Abstract
A finite element-based derivation of the transmission loss (TL) of anisotropic layered infinite plates is presented in this paper. The wave-finite element method (WFE) is used to represent the plate with a finite element model of a single unit cell. The incident acoustic field is a known plane wave, and the reflected and transmitted pressures are supposed to be plane waves with unknown amplitudes and phases. The periodicity conditions on the unit cell allow to find a simple matrix equation linking the amplitudes of the transmitted and reflected fields as a function of the incident one. This approach is validated for several cases against classical analytical models for thin plates and sandwich constructions, where the results agree perfectly for a reasonable mesh size. The method is then used to study the effect of stacking order in a laminated composite plate. The main interest of the method is the use of finite elements, which enables a relative easy modelling since most packages readily include different formulations, compared to analytical models, where different formulations have to be implemented for every kind of material.
Highlights
Sound transmission modelling is a very important topic in the industry, yet it is often still difficult to calculate for complex geometries or materials
Finite Element (FE) modelling has the practical advantage over analytical models that most constitutive laws and couplings between materials are already implemented in commercial codes
A new method for computing the transmission loss of infinite plates made of arbitrarily layered materials has been presented in this paper
Summary
Sound transmission modelling is a very important topic in the industry, yet it is often still difficult to calculate for complex geometries or materials. The Transfer Matrix Method (TMM) [6, 7] is a general framework used to compute acoustic transmission features of infinite plane isotropic layerings comprising elastic solids, poroelastic materials and air gaps. The WFE was used to compute vibroacoustic indicators such as group velocities and modal densities for use in Statistical Energy Analysis (SEA) [9, 10] Extensions of this method towards the calculation of forced responses of waveguides have been proposed [11], without considering fluidstructure coupling. Since the periodic structure theory deals primarily with infinite structures, the WFE can be used to compute the transmission loss of infinite plane structures excited by a superposition of plane waves directly, without having to resort to SEA The derivation of this application is proposed in this paper, making use of the WFE framework for a plate with homogeneous properties in its plane.
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