ABSTRACT
When it comes to the vibrations of the thick, irregularly shaped compressor casing (which includes the cylinders, the crank case, often the motor housing, and so on), the equations of motion for shells or plates are only useful in the most approximate sense. Rather, the compressor casing has to be viewed as a three-dimensional solid. It is, therefore, worthwhile to examine the derivation of the governing equations, even while in a practical sense, finite element approaches will most likely have to be used because of the complexity of the geometry. However, these equations (or their equivalent energy expressions) are the foundation of the finite element formulation, and we will use these equations to derive the three-dimensional acoustic wave equation by reduction. See also Ramani et al. (1994a, b).
