amir reza askari

This paper aims to investigate the influence of bearing elastic properties on nonlinear dynamics of unbalanced rotors. Accounting for the influence of asymmetric magnetic pull, the governing equations of motion associated with the rotor are obtained using the nonlinear Euler-Bernoulli beam theory. Adopting the Galerkin projection method, the reduced equations of motion are extracted and then solved analytically through the method of multiple time scales for the cases of free vibrations and primary resonances. Aside from the numerical simulations, the present findings are compared and successfully validated by those published in the previous studies. Afterward, a detailed parametric study is conducted to assess the influences of asymmetric magnetic pull, nonlinear stiffnesses of the bearings and the eccentricity on nonlinear dynamics of the system. Results reveal that accounting for the influence of asymmetric magnetic pull decreases the natural frequencies of the system. In addition, it is observed that increasing the eccentricity increases the amplitudes of vibrations and also broadens the bistable resonance zone.

This paper introduces piezoelectric excitation as a balancing mechanism for mode-localized mass micro-sensors. To this end, adopting the Hamilton principle together with the Ritz method, the non-linear reduced equations of motion governing electrostatically coupled micro-beams with piezoelectric layers are obtained. The free vibration equations associated with the present system are also extracted by linearizing the motion equations around the previously determined static configuration of the system. Solving the free vibration equations, the eigenvalue loci of the system are then plotted. Afterward, the influence of piezoelectric excitation on the veering phenomenon is studied. The results, whose accuracy is successfully validated by those available in the literature, reveal that piezoelectric excitation can drastically affect the veering phenomenon. For instance, it is observed that the application of the electrostatic voltage of 4V can be compensated by the piezoelectric excitation of -35.4695 mV so that the veering phenomenon will occur at the same coupling voltage. Given this important observation, the possibility of employing piezoelectric excitation in designing tunable resonant mass micro-sensors that operate based on the mode-localization phenomenon suggests itself.

Recently, it has been substantiated that besides initially curved micro-structures, pressurized flat micro-plates can also experience snap-through instability. Given the potential applications of these micro-plates in designing high-sensitive sensors, the present work aims to investigate the bi-stable behavior of such structures when they are integrated with a piezoelectric layer. To this end, the modified couple stress theory together with the geometric nonlinear Kirchhoff plate model are employed. Hiring Galerkin’s method, the reduced governing equilibrium, and stability equations are then achieved. The limit points associated with the micro-plate equilibrium path are then determined through the simultaneous solution of these equations. The present findings are compared and validated by available results in the literature. The influence of the piezoelectric actuation on the bi-stable response of the system is then investigated. The results reveal that the shape of the micro-plate equilibrium path and the number and the position of its limit points can seriously be affected by applying the piezoelectric voltage. Despite the previous studies, the present paper shows that applying positive piezoelectric voltage does not decrease the pull-in threshold of the system all the time and can sometimes increase it when the micro-plate undergoes large differential pressures. Furthermore, the results reveal that applying positive piezoelectric voltages expands the snapping zone while negative ones downsize this region. The present results can be very useful for micro-electromechanical system engineers.

The present paper investigates the influence of higher-order boundary conditions caused by accounting the small scales effect on free vibrations of bi-directional functionally graded thick conical micro-shells. The present model accounts for the gradation of the material length scale parameter as one of the micro-shell mechanical properties along its thickness as well as its axial axis. The modified couple stress as well as the first-order shear deformable love shell theories together with the Ritz method are employed to obtain the eigenvalue eigenvector equations governing on the free vibrations of the micro-structure. These equations are solved for some different types of boundary conditions. The present findings are compared and successfully validated by the available results in the literature. The influences of small scales, higher-order boundary conditions and power law distribution indices in both the transversal and axial directions on free vibrations of conical micro-shells are then investigated. The results reveal that higher-order boundary conditions play a crucial role in dynamics of conical micro-shells especially when these boundary conditions directly affect the eigenmodes which are dominant in the dynamics of the structure. In addition, it is observed that although the dynamics of the present conical micro-shell is affected by the power law distribution indices in both the transversal and axial directions, it is more sensitive to the transversal one.

The objective of the present paper is to investigate the size-dependent response of a fully clamped rectangular micro-plate under random base excitation. The size-dependent Kirchhoffchr('39')s plate model based on the modified couple stress theory is utilized in the theoretical formulation. The equations of motion which account for the packaging effect and axial residual stresses are derived using Hamiltonchr('39')s principle. To find the spectral density and mean square value of the micro-plate deflection, the standard modal summation method is employed where the micro-plate mode-shapes are extracted using the extended Kantorovich method. A convergence study is conducted to find the number of modes which must be included in the response. It is found that using the first six symmetric mode-shapes for the present micro-plate leads to very accurate results, while single-mode solution gives the mean square value of the response with a maximum error of 10%. Furthermore, the results reveal that the size effect on the mean square value of the mid-point deflection is usually negligible when the ratio of the plate thickness to its material length scale parameter becomes larger than 15.

In this paper some mechanical amplifiers have been investigated then a new model has been introduced, designed and analysed. This new mechanism can present a large amplification ratio in a very compact size. High natural frequency and the absence of lateral motion are the advantages of this new model toward the other models introduced here. In order to present an analytical investigation for this new mechanism, the pseudo rigid model is utilized and optimized for the best working conditions. This model is also analysed and verified using finite element method. The results of FEM are utilized to specify the effect of parameters which cannot be seen in pseudo rigid model. An optimized model with its dimensions sketched finally.