Analytical model of sound transmission through composite doubly curve shell using a layerwise theory

Abstract

This study presents an analytical investigation of the sound transmission loss behavior of an infinite composite with double curvature using layerwise theory. The governing equations for the doubly curved shell are obtained through Hamilton’s principle, and the displacement field is formulated based on layerwise theory, expressed as the summation of displacements across individual layers. To model the displacement along the shell thickness, a linear Lagrange interpolation function is employed within each layer. The displacement field is formulated as a combination of the displacements associated with individual layers, leading to the structural strain being expressed as the summation of the contributions from each layer. The accuracy and reliability of the proposed formulation are validated by comparing its results with those from previous studies. The findings demonstrate that the layerwise theory provides a precise framework for predicting sound transmission loss and acoustic pressure. Key parameters influencing sound transmission loss are also analyzed. The results indicate that doubly curved shells exhibit superior sound transmission loss at lower frequencies compared to flat plates. Furthermore, while an increase in curvature radius does not affect the coincidence frequency, it results in the reduction of curve frequency. Additionally, under constant mechanical properties, the coincidence frequency remains identical for both plates and doubly curved shells, and the curvature radius does not affect the dip of this transition.