A Tchebyshev point interpolation meshless method for vibration and acoustic response prediction of double-layer shells

This study proposes a model for predicting the acoustic characteristics of a double-layered composite shell in an infinite fluid domain. The analyzed structure consists of double-layered cylindrical shells, hyperbolic shells, and circular bulkheads. Based on the displacement continuity conditions between adjacent segments, their coupling relationships are derived. The kinetic energy, strain energy, and potential energy formulas for the double-layered shell are derived using energy principles, and the vibration control equations for the double-layered shell are established through Hamiltonian variation. The external acoustic fluid surrounding the composite shell is considered based on the meshless Kirchhoff-Helmholtz integral equation. By incorporating the structural-acoustic compatibility relationship in the form of fluid work, the meshless shape functions, obtained through the Tchebychev point interpolation method (TPIM) and circumferential Fourier series, are employed to approximate the structural displacements and fluid acoustic pressures, thereby establishing and solving the vibration and acoustic coupling model. The developed meshless vibration and acoustic model is validated through comparative cases related to finite element/boundary element solutions. Additionally, the influence of parameters such as geometric configuration, material properties, and loading conditions on the acoustic characteristics of the double-layered composite shell is discussed, providing guidance for lightweight and low-noise design of double-layered structures.