Non-Linear Forced Vibration of a Pseudoelastic SMA Hybrid Composite Beam

Abstract — One of the most encountered dynamic problems in structures is the undesirable vibrations. By virtue of hysteresis-induced damping effect and variation of Young’s modulus, shape memory alloys are good viable candidate to overcome this problem. In this regard non linear forced vibration of a continuous SMA-embedded composite beam is performed by a proposed procedure, taking into account the phase transformation and also material nonlinearity effects, for the first time. Due to the phase transformation, the equations of motion are coupled with phase transformation’s kinetic equations of the SMA wires. The one-dimensional Brinson’s constitutive equation of SMA is employed to model the pseudoelastic behavior of the SMA wires. The equations of motion are derived using Hamilton’s principle. Transient finite element along with Newmark time integration method are employed to solve the resulted dynamic equation. In this paper, influence of the SMA wires on the vibration suppression of a composite beam as well as the temperature effects on the hysteresis behavior at the pseudoelastic conditions are investigated. Index Terms—vibration resonance, smart materials, shape memory alloys, dissipation energy, material nonlinearity I