Implementation of a constrained Ritz series modeling technique for acoustic cavity-structural systems

A prior study [Ginsberg, J. H. (2010b). J. Acoust. Soc. Am. 127, 2749-2758] used Ritz series in conjunction with Hamilton's principle to derive general equations describing the time domain response of an acoustic cavity bounded by an elastic structure. The equations of motion are supplemented by constraint equations that explicitly enforce velocity continuity at the cavity's surface. These constraints are imposed by the surface traction, which is represented by unknown coefficients of Ritz-type series. The resulting set of equations are differential-algebraic type. Three methods are presented to convert the governing equations to forms that are familiar to structural acoustics, including one that transforms them from differential-algebraic type to the standard ordinary differential equations associated with linear multi-degree-of-freedom vibratory systems. In cases where only the structure is excited, the formulation offers options as to how displacement/velocity boundary conditions on the nonstructural boundary are enforced, as well as whether zero pressure boundary conditions are enforced at all. An example of a one-dimensional waveguide that is closed at one end by an oscillator is used to explore the quality of solutions obtained from each of these options. Results for natural frequencies and mode functions are examined for accuracy and convergence.