Computation of the homogeneous and forced solutions of a finite length, line-driven, submerged plate

Abstract

A formulation is developed to predict the vibration response of a finite length, submerged plate due to a line drive. The formulation starts by describing the fluid in terms of elliptic cylinder coordinates, which allows the fluid loading term to be expressed in terms of Mathieu functions. By moving the fluid loading term to the right-hand side of the equation, it is considered to be a force. The operator that remains on the left-hand side is the same as that of the in vacuo plate: a fourth-order, constant coefficient, ordinary differential equation. Therefore, the problem appears to be an inhomogeneous ordinary differential equation. The solution that results has the same form as that of the in vacuo plate: the sum of a forced solution, and four homogeneous solutions, each of which is multiplied by an arbitrary constant. These constants are then chosen to satisfy the structural boundary conditions on the two ends of the plate. Results for the finite plate are compared to the infinite plate in both the wave number and spatial domains. The theoretical predictions of the plate velocity response are also compared to results from finite element analysis and show reasonable agreement over a large frequency range.

Parametric Study of Periodic Structures

“…That research showed that the tuning capabilities of simple RL shunt circuits were combined with the filtering characteristics of periodic structures to obtain a tunable periodic plate, and the resulting smart structure experienced significant reductions in its noise radiation capability. Numerical simulations demonstrated the applicability of Bloch theorem [5] for unit-cell analysis on the in vacuo plate [6] as a tool to predict the frequency ranges of effective structural acoustic control. Also, experiments were performed to validate the numerical predictions, and demonstrate the effectiveness of the proposed strategy.…”

Experimental and Numerical Investigation of the Capabilities of Periodic Plates for Vibration Attenuation

“…That research showed that the tuning capabilities of simple RL shunt circuits were combined with filtering characteristics of periodic structures to obtain a tunable periodic plate, and the resultant smart structure experienced significant reductions in its noise radiation capability. Numerical simulations demonstrated the applicability of Bloch theorem [5] for unit-cell analysis on the in vacuo plate [6] as a tool to predict the frequency ranges of effective structural acoustic control. Also, experiments were performed to validate the numerical predictions, and to demonstrate the effectiveness of the proposed strategy.…”