Padmanabhan C., Saisankaranarayana K.

In this paper a Component Mode Synthesis (CMS) method is developed for finding the natural frequencies of large acoustic cavities with high modal density.The cavity under consideration is a periodic structure. Since conventional FE techniques require large number of elements due to the high modal density, two new formulations using Chebyshev polynomial and trigonometric shape functions are proposed. These result in significantly smaller number of elements.The large acoustic cavity is divided into periodic subcavities. The physical pressures of the subcavities are transformed into a reduced set of generalized coordinates through a matrix of component modes. The subcavity equations of motion in terms of the reduced generalized coordinates are coupled to obtain the global equations of motion of the combined system. This is done by using binary indexing for reducing the number of coupling terms and enforcing the compatibility and equilibrium conditions along the component interface. The solution of the eigenvalue problem of reduced order is obtained to get the approximate eigenvalues of the complete cavity. The accuracy and computational efficiency is clearly demonstrated using a railway coach acoustic model. This model is divided into subcavities; each subcavity has been analyzed using finite element method and they are coupled using normal modes and constrained modes of subcavities. Characteristic constrained modes (CC modes) are used for reducing the large number of constraint modes.