Abstract
This work presents the modelling of acoustic wave-based devices of various geometries through a mapped orthogonal functions method. A specificity of the method, namely the automatic incorporation of boundary conditions into equations of motion through position-dependent physical constants, is presented in detail. Formulations are given for two classes of problems: (i) problems with guided mode propagation and (ii) problems with stationary waves. The method’s interest is demonstrated by several examples, a seven-layered plate, a 2D rectangular resonator and a 3D cylindrical resonator, showing how it is easy to obtain either dispersion curves and field profiles for devices with guided mode propagation or electrical response for devices with stationary waves. Extensions and possible further developments are also given.
Highlights
This work presents the modelling of acoustic wave-based devices of various geometries through a mapped orthogonal functions method
Acoustic waves play a key role in many fields such as non-destructive testing (NDT) for material inspection or evaluation and with the advances in reliability, structural health monitoring (SHM) with continuous screening and early warning of defect growth and structural failure
065307-3 Lefebvre et al This paper aims at explaining the fundamentals of the mapped orthogonal functions method and reviewing all its potentialities in characterizing the acoustic wave-based devices with guided mode propagation and with stationary waves
Summary
Acoustic waves play a key role in many fields such as non-destructive testing (NDT) for material inspection or evaluation and with the advances in reliability, structural health monitoring (SHM) with continuous screening and early warning of defect growth and structural failure. Among computational methods that have been used are the transfer matrix approach developed by Thomson[1] and the global matrix method by Knopoff[2] applicable to multilayered plates and cylindrical structures.[3] The global matrix method was proposed to overcome the problem of numerical instability of the solution given by the transfer matrix method, known as the large fd problem when layers of large thickness d are present and high frequencies f are being considered. This is crucial when inhomogeneous waves are considered. The global matrix method is robust, it does not suffer from numerical instability, but is computationally expensive in time and memory resources
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