Vibration analysis of a beam with embedded shape memory alloy wires

In this study, analytical relations for evaluating the exact solution of natural frequency and mode shape of beams with embedded shape memory alloy (SMA) wires are presented. Beams are modeled according to Euler-Bernoulli, Timoshenko and third order beam (Reddy) theories. A relation is obtained for determining the effect of axial load generated by the recovery action of pre-strained SMA wires. By defining some dimensionless quantities, the effect of different mechanical properties on the frequencies and mode shapes of the system are carefully examined. The effect of axial load generated by SMA wires with buckling load and frequency jump is accurately studied.