A method to retrieve the elastic constants of rectangular wooden plates is presented, relying on the measurement of a set of eigenfrequencies and the identification of the corresponding mode shapes, and belonging to the more general category of non-destructive inverse parameter estimation methods. Compared to previous work, the current method is effective with any choice of boundary conditions. Furthermore, the error function is linear in the elastic constants, which may be computed easily via a matrix inversion. This framework lends itself naturally to a physical interpretation of the results in terms of linear combinations of eigenmodes, yielding new sets of modes and associated combined mode shapes in which the elastic constants are completely uncoupled. Several numerical benchmark tests and experimental cases are treated in detail, highlighting the reliability of the proposed methodology in cases of interest in acoustics and musical acoustics.

中文翻译：

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一种利用最小二乘和Chladni模式估计矩形正交各向异性板弹性常数的方法

提出了一种基于一组特征频率的测量和相应模态振型的识别来反演矩形木板弹性常数的方法，属于更通用的无损逆参数估计方法。与以前的工作相比，当前的方法对于任何边界条件的选择都是有效的。此外，误差函数在弹性常数中是线性的，可以通过矩阵求逆轻松计算。该框架很自然地适合根据本征模态的线性组合对结果进行物理解释，产生新的模态集和相关的组合模态形状，其中弹性常数完全解耦。详细处理了几个数值基准测试和实验案例，突出了所提出的方法在声学和音乐声学感兴趣的情况下的可靠性。