21 July 2004 Spectral element formulation for SMA beams under random vibration excitation
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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.
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Fabrizio L. Scarpa, Massimo Ruzzene, Mohammed Roshdi Hassan, "Spectral element formulation for SMA beams under random vibration excitation", Proc. SPIE 5387, Smart Structures and Materials 2004: Active Materials: Behavior and Mechanics, (21 July 2004); doi: 10.1117/12.545968; https://doi.org/10.1117/12.545968

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