Acoustic radiation response of functionally graded sandwich plates cored by butterfly-shaped honeycombs with negative Poisson’s ratio

Compared to the conventional cellular cores, the cellular cores auxetic metamaterials with negative Poisson’s ratios have unique mechanical deformation characteristics, superior strength to density ratio and high stiffness, both of which can be used to build lightweight sandwich constructions. The purpose of this study is to investigate the vibration acoustic response of porous functionally graded honeycomb sandwich plates with a negative Poisson’s ratio (NPR). Under simply supported boundary conditions, the dynamic equation of the sandwich plate is derived based on the Hamilton principle, and the eigenvalue of the modal function matrix is coupled with the Navier method to obtain the natural frequency. The theoretical calculation results are compared with the finite element software COMSOL simulation results, so as to verify the validity and correctness of the theoretical model proposed in this paper. The far-field radiation sound pressure level of sandwich plate under point force loading is derived by Rayleigh integral theory. The correctness of the proposed model is verified by comparing the radiation sound pressure level calculated by the theoretical model with the results obtained by the finite element software simulation. The effects of porous functionally graded materials (FGM) and cellular structure parameters on the acoustic radiation characteristics of sandwich plates are discussed in detail. The results show that: The relative error between the theoretical results and the literature results is 5.43 %. Under the same conditions, the amplitude of the radiation sound pressure level (SPL) decreases by about 29.48 % in the low frequency stage, 28.9 % in the medium frequency stage and 11.08 % in the high frequency stage under the point excitation when the cellular side length is 6 mm compared with 8 mm in the low frequency stage. The movement trend and amplitude of the sandwich plate’s emitted SPL are significantly impacted by changes in the characteristics of the cellular structure.