Abstract
The remarkable properties of shape memory alloys (SMA) are attracting significant technological interest in many fields of science and engineering. In this paper, a nonlinear dynamic analytical model is developed for a laminated beam with a shape memory alloy layer. The model is derived based on Falk’s polynomial model for SMAs combined with Timoshenko beam theory. In addition, axial velocity, axial pressure, temperature, and complex boundary conditions are also parameters that have been taken into account in the creation of the SMA dynamical equation. The nonlinear vibration characteristics of SMA laminated beams under 1:3 internal resonance are studied. The multi-scale method is used to solve the discretized modal equation system, the characteristic equation of vibration modes coupled to each other in the case of internal resonance, as well as the time-history and phase diagrams of the common resonance amplitude in the system are obtained. The effects of axial velocity and initial conditions on the nonlinear internal resonance characteristics of the system were also studied.
Highlights
Shape memory alloy (SMA) is widely used in machinery, electronics, aerospace, civil engineering, energy, and medicine
SMA particles, wires, or strips are often inserted into other matrix materials, or an SMA membrane is applied over the surface of a beam or plate matrices to form an SMA composite structure [1]
Ren et al [4,5,6] carried out a series of work on SMA composite beams which analyzed the influence of fiber laying angle and the content percentage of SMA on the equivalent damping ratio of the beam, and the vibration frequency response characteristics of the beam structure
Summary
Shape memory alloy (SMA) is widely used in machinery, electronics, aerospace, civil engineering, energy, and medicine. Asadi [14,15] built a control equation for laminated beams with SMA fibers that considered the effects of thermal and aerodynamic loads using Brinson’s polynomial constitutive model; they investigated the thermodynamic behavior of SMA laminated beams These investigations have found many interesting and complex dynamics of the laminated beam, in the meantime, nonlinear dynamics with an internal resonance have been promoted. Considering the present work aims to of axial velocity, the multi-scale method is used to solve the nonlinear vibration equation investigate the nonlinear dynamics of the axially SMA beam with internal resonances. Based on the Landau–Devonshire thermodynamics theory, Falk proposed a polynoof axial velocity, the multi-scale method is used to solve the nonlinear vibration equation mial free energy equation, Savi and Braga [27] obtained the coefficients of the free of clamped-hinged SMA laminated beam, and 1:3 internal resonances are analyzed. Verse vibration equation of the main beam can be obtained
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
