论文标题
简单支撑的厚壁弹性弹性圆柱的谐波站立波激发：精确的3D线性弹性响应
Harmonic Standing-Wave Excitations of Simply-Supported Thick-Walled Hollow Elastic Circular Cylinders: Exact 3D Linear Elastodynamic Response
论文作者
论文摘要
在线性弹性动力学的框架内研究了在其弯曲表面上受到二维谐波站立式激发激发二维谐波站立式激发激发的强制振动响应。使用最近发布的Navier-Lamé方程的参数溶液构建了圆柱体稳态位移场的精确半分析溶液。站立边界条件的形式应用会生成三个依赖参数的$ 6 \ times6 $线性系统，每个系统都可以在数值上求解，以确定在各种条件下缸位移场的参数响应。解决方案的方法是直接的，并证明了一种通用方法，该方法可用于解决许多其他涉及各向同性弹性缸的弹性动力学反应问题。作为一种应用，考虑了几个示例，获得的解决方案用于计算一些特定的低阶激发案例中的稳态频率响应。在每种情况下，溶液都会产生一系列与简单支持的圆柱体的固有频率的唯一子集完全对应的共振。被认为是对结构力学和声学的一般理论兴趣，实际上是涉及厚壁的空心弹性缸的基准强制振动问题。
The forced-vibration response of a simply-supported isotropic thick-walled hollow elastic circular cylinder subjected to two-dimensional harmonic standing-wave excitations on its curved surfaces is studied within the framework of linear elastodynamics. Exact semi-analytical solutions for the steady-state displacement field of the cylinder are constructed using recently-published parametric solutions to the Navier-Lamé equation. Formal application of the standing-wave boundary conditions generates three parameter-dependent $6\times6$ linear systems, each of which can be numerically solved in order to determine the parametric response of the cylinder's displacement field under various conditions. The method of solution is direct and demonstrates a general approach that can be applied to solve many other elastodynamic forced-response problems involving isotropic elastic cylinders. As an application, and considering several examples, the obtained solution is used to compute the steady-state frequency response in a few specific low-order excitation cases. In each case, the solution generates a series of resonances that are in exact correspondence with a unique subset of the natural frequencies of the simply-supported cylinder. The considered problem is of general theoretical interest in structural mechanics and acoustics and more practically serves as a benchmark forced-vibration problem involving a thick-walled hollow elastic cylinder.
