DYNAMIC ANALYSIS OF SANDWICH TAPERED POROUS MICRO-BEAMS CONSIDERING SIZE EFFECT

Based on the modified couple stress theory, a size-dependent dynamic model of large overall rotating hub-flexible sandwich tapered Euler-Bernoulli micro-beams made from functionally graded materials with porosities is developed to study their dynamic characteristics. The functionally graded sandwich tapered micro-beams are composed of a core with inperfect functionally graded materials sandwiched between two homogeneous face sheets, which can decline the influence of the traditional sandwich structure debonding damage caused by the mismatch of stiffness properties between their core and face sheets. The high-order rigid-flexible coupled dynamic equations of the system applied to large deformation are derived by considering the von Kármán geometric nonlinear strain and adopting Lagrange's equation of the second kind. The method of assumed modes is used to describe the chordwise and axial deformations of micro-beams. The dynamic stiffening effect is captured the nonlinear coupling term obtained by longitudinal shortening caused by the transverse bending deformation of the micro-beams. Then, under the effects of different parameters, such as the width of face sheets of the tapered micro-beams, rotating angular velocity, material gradient index, size-dependency, porosities and volume fractions of each layer structure, the dynamic characteristics of functionally graded sandwich micro-beams in the plane are investigated. The functionally graded sandwich tapered micro-beams combine the characteristics of the functionally graded rectangular micro-beams and the tapered micro-beams. Compared with the functionally graded rectangular micro-beams, these characteristics make the natural frequency of the functionally graded sandwich tapered micro-beams increase and lead to different influences of porosities on the natural frequencies of the structures. Moreover, since the coupling potential energy of the chordwise and axial motions is involved in the strain energy of the flexible micro-beams, the equilibrium position of the system migrates in the steady state. It is observed that interesting frequency veering and mode shift phenomena of the system are observed when the size-dependency changes.