Dynamic response of cantilever beam made of shape memory alloy by differential quadrature method ..

Yousefzadeh, Shahrouz; Nasrollah Barati,, Amir Hossein; Doustdar,, Mohammad Mehdi

Dynamic response of cantilever beam made of shape memory alloy by differential quadrature method ..

Document Type : Dynamics, Vibrations, and Control

Authors

¹ Assistant Professor.Department of Mechanical Engineering, Aligudarz Branch, Islamic Azad University, Aligudarz,. Iran

² Assistant Professor, Department of Mechanics, Aligudarz Branch, Islamic Azad University, Aligudarz, Iran

³ Professor, Technical and Engineering Faculty, Imam Hossein University, Tehran, Iran

Abstract

In this research, the forced vibration of a cantilever beam made of shape memory alloy in contact with fluid was investigated. The governing equations are derived based on the first-order shear theory and Hamilton's principle, and the Boyd-Lagodas three-dimensional model was used to model the behavior of superelastic material. The pressure applied from the fluid to the beam was obtained by solving Laplace's equation and satisfying its boundary conditions. Also, in the state without phase change (pure Austenite), the investigated cantilever beam was analyzed in linear conditions and compared with the results of other researchers. In the following, to analyze the vibrations of the cantilever beam made of shape memory alloy and to solve the equations in the state where the phase transformation was performed, the method of square differences, Newmark, and the return mapping algorithm were used. At the end, the effect of different geometric parameters on the beam is studied. The results show that the numerical method used to analyze the time and frequency response of the shape memory alloy beam has high convergence and predicts well the nonlinear effects of the material due to phase transformation during motion.

Graphical Abstract