TRANSVERSE FREE VIBRATIONS OF A COMPOSITE BEAM WITH EMBEDDED SMA WIRES SUBJECTED TO THERMAL

Based on Brinson's one-dimensional thermomechanical constitutive equations of shape memory alloys(SMA)and micro-mechanical law of composites, the one-dimensional thermomechanical constitutive relations of composite beams with embedded shape memory alloy wires subjected to thermal load are established. Using the geometrically nonlinear theory of axially extensible Euler-Bernoulli beams, the general dynamic governing equations for free vibration of composite beams with embedded shape memory alloy wires subjected to a uniform temperature rise are set up. Small amplitude free vibration model near the thermal post-buckling configuration is presented. The vibration responses of a clamped-clamped composite beam with embedded SMA wires in heating process are studied by shooting method and the characteristic curves of the first to fourth-order frequencies versus temperature rise of the beam with different relative volume fraction of SMA wires are obtained. Numerical results show that the recovery stress and the variation of modulus of elasticity have influence on the natural frequencies of the beam, which is an effective way to realize active control of the natural frequencies of the beam.