Spectral element formulation for SMA beams under random vibration excitation

A complex modulus approach typical of viscoelastic materials is used to linearize the equation of motions of a combined beam-rod SMA pseudoelastic element and use a Spectral Finite Element formulation to study the dynamic behavior in the frequency domain. The complex modulus approach allows using viscoelastic SFE formulations presented in literature and adapt them to Ni-Ti alloy elements with different tensile pre-strain levels. The dispersion relations of Love rod and Euler-Bernoulli beams are discussed in view of the use of the experimental available complex modulus curves of the materials. As a demonstration of the use of the SFE technique, a cantilever beam loaded with a tip force is then modeled with a single Spectral Element, with increased accuracy of lower number of linear FE elements per unit wavelength.