Continuous nonlinear eigenvalue solver with applications to the design of electro/magnetorheological sandwich structures

Abstract

Smart sandwich structures comprising an electro- or a magnetorheological material have the potential to attenuate vibration over a wide range of frequencies. The analysis of their vibration behaviour with respect to the continuous variation of the field intensity is thus a major challenge for research and industry to maximize damping treatments. The numerical higher order homotopy method we propose models the effects of a continuous variation of the field intensity on resonant frequencies and loss factors by means of Taylor expansions. Comparisons between our continuous approach and the classical incremental method are proposed for state of the art sandwich beams and plate structures comprising ER/MR fluids to highlight the benefits of our continuous methods in terms of maximal damping determination.