Forced harmonic response of viscoelastic structures by an asymptotic numerical method

• Published in: Computers & structures Vol. 87; no. 1; pp. 91 - 100
• Main Authors: Abdoun, F., Azrar, L., Daya, E.M., Potier-Ferry, M.
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 2009; Elsevier
• Subjects: Beam; Computational techniques; Exact sciences and technology; FEM; Fundamental areas of phenomenology (including applications); Mathematical methods in physics; Physics; Plate; Sandwich; Solid mechanics; Static elasticity (thermoelasticity...); Structural and continuum mechanics; Vibration; Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...); Viscoelastic; Sandwich; Beam; Vibration; Viscoelastic; FEM; Plate; Viscoelasticity; Path following method; Forced vibration; Sandwich structure; Harmonic analysis; Passive system; Continuation method; Modeling; Power series; Frequency effect; Predictor corrector method; Finite element method; Matrix inversion; Series expansion; Structural analysis; Analytical continuation
• ISSN: 0045-7949; 1879-2243
• DOI: 10.1016/j.compstruc.2008.08.006

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.