In this article, the free vibration analysis of magneto-electro-elastic (MEE) Timoshenko micro beam model based on surface stress effect and modified strain gradient theory (MSGT) under moving nano-particle is presented. The governing equations of motion using Hamilton’s principle are derived and these equations are solved using differential quadrature method (DQM). The effects of dimensionless electric potential, dimensionless magnetic parameter, material length scale parameter, external electric voltage, external magnetic parameter, slenderness ratio, temperature change, surface stress effect, two parameters of elastic foundation on the dimensionless natural frequency are investigated. It is shown that the effect of electric potential and magnetic parameter simultaneously increases the dimensionless natural frequency. On the other hands, with considering two parameters, the stiffness of MEE Timoshenko micro beam model increases. It can be seen that the dimensionless natural frequency of micro structure increases by MSGT more than modified couple stress theory (MCST) and classical theory (CT). It is found that by increasing the mass of nano-particle, the dimensionless natural frequency of system decreases. The results of this study can be employed to design and manufacture micro-devices to prevent resonance phenomenon or as a sensor to control the dynamic stability of micro structures. Manuscript profile

In this article, the nonlocal biaxial buckling load and bending analysis of polymeric piezoelectric nanoplate reinforced by carbon nanotube (CNT) considering the surface stress effect is presented. This plate is subjected to electro-magneto-mechanical loadings. Eshelby-Mori-Tanaka approach is used for defining the piezoelectric nanoplate material properties. Navier’s type solution is employed to obtain the critical buckling load of polymeric piezoelectric nanoplate for classical plate theory (CPT) and first order shear deformation theory (FSDT). The influences of various parameters on the biaxial nonlocal critical buckling load with respect to the local critical buckling load ratio () of nanoplate are examined. Surface stress effects on the surface biaxial critical buckling load to the non-surface biaxial critical buckling load ratio () can not be neglected. Moreover, the effect of residual surface stress constant on is higher than the other surface stress parameters on it. increases by applying the external voltage and magnetic fields. The nonlocal deflection to local deflection of piezoelectric nanocomposite plate ratio () decreases with an increase in the nonlocal parameter for both theories. And for FSDT, decreases with an increase in residual stress constant and vice versa for CPT. Manuscript profile

In this article, the effect of size-dependent on the buckling and vibration analysis of functionally graded (FG) double-layer boron nitride plate based on classical plate theory (CPT) under electro-thermo-mechanical loadings which is surrounded by elastic foundation is examined. This subject is developed using modified couple stress theory. Using Hamilton's principle, the governing equations of motion are obtained by applying a modified couple stress and von Karman nonlinear strain for piezoelectric material and Kirchhoff plate. These equations are coupled for the FG double-layer plate using Pasternak foundation and solved using Navier’s type solution. Then, the dimensionless natural frequencies and critical buckling load for simply supported boundary condition are obtained. Also, the effects of material length scale parameter, elastic foundation coefficients and power law index on the dimensionless natural frequency and critical buckling load are investigated. The results demonstrate that the dimensionless natural frequency of the piezoelectric plate increases steadily by growing the power law index. ‌‌Also, the effect of the power law index on the dimensionless critical buckling load of double layer boron nitride piezoelectric for higher dimensionless material length scale parameter is the most. Manuscript profile

In this paper, the influence of the elastic foundation on the free vibration and buckling of thin-walled piezoelectric-based functionally graded materials (FGM) cylindrical shells under combined loadings is investigated. The equations of motion are obtained by using the principle of Hamilton and Maxwell's equations and the Navier's type solution used to solve these equations. Material properties are changed according to power law in the direction of thickness. In this study, the effects of Pasternak elastic foundation coefficients and also the effects of material distribution, geometrical ratios and loading conditions on the natural frequencies are studied. It is observed that by increasing Pasternak elastic medium coefficients, the natural frequencies of functionally graded piezoelectric materials (FGPM) cylindrical shell always increases. The mode shapes of FGPM cylindrical shell has been shown in this research and the results show that the distribution of the radial displacements is more significant than circumferential and longitudinal displacements. Manuscript profile

In this article, bending, buckling, and free vibration of viscoelastic sandwich plate with carbon nanotubes reinforced composite facesheets and an isotropic homogeneous core on viscoelastic foundation are presented using a new first order shear deformation theory. According to this theory, the number of unknown’s parameters and governing equations are reduced and also the using of shear correction factor is not necessary because the transverse shear stresses are directly computed from the transverse shear forces by using equilibrium equations. The governing equations obtained using Hamilton’s principle is solved for a rectangular viscoelastic sandwich plate. The effects of the main parameters on the vibration characteristics of the viscoelastic sandwich plates are also elucidated. The results show that the frequency significantly decreases with using foundation and increasing the viscoelastic structural damping coefficient as well as the damping coefficient of materials and foundation. Manuscript profile

In this paper, the pull-in instability of piezoelectric polymeric nanocomposite plates reinforced by functionally graded single-walled carbon nanotubes (FG-SWCNTs) based on modified strain gradient theory (MSGT) is investigated. Various types of SWCNTs are distributed in piezoelectric polymeric plate and also surface stress effect is considered in this research. The piezoelectric polymeric nanocomposite plate is subjected to electro-magneto-mechanical loadings. The nonlinear governing equations are derived from Hamilton's principle. Then, pull-in voltage and natural frequency of the piezoelectric polymeric nanocomposite plates are calculated by Newton-Raphson method. There is a good agreement between the obtained and other researcher results. The results show that the pull-in voltage and natural frequency increase with increasing of applied voltage, magnetic field, FG-SWCNTs orientation angle and small scale parameters and decrease with increasing of van der Waals and Casimir forces, residual surface stress constant. Furthermore, highest and lowest pull-in voltages are belonging to FG-X and FG-O distribution types of SWCNTs. Manuscript profile