Abstract Thin plates with attached concentrated masses are considered. Time-harmonic flexural waves are generated by a force applied over a finite region of the plate. The problem of calculating the resulting plate response reduces to calculating the displacement of the masses, and this is done by solving a finite system of linear algebraic equations in the manner of previous work by Evans and Porter. Numerical results for two masses are presented and compared with finite element computations. Analytical results for N masses arranged around a circle concentric with a circular forcing region are obtained; it is shown that results for a corresponding thin solid ring are recovered as N goes to infinity. Similar results are obtained for a scattering problem, with an incident plane wave.

中文翻译：

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加载集中质量的无限薄板的动态响应

摘要 考虑附有集中质量的薄板。时谐弯曲波由施加在板的有限区域上的力产生。计算所得板响应的问题简化为计算质量的位移，这是通过以 Evans 和 Porter 先前工作的方式求解线性代数方程的有限系统来完成的。给出了两个质量的数值结果并与有限元计算进行了比较。获得了围绕与圆形受力区域同心的圆排列的 N 个质量的分析结果；结果表明，随着 N 趋于无穷大，相应的薄实心环的结果会恢复。对于具有入射平面波的散射问题，可以获得类似的结果。