LAUSR

Abstract The free linear vibration of an adaptive sandwich beam consisting of a frequency and field-dependent magnetorheological fluid core and an axially functionally graded constraining layer is investigated. The Euler-Bernoulli and Timoshenko beam theories are utilized for defining the longitudinal and lateral deformation of the sandwich beam. The Rayleigh-Ritz method is used to derive the frequency-dependent eigenvalue problem through the kinetic and strain energy expressions of the sandwich beam. In order to deal with the frequency dependency of the core, the approached complex eigenmodes method is implemented. The validity of the formulation and solution method is confirmed through comparison with the results available in the literature. Finally, the effects of the magnetic field, axially functionally graded material power-law index, constraining, and core layers thickness on the free vibration behavior of the sandwich beam are studied thoroughly for clamped–clamped, simply supported, and clamped-free boundary conditions. It is shown that any change in each of these parameters would have significant effects on the beam's free vibration properties.