A semi-analytical method using auxiliary sine series for vibration and sound radiation of a rectangular plate with elastic edges

TL;DR

This paper introduces a semi-analytical sine series method for efficiently analyzing the vibration and sound radiation of elastically restrained rectangular plates, validated by experiments and simulations.

Contribution

It presents a novel semi-analytical approach using auxiliary sine series for vibration and sound radiation analysis of plates with elastic edges, applicable under various excitations and boundary conditions.

Findings

Accurate prediction of vibration modes and frequencies.

Efficient computation of sound radiation and transmission loss.

Validated results with experimental and simulation data.

Abstract

This paper proposes an efficient semi-analytical method using auxiliary sine series for transverse vibration and sound radiation of a thin rectangular plate with edges elastically restrained against translation and rotation. The formulation, constructed by two-dimensional sine and/or cosine series, can approximately express the bending displacement, and calculate vibration and sound radiation under excitation of point force, arbitrary-angle plane wave, or diffuse acoustic field with acceptable accuracy. It is also applied for baffled or unbaffled conditions. A post-process program is developed to predict vibrating frequencies and modes, mean square velocity spectrum, and sound transmission loss via reduced-order integrals of radiation impedances. The method is validated by experiment and simulation results, demonstrating accurate and efficient computation using a single program for transverse vibration and sound radiation of a plate under different elastic boundary conditions and different excitations. Formulas given in this paper provide a basis for the code development on transverse vibration and sound radiation analysis of thin plates.