Abstract
Plates are common structural elements of most engineering structures, including aerospace, automotive, and civil engineering structures. The study of plates from theoretical perspective as well as experimental viewpoint is fundamental to understanding of the behavior of such structures. The dynamic characteristics of plates, such as natural vibrations, transient responses for the external forces and so on, are especially of importance in actual environments. In this paper, we consider natural vibrations of an elastic plate and the propagation of a wavepacket on it. We derive the two-dimensional equations that govern the spatial and temporal evolution of the amplitude of a wavepacket and discuss its features. We especially consider a directional wavepacket on an elastic plate, which propagation direction is centered around a main direction, but which wavenumber and frequency are fixed by a certain value. The fact that its envelope becomes time-invariant and is governed by the Schrödinger–Nohara type equation is shown.
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Nohara, B.T. A Comment on Governing Equations of Envelope Surface Created by a Two-Dimensional Directional Wavepacket Centered around a Propagation Direction on an Elastic Plate. Nonlinear Dynamics 35, 175–186 (2004). https://doi.org/10.1023/B:NODY.0000020989.19051.1c
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DOI: https://doi.org/10.1023/B:NODY.0000020989.19051.1c