A two-dimensional analytical piezothermoelastic solution for a functionally graded material (FGM) hollow sphere with integrated piezoelectric layers as a sensor and actuator subjected to non-axisymmetric loads is carried out. A feedback gain control algorithm is used for the active control of stress and displacement of an FGM hollow sphere. The material properties of the FGM layer are assumed to be graded in the radial direction according to a power law function. Governing differential equations are developed in terms of the components of the displacement field, the electric potential, and the temperature of each layer of the smart FGM hollow sphere. These equations are solved analytically using the Legendre polynomials and the system of Euler differential equations. The effects of grading index of material properties and feedback gain on the mechanical-electrical responses are demonstrated in detail.
Presented in this paper is a numerical solution for torsional vibration analysis of a functionally porous nanotube under a magnetic field. The size effect in microscale can be captured using the nonlocal couple stress theory that predicts softening and hardening in micro-size. The torsional vibration of functionally porous nanotube with magnetic field based on nonlocal couple stress theory is examined. The governing equation is derived using Hamilton’s principle and the generalized differential quadrature method (GDQM) was employed to solve it. A comparison between the results of this work with the other paper reveals the accuracy of this study. The effects of some parameters such as porosity, magnetic field, and small-scale parameters were investigated. The results show that different materials have different behavior in micro-size that can be covered softening and hardening.
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