Derivation of a Ritz series modeling technique for acoustic cavity-structural systems based on a constrained...

Area of Science:

• Acoustics
• Solid Mechanics
• Mathematical Physics

Background:

• Coupled acoustic-structure interaction is crucial in many engineering applications.
• Modeling these systems often involves complex boundary conditions and fluid-structure interfaces.
• Hamilton's principle offers a powerful variational framework for dynamic system analysis.

Purpose of the Study:

• To adapt Hamilton's principle for analyzing the coupled response of confined acoustic domains and elastic structures.
• To develop a method that rigorously enforces fluid-solid interface continuity conditions.
• To provide a systematic approach for deriving governing equations for acoustic-structure systems.

Main Methods:

• Hamilton's principle is modified to include surface traction as a Lagrange multiplier.
• Ritz series expansions are used to represent structural displacement, fluid velocity potential, and traction.
• The velocity potential is chosen as the fluid's state variable to ensure irrotational flow.
• Calculus of variations is applied to derive linear differential-algebraic equations.

Main Results:

• The adapted Hamilton's principle yields equations identical in form to those for nonholonomic constrained mechanical systems.
• The method ensures continuity conditions at the fluid-solid interface through Lagrange multipliers.
• Series representations of fluid properties (velocity, displacement, pressure) are derived from the velocity potential.
• The approach facilitates the description of mechanical energies and virtual work.

Conclusions:

• The adapted Hamilton's principle provides a unified and rigorous framework for modeling coupled acoustic-structure dynamics.
• The use of Lagrange multipliers and Ritz series offers a flexible and systematic approach.
• The derived differential-algebraic equations are suitable for analyzing complex boundary value problems in acoustics and structural mechanics.