Slenderness effects in the free vibration of laminated magnetoelectroelastic beams

A semi-analytical discrete-layer approach is used to evaluate slenderness effects in the free vibration of laminated magnetoelectroelastic beams under various boundary conditions. Piecewise continuous approximations are used through the thickness direction of the beam and either continuous polynomial or trigonometric functions are used in the axial direction. Conventional beam models, including those of Euler–Bernoulli and Timoshenko, can be recovered to predict frequency estimates and are compared with results of the present model. Numerical examples are used to show the effects of beam slenderness on frequency and modal order for beams under simply-supported, fixed–fixed, and cantilever conditions. The results of these analyses clearly illustrate the thickness effects for axial, torsional, and bending modes and also provide some results useful for comparison for theses laminated beams. (paper)