Analyzing the nonlinear dynamic stability of axially moving carbon nanotube reinforced composite (CNTRC) piezoelectric viscoelastic nano/micro plate under time dependent harmonic biaxial loading is the purpose of the present study. The nano/micro plate is made from Polyvinylidene Fluoride (PVDF). It moves in the positive direction of the x-axis at a constant velocity and supported by a nonlinear viscoelastic piezoelectric foundation (Zinc Oxide). A viscoelastic material is assumed in the Kelvin-Voigt model. Nano/micro plate is exposed to electric potential, 2D magnetic field and uniform thermal gradient. Maxwell's relations are used to integrate magnetic field effects. The nano/micro plate as well as smart foundation are subjected to electric potential in thickness direction. The effective elastic properties are estimated using the Eshelby-Mori-Tanaka approach. Von-Kármán's theory provides the basis for the nonlinear strain-displacement relationship. According to various shear deformation plate theories, a novel formulation is presented that incorporates surface stress effects via Gurtin-Murdoch elasticity theory. A modified couple stress theory (MCST) is used in order to consider small scale parameter. It is possible to derive the governing equations by using the energy method and Hamilton's principle. An analysis is conducted using Galerkin procedure and finally the incremental harmonic balance method (IHBM) to obtain the dynamic instability region (DIR). Among the parameters that will be examined are small-scale parameter, alternating and direct applied voltages, magnetic field intensity, surface effects as well as axially moving speed. The results demonstrate that increasing the axial speed of the nano/micro plate causes the system to become more unstable. As a result, if the smart foundation is considered, in addition to increasing the excitation frequency, the area of the instability zone will also decrease by at least 50%. It is estimated that in a static state (not moving), the area of the instability zone is reduced by more than 70%.

The vibration analysis is an important step in the design and optimization of microsensors. In most of the cases, COMSOL software is employed to consider the size-dependency on the dynamic behavior in the MEMS sensors. In this paper, the Modified Couple Stress Theory (MCST) is used to capture the size effect on dynamic behavior in a microsensor with two layers of the silicon and piezoelectric. The governing equations of the system and also associated boundary conditions are derived based on the MCST and using Hamilton’ s principle by obtaining the total kinetic and potential energies of the system. Then, the obtained governing equations are solved using an analytical approach to determine the natural frequencies of the system. The first, second and third natural frequencies of the microsensor are determined using an analytical approach. Finally, the natural frequency variations of the system are presented with respect to different values of the system parameters such as dimensionless parameters of the sensor geometric, the thickness of the silicon and piezoelectric layers and also the dimensionless material length scale parameter. The obtained results show that the material length scale parameter values and also the length, width, and thickness of each layer of the sensor are extremely effective on the vibration characteristics of the piezoelectric cantilever-based Micro Electro Mechanical System (MEMS) sensors. Also, the results show that the first natural frequency of the microsensor will decrease with either increasing dimensionless material length scale parameter or decreasing the thickness of silicon and piezoelectric. This analytical approach presents an efficient method to predict the dynamic behavior of microsensors and consequent optimization in their design procedure.

This paper develops the Refined Zigzag Theory (RZT) for nonlinear dynamic response of an axially moving functionally graded (FG) Nano beam integrated with two magnetostrictive face layers based on the modified couple stress theory (MCST). The Sandwich Nano beam (SNB) subjected to a temperature difference and both axial and transverse mechanical loads. The material properties of FG core layer depend on the environment temperature and are assumed to vary in thickness direction. The SNB is surrounded by elastic medium, which is simulated by viscoPasternak model. The von-Karman nonlinear strain-displacement relationships are employed to consider the effect of geometric nonlinearities. In order to obtain governing motion equations and boundary conditions the energy method as well as Hamilton’ s principle is applied. The differential quadrature method (DQM) is used for space domain and the Newmark-β method is taken into account for time domain response of the axially moving SNB. The detailed parametric study is conducted to investigate the effects of surrounding elastic medium, material length scale parameter, magnetostrictive layers, temperature difference, environment temperature, velocity of the SNB, axial and transverse mechanical loads and volume fraction exponent on the dynamic response of the SNB. Results indicate that the maximum deflection of the system can be controlled by employing negative values of velocity feedback gain values. In addition, the system loses its stability when the velocity of SNB is increased.

In this article, the size effect on the dynamic behavior of a simply supported multi-cracked microbeam is studied based on Modified Couple Stress Theory (MCST). At first, based on MCST, the equivalent torsional stiffness spring for every open edge crack at its location is calculated; in this regard, the Stress Intensity Factor (SIF) is also considered for all open edge cracks. Hamilton’ s principle has been used in order to achieve the governing equations of motion of the system and associated boundary conditions are derived based on MCST. Then the natural frequencies of multi-cracked microbeam are analytically determined. After that, the Numerical solutions have been presented for the microbeam with two open edge cracks. Finally, the variation of the first three natural frequencies of the system is investigated versus different values of the depth and the location of two cracks and the material length scale parameter. The obtained results express that the natural frequencies of the system increase by increasing the material length scale parameter and decrease by moving away from the simply supported of the beam and node points, in addition to increasing the number of cracks and cracks depth.

In the present article, forced vibration control of Timoshenko’s micro sandwich beam based on modified couple stress theory (MCST) is studied. The face sheets are made of three-phase reinforced nanocomposite including resin, piezoelectric and CNT\CNR\GPL materials, and top and bottom layers operate as actuator and sensor, respectively. The micro sandwich beam is placed on Kerr’s foundation and subject to harmonic force with resonance excitation frequency. By considering the equations of motion in the state-space form and using LQR, the amplitude of forced vibrations of the micro beam is optimized. Furthermore, the effects of various parameters including the volume fraction of CNT, GPL and CNR, three parameters of Kerr’s elastic foundation and three natural frequency modes on the suppression and settling time and forced vibration response of a micro sandwich beam is investigated. In this research, for various types and volume fractions of nanocomposites, the second and third natural frequency modes increase 3.5 and 6.7 times, respectively, compared to first natural frequency mode. Also, the Kerr foundation increases the first, second and third mode of natural frequency by about 46%, 13.1% and 7.7%, respectively.

In this article, dynamic modeling of double walled cylindrical functionally graded (FG) microshell is studied. Size effect of double walled cylindrical FG microshell are investigated using modified couple stress theory (MCST). Each layer of microshell is embedded in a viscoelastic medium. For the first time, in the present study, has been considered, FG length scale parameter in double walled cylindrical FG microshells, which this parameter changes along the thickness direction. Taking into consideration the first-order shear deformation theory (FSDT), double walled cylindrical FG microshell is modeled and its equations of motions are derived using Hamilton's principle. The novelty of this study is considering the effects of double layers and MCST, in addition to considering the various boundary conditions of double walled cylindrical FG microshell. Generalized differential quadrature method (GDQM) is used to discretize the model and to approximate the equation of motions and boundary conditions. Also, for confirmation, the result of current model is validated with the results obtained from molecular dynamics (MD) simulation. Considering length scale parameter (l=R/3) on MCST show, the results have better agreement with MD simulation. The results show that, length, thickness, FG power index, Winkler and Pasternak coefficients and shear correction factor have important role on the natural frequency of double walled cylindrical FG microshell.

Due to the extensive development and increasing use of microsystems, it is important to predict the behavior of these structures, especially their vibration behavior. In this study, a micro sensor that has been damaged by a crack is investigated. The damaged micro sensor is modeled as a micro beam with a crack. In this modeling, the crack is modeled as a torsion spring. In the modeling, flexoelectric effect, piezoelectric effect, and electric field caused by the applied voltage have been considered. After mathematical modeling, the governing equations have been extracted using Hamilton's principle based on the modified couple stress theory(MCST). The results of the analytical solution of the equations show that increasing the voltage applied to the micro sensor causes the natural frequency to increase and increasing the piezoelectric constant causes the effective stiffness of the micro structure to increase and as a result the natural frequency increases. Also, the results show that changing the flexoelectric constant in the micro sensor does not significantly change the natural frequency of the system.

In this research, the effect of rotation on the free vibration is investigated for the size-dependent cylindrical functionally graded (FG) nanoshell by means of the modified couple stress theory (MCST). MCST is applied to make the design and the analysis of nano actuators and nano sensors more reliable. Here the equations of motion and boundary conditions are derived using minimum potential energy principle and first-order shear deformation theory (FSDT). The formulation consists of the Coriolis, centrifugal and initial hoop tension effects due to the rotation. The accuracy of the presented model is verified with literatures. The novelty of this study is the consideration of the rotation effects along with the satisfaction of various boundary conditions. Generalized differential quadrature method (GDQM) is employed to discretize the equations of motion. Then the investigation has been made into the influence of some factors such as the material length scale parameter, angular velocity, length to radius ratio, FG power index and boundary conditions on the critical speed and natural frequency of the rotating cylindrical FG nanoshell.