The Modal Formulation and Adaptive-Passive Control of the Nonself-Adjoint One-Dimensional Acoustic System With a Mass-Spring Termination

Abstract

This paper investigates the use of mass-spring type of impedances as absorbing elements for interior noise control. The general modal formulation for a one-dimensional acoustic system terminated by a spring-supported piston is presented. The boundary value problem has a nonself-adjoint operator which renders the mode functions unorthogonal. This is overcome by defining an associated self-adjoint operator in Hilbert space and using an operator-theoretic formulation of the problem. Orthogonal mode functions and an expansion theorem are presented which can be used to construct a series solution for the forced response. A numerical study is performed for the case of single frequency excitation in which the impedance parameters are optimized by minimizing the cost function. The results from the numerical simulations indicate the feasibility of interior noise control using tunable mechanical impedances, and provide guidelines and restrictions in designing such a system.