivity of the results to the geometrical and mechanical parameters is declared. The results are compared with those obtained from the classical plate theory and the finite element method.

摘要

准确而深刻地理解粘弹性板的动力学行为是设计这些结构以及优化其机械/振动行为的关键任务。在本研究中，环形扇形板在不对称冲击和谐波横向载荷下的动态响应是解析确定的。径向边缘的边界条件是简单支持的，但对于圆形边界，则研究不同的情况。利用Hamilton原理，基于一阶剪切变形理论推导出运动控制方程。聚合物扇形板的粘弹性行为被认为是标准的线性剪切固体和弹性体。可变系数。此外，平行地，以相同的程序获得经典板理论，以检验每种理论的影响。然后，声明了结果对几何和机械参数的敏感性。结果与从经典板理论和有限元方法获得的结果进行了比较。