This article deals with the dynamic response of laterally unbounded, horizontally layered plates subjected to dynamic sources applied at arbitrary locations, which is ultimately a classical problem. This response is most often obtained via a modal superposition in terms of the complex Lamb modes by casting the equations in the frequency–space domain, followed by a Fourier inversion into the space–time domain. Then again, a much less often used alternative method relies on formulating the problem directly in the time domain in terms of a modal superposition in the wavenumber domain, which is followed by a Fourier inversion into the space–domain, as considered in further detail herein. This alternative can offer powerful advantages in some cases, such as dealing easily with anisotropy, or with slowly propagating waves even in the absence of damping. At the same time, however, it is beset by difficulties associated with the Fourier inversion into the space–domain. As a matter of fact, during forcing, the truncation of the modal series and of the numerical integrals is hindered by poorly convergent behaviors. Here we overcome both of these difficulties by considering the asymptotic, static behavior of the integrands. We find that by introducing a regularizing term, the response can be effectively separated into near and far fields, despite the fact that these frequency-domain concepts are alien to a wavenumber–time formulation. The so-defined far field is free of sharp variations and can then be computed in a numerical grid that is optimized regarding the propagating wavelengths, which only depend on the time-spectral content of the excitation and not on its space-spectrum. Finally, we also propose a hybrid way to compute the remaining near field by combining with a non-modal formulation, expressed in the wavenumber–Laplace domain.

本文讨论了在任意位置施加动态源的横向无边界，水平分层板的动力响应，这最终是一个经典问题。这种响应通常是通过在复杂的Lamb模式下通过模态叠加来获得的，方法是在频-空域中转换方程，然后进行傅立叶反演到时-空域。再说一次，很少使用的替代方法依赖于直接在时域中根据波数域中的模态叠加来表达问题，然后通过傅立叶反演到空间域中，如本文进一步详细讨论的那样。在某些情况下，这种替代方法可以提供强大的优势，例如轻松处理各向异性，或者即使没有阻尼也可以缓慢传播波。然而，与此同时，它又受到与傅立叶反演到空间域相关的困难的困扰。实际上，在强制过程中，收敛性较差的行为会阻止模态序列和数值积分的截断。在这里，我们通过考虑被整数的渐近静态行为来克服这两个困难。我们发现通过引入正则项，尽管这些频域概念与波数-时间公式无关，但可以将响应有效地分为近场和远场。这样定义的远场没有剧烈变化，然后可以在数值网格中进行计算，该数值网格针对传播的波长进行了优化，该波长仅取决于激发的时间光谱含量，而不取决于激发的空间光谱。最后，