Abstract
This work presents an asymptotic numerical method for forced harmonic vibration analyses of viscoelastic structures. A mathematical formulation that may account for various viscoelastic models is presented. Power series expansions and Padé approximants of the displacement and frequency are developed and the finite element method is used for numerical solution. Only some matrix inversions and a few iterations are needed for large frequency ranges. Iterations of the process lead to a powerful continuation method for harmonic responses of viscoelastic structures with constant and frequency dependent coefficients. For numerical tests, undamped, viscoelastic and sandwich viscoelastic beams and plates are considered. Passive control, response curves and equivalent damping characteristics are obtained for various frequency ranges, excitation amplitudes and viscoelastic models.