Lumped mass acoustic and membrane eigenanalysis using the global collocation method

Abstract

The paper proposes a direct way to build lumped masses for performing eigenvalue analysis using the global collocation method in conjunction with tensor product Lagrange polynomials. Although the computational mesh is structured, it has a non-uniform density, in such a way that the internal nodes are located at the position of Gaussian points or the images of the roots of Chebyshev polynomials of second kind. As a result, the mass matrix degenerates to the identity matrix. In this particular nodal collocation procedure, no complex eigenvalue appears. The theory is successfully applied to rectangular and circular acoustic cavities and membranes.

Keywords

• global collocation
• CAD/CAE integration
• acoustics
• membranes