Alireza Asnafi

Thermomechanical instability in pseudo-elastic cantilever energy harvesters driven by non-Gaussian stochastic excitations was investigated in this paper. It was shown that the interplay of nonlinear restoring forces and SMA hysteresis yields rich dynamic behavior that markedly affects stable zones and energy output. Although nonlinearities can enhance harvesting efficiency, they may also induce chaos under certain thermomechanical and stochastic conditions. Despite extensive numerical studies, a fully analytical, nondimensional framework for combined thermomechanical and stochastic forcing in SMA-based cantilevers is lacking. Here, using the modified Melnikov’s function for stochastic systems, we develop such a framework and derive stability boundaries as functions of ambient temperature variation and noise bandwidth. Our results illuminate how operating near edited parameter regimes can maximize energy conversion while maintaining robust performance, and provide design guidelines for MEMS energy harvesters subject to realistic, broadband excitations. The analytical predictions are corroborated with some Poincaré mapping of selected results.

In this study, the instability borders of a two-dimensional simply supported laminated plate made from a magnetic shape memory alloy (MSMA), functioning as a vibration harvester under non-Gaussian in-plane bounded noises, were obtained using an analytical approach. The nonlinear governing equation of vibration was derived by considering large deformations, randomness, magnetostriction effects, super elasticity, and broadband excitation. By introducing dimensionless parameters, we aimed to achieve general, case-independent results. The modified version of Melnikov’s function for random systems was first derived and then used to obtain fully analytic results for the instability zones of the response. These boundaries were plotted based on noise properties (amplitude, frequency, and bandwidth) along with variations in magnetic field intensity (MFI) and plate aspect ratio. We believe that the findings and results of this article can help identify suitable operating zones for a broad spectrum of these types of vibration energy harvesters.

The main aim of this article is to obtain the probability density function of the response of an SMA beam under lateral white-noise excitation and study the bifurcation phenomenon through a fully analytic approach. Firstly, an efficient constitutive stress–strain relation for a shape memory alloy material supporting both martensite and austenite phases is considered. Secondly, the governing equation of motion for a typical SMA simply supported beam is derived using some dimensionless parameters. Thirdly, the corresponding probability density function of the response is computed analytically using the powerful Fokker–Planck–Kolmogorov equation, and finally, the bifurcation phenomenon for parameter variations of the beam is investigated. The results show how geometric (beam aspect ratio), force (the mean value of the white-noise excitation), and environmental (working temperature) factors can affect the nonlinear behavior and response bifurcation of the beam. A numerical validation is also done that guarantees the correctness of the method and results.

ABTRACT In this article, the dynamic stability and chaotic behavior of a shape memory alloy (SMA) beam with large deformation under simultaneous lateral and axial excitations is investigated through a fully analytic approach. First, the nonlinear governing equation of motion is derived. Second, Melnikov’s method, as an analytic approach, is employed to obtain the chaos zones. After that, by introducing non-dimensional parameters, border curves of chaotic areas were evaluated and plotted for some case studies which give a reader a precise and clear look at how the material and load properties can affect the chaos zones. Finally, the sufficient condition is approved via corresponding poincaré maps.

In this study, the chaotic behavior of a viscoelastic plate under integrated non-Gaussian additive and multiplicative bounded noise is investigated with an analytical approach. First, the governing equation of motion of the system was derived by introducing a set of dimensionless parameters. After that, the modified version of Melinkov’s function in terms of statistical indices was obtained, and then, for a spectrum of bounded noises, the boarder curves of chaotic areas were obtained. The model of sine/cosine Wiener was chosen for the bounded noise which enables the researcher to produce a range of wide and narrowband noises. For the case that the excitation is only additive, or only multiplicative, and that both excitations exist simultaneously, the effect of variations in structural properties and noise characteristics on the chaos area were investigated. It was shown that at frequencies close to the natural frequency of the corresponding linear system, narrowband excitations affected the chaotic behavior more than the wideband ones and vice versa. To validate the results, a numerical simulation was also made.