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The nonlocal nonlinear vibration analysis of embedded laminated microplates resting on an elastic matrix as an orthotropic Pasternak medium is investigated. The small size effects of micro/nano-plate are considered based on the Eringen nonlocal theory. Based on the orthotropic Mindlin plate theory along with the von Kármán geometric nonlinearity and Hamilton's principle, the governing equations are derived. The differential quadrature method (DQM) is applied for obtaining the nonlinear frequency of system. The effects of different parameters such as nonlocal parameters, elastic media, aspect ratios, and boundary conditions are considered on the nonlinear vibration of the micro-plate. Results show that considering elastic medium increases the nonlinear frequency of system. Furthermore, the effect of boundary conditions becomes lower at higher nonlocal parameters.

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In the present work, nonlinear vibration analysis of polymeric nanocomposite microplates integrated with polyvinylidene fluoride (PVDF) layers as sensors and actuators is investigated. The middle layer is reinforced with carbon nanotubes (CNTs) and it's equivalent material properties are obtained by Mori–Tanaka approach. The nanocomposite and PVDF layers are subjected, respectively, to 2D magnetic and 3D electric fields. The system is rested on an elastic medium which is simulated with orthotropic Pasternak foundation. Based on the quasi‐3D sinusoidal shear deformation plate theory (SSDPT), the motion equations are derived considering surface effects using Gurtin–Murdoch theory. A partial‐differential (PD) controller is applied for the active control of the frequency through a closed‐loop control with bonded distributed PVDF sensors and actuators. Differential quadrature method (DQM) is applied in order to obtain the nonlinear frequency of microstructure. The detailed parametric study is conducted, focusing on the combined effects of the nonlocal parameter, magnetic field, surface stress, elastic medium, volume percent of CNTs, applied voltage, controller, and boundary conditions on the vibration behavior of microstructure. Results depict that applying the controller, the frequency significantly decreases. This investigation may be important for the design and smart control of microdevices. POLYM. COMPOS., 39:1936–1949, 2018. © 2016 Society of Plastics Engineers

This article evaluates the wave velocity of a leptadenia pyrotechnica rheological elastomer (LPRE) microbeam surrounded by micro piezoelectric and porosity of functionally graded materials' (FGMs) layers. Different models of graphene nano plates (GPLs) for reinforcing the face sheet are assumed by adopting Halpin–Tsai modified micromechanics theory to obtain the Poisson's ratio and Young modulus of the smart layer. The material properties of the whole system as a viscoelastic state are hypothesized using the Kelvin–Voigt theory. The motion final equations are gained by utilizing the theory of Timoshenko and the couple stress model. An analytical solution method is adopted for computing the velocity of wave, cutoff frequency, and escape frequency from the motion final equations. The influences of different distribution and volume percent of GPLs, FGM properties as well as gradient index, the numeral parameter of any layer, damping of structure, and exerted voltage on the velocity of wave microbeam are studied. Moreover, it has been seen that a rise in the FGM index leads to reduced phase velocity, cutoff, and escape frequencies. Meanwhile, enhancing the volume percent of GPLs increases the wave velocity of the microstructure beam.