A highly accurate spectral dynamic stiffness method for efficient broadband modal and dynamic response analysis of membranes assemblies with arbitrary boundary conditions

•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.