Effect of general coupling conditions on the vibration and power flow characteristics of a two-plate built-up plate structure

Abstract

This paper presents the modeling approach, dynamic response analysis and the effect of coupling junction properties on the vibration characteristics of two plates elastically coupled in the form a T shaped structure with elastic boundary conditions. These built-up plate structures are the most commonly used configurations in the design of engineering platforms both floating and stationary. The coupling junction has been represented as a combination of translational and rotational spring stiffness’s, thus making the junction state general in nature. The analysis has been carried out using a Fourier cosine series representation for the bending and in-plane plate displacements modified with inclusion of derived auxiliary function. The derived auxiliary functions are also presented in form of the product of a single Fourier cosine series expansion and one polynomial function. The Rayleigh-Ritz method is employed to the Lagrangian function to derive the natural frequency and dynamic response matrix. Both the free vibration and power transmission characteristics of the plate structure has been numerically presented. Validation of the modified Fourier function has been presented for an L shaped plate structure in comparison with existing literature results for free vibration analysis. Finally, the effect of variation of the coupling junction condition on the vibration and power flow characteristics of the T-plate structure has been presented. The modified Fourier function has proved to generate simple theoretical formulations and accurate results in numerical analysis of a T plate coupled configuration. The modified Fourier series function can be universally and efficiently extended to undertake vibration analysis of any type of coupled plate system with any configuration of boundary or coupling configurations. Communicated by J. Logo