Power transmission in L-shaped plates including flexural and in-plane vibration

Abstract

In this paper, power flow propagation in plates connected in an L-joint is investigated in both the low and high frequency ranges. An exact solution is derived to describe the flexural, in-plane longitudinal and in-plane shear wave motion in the plates. The coupled plates are simply supported along two parallel sides, and free at the other two ends. A point force is used to generate flexural wave motion only. The flexural wave coefficients are determined from the boundary conditions, continuity equations at the driving force locations, and continuity equations at the corner junction of the plates. Structural intensity expressions are used to examine the structural noise transmission in the low and high frequency ranges. The contributions from the individual wave types are also examined.

Wave motion analysis of finite coupled plates with Reverberation Ray Matrix Method

“…Where u is the longitudinal displacement, v is the y-direction, w is the lateral displacement, The following relationship should be satisfied by force and displacement [4]. N is the out-plane shear force, the in-plane axial force, the in-plane shear force, separately.…”

“…Cuschieri J M, et al [2] employed power flow to research the L-shaped plate, when the flexural wave number multiplied by the thickness was less than 0.1, the in-plane wave plate could be ignored. Wave power flow and flexural wave power flow of finite L-shaped plate were researched by Kessissoglou, et al [3][4]. Wave method results show that in-plane wave of L-shaped plate can be converted into out-plane wave through the connected line.…”

Finite-difference time-domain analysis of structure-borne sound using a plate model

“…The continuity equations described above, and the finite-difference equations obtained as the discrete forms of Eqs. (1), (2), and (3), are solved together as simultaneous equations with sparse matrices. This equations are solved in every time step, and the time development of vibration propagation is calculated.…”

“…In order to cope with such a problem, the development of an efficient calculation method, which has less memory requirement and is able to perform faster calculation, is necessary. For this reason, vibration analysis methods applying the 2-dimensional plate model have been proposed [2,3]. In such research, the computational costs of memory and calculation time are aimed to be reduced by decreasing the discrete meshes to 2 dimensions.…”

“…In order to predict such transmission characteristics of vibration, prediction methods using wavebased numerical analysis have been proposed [1][2][3]. Toyoda and Takahashi [1] proposed 3-dimensional elastic wave analysis for structure-borne sound by the finite-difference time-domain (FDTD) method.…”