Derivation of a Ritz series modeling technique for acoustic cavity-structural systems based on a constrained Hamilton’s principle

Abstract

Hamilton's principle for dynamic systems is adapted to describe the coupled response of a confined acoustic domain and an elastic structure that forms part or all of the boundary. A key part of the modified principle is the treatment of the surface traction as a Lagrange multiplier function that enforces continuity conditions at the fluid-solid interface. The structural displacement, fluid velocity potential, and traction are represented by Ritz series, where the usage of the velocity potential as the state variable for the fluid assures that the flow is irrotational. Designation of the coefficients of the potential function series as generalized velocities leads to corresponding series representations of the particle velocity, displacement, and pressure in the fluid, which in turn leads to descriptions of the mechanical energies and virtual work. Application of the calculus of variations to Hamilton's principle yields linear differential-algebraic equations whose form is identical to those governing mechanical systems that are subject to nonholonomic kinematic constraints. Criteria for selection of basis functions for the various Ritz series are illustrated with an example of a rectangular cavity bounded on one side by an elastic plate and conditions that change discontinuously on other sides.