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Nonlinear dynamic response dissipation of plates with heterogeneous orthotropic distributions of shape memory alloy micro-wires undergoing 3D phase-transformations

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Abstract

The common 1D transformation models of shape memory alloy (SMA) wires hosted in rectangular plates cannot accurately model the actual 3D stress field, 3D complete/incomplete direct and converse transformations, and the dissipative nature of the SMA wires. Present research resolves these serious problems by utilizing a 3D Lagoudas transformation/pseudoelasticity model that is extended by incorporating a more general bridging-based micromechanical model that includes the host matrix and orthotropy. The SMA micro-wires are assumed to constitute a nonuniform transverse distribution and be oriented parallel to one of the edges of the plate. In contrast to the spherical inclusions, the micro-wires induce not only heterogeneity but also orthotropy. The 3rd-order shear deformation plate theory, principle of minimum potential energy, and a highly accurate 80-degrees-of-freedom element are employed to derive the governing equations of the dynamic responses of the FG-SMA plate. A novel comprehensive solution/transformation algorithm is proposed to track the time variations of the lateral deflection, martensite volume fraction, and hysteresis loops of the dynamic stress–strain curve. The results elucidate that for a fixed weight, the X-FG transverse distribution of the SMA phase leads to the most notable vibration dissipations in comparison with the K-FG, V-FG, and uniform distributions when the plate is thick and the bending is the dominant deformation mode (movable supports). However, the K-FG pattern may be recommended for the thinner FG-SMA plates. Moreover, the common asymmetric V-FG pattern may lead to the worst performances even in comparison with the uniform distribution of the SMA phase.

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  1. Faculty of Mechanical Engineering, K.N. Toosi University of Technology, 19991-43344, Tehran, Iran

    M. Shariyat

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  1. M. Shariyat
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Shariyat, M. Nonlinear dynamic response dissipation of plates with heterogeneous orthotropic distributions of shape memory alloy micro-wires undergoing 3D phase-transformations. J Braz. Soc. Mech. Sci. Eng. 44, 174 (2022). https://doi.org/10.1007/s40430-022-03472-4

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  • DOI: https://doi.org/10.1007/s40430-022-03472-4

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