A highly accurate spectral dynamic stiffness method for efficient broadband modal and dynamic response analysis of membranes assemblies with arbitrary boundary conditions. (15th July 2022) - Liu, Xiang; Zhao, Xueyi; Liu, Xiao
Highlights: Spectral dynamic stiffness (SDS) is developed for damped membranes with general BCs. General BCs are described by modified Fourier series with rapid convergence rate. Analytical expression of J0 count in the Wittrick-Williams algorithm is derived. SDS matrices can be assembled to model complex geometries subject to arbitrary BCs. It is demonstrated to be highly efficient/accurate within whole frequency ranges. Abstract: A highly accurate and efficient spectral dynamic stiffness (SDS) formulation is presented for the broadband dynamic analysis of damped membranes and their assemblies with arbitrary boundary conditions (BCs). First, the general solution satisfying exactly the governing differential equations is derived, and any general BCs are represented by the modified Fourier series (MFS). Second, the modified Fourier coefficients of the force BCs are associated with those of the displacement BCs by eliminating the coefficients in the general solution, where the SDS matrix is formulated. The SDS elements can be assembled through line nodes to model complex geometries and arbitrary BCs can be described. Finally, highly reliable and efficient eigenvalue and dynamic response solution techniques are employed. The performance of the proposed method is illustrated by convergence and efficiency studies. Modal analysis and damped dynamic response analysis are performed for either individual membranes or complex membrane assemblies subjected to general BCs. This method is demonstrated to be more versatile than the classical dynamic stiffness method, and yields highly accurate results with reasonable computational efficiency by comparison with the FEM. Due to these excellent features, this method can serve as a powerful alternative tool for the fluid–structure interaction and broadband vibro-acoustic problems.