Abstract
The study of the bifurcation, random vibration, chaotic dynamics, and control of laminated composite beams are research hotspots. In this paper, the parametric random vibration of an axially moving laminated shape memory alloy (SMA) beam was investigated. In light of the Timoshenko beam theory and taking into consideration axial motion effects and axial forces, a random dynamic equation of laminated SMA beams was deduced. The Falk’s polynomial constitutive model of SMA was used to simulate the nonlinear random dynamic behavior of the laminated beam. Additionally, the numerical of the probability density function and power spectral density curves was obtained through the Monte Carlo simulation. The results indicated that the large amplitude vibration character of the beam can be caused by random perturbation on axial velocity.
Highlights
Moving structures are widely found in aerospace, civil engineering, machinery, and transportation industries
For an shape memory alloy (SMA)-laminated beam with a complex structure and complicated stress conditions, it is sometimes difficult to obtain the dynamic equation of the system by using other constitutive models, and the nonlinear dynamics characteristics of the system can be obtained and analyzed by using this constitutive model
Equation (4) is solved, and the system steady-state probability density function is simulated using the Monte Carlo algorithm, which is a method that uses random numbers to solve many computational problems based on probability and statistical theory methods
Summary
Moving structures are widely found in aerospace, civil engineering, machinery, and transportation industries. Burak et al [8] used a method of multiple time scales (a perturbation method) to examine the nonlinear vibration and stability of axially moving beams with variable velocity and axial force values. Given the possibility of complex nonlinear dynamics in the system, such as sharp vibration, the resonance of parametric vibration with forced vibration, bifurcation, and chaos, in response to axial velocity and external excitation, studying the transverse vibration mechanism of axially moving beams is both theoretically and practically useful for optimizing engineering system components. By considering the effects of shear modulus and moment of inertia, Li et al [25] used the multiple time scale method to examine the steady-state response of an axially moving viscoelastic Timoshenko beam to forced transverse nonlinear vibration. The effects of random perturbation intensity and axial velocity on steady-state response are analyzed
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