In this paper, homotopy perturbation and modified Lindstedt-Poincare methods are employed for nonlinear free vibrational analysis of simply supported and double-clamped beams subjected to axial loads. Mid-plane stretching effect has also been accounted in the model. Galerkin's decomposition technique is implemented to convert the dimensionless equation of the motion to nonlinear ordinary differential equation. Homotopy and modified Lindstedt-Poincare (HPM) are applied to find analytic expressions for nonlinear natural frequencies of the beams. Effects of design parameters such as axial load and slenderness ratio are investigated. The analytic expressions are valid for a wide range of vibration amplitudes. Comparing the semi-analytic solutions with numerical results, presented in the literature, indicates good agreement. The results signify the fact that HPM is a powerful tool for analyzing dynamic and vibrational behavior of structures analytically. تفاصيل المقالة

In this research, a functionally graded microbeam bonded with piezoelectric layers is analyzed under electric force. Static and dynamic instability due to the electric actuation is studied because of its importance in micro electro mechanical systems, especially in micro switches. In order to prevent pull-in instability, two piezoelectric layers are used as sensor and actuator. A current amplifier is used to supply input voltage of the actuator from the output of the sensor layer. Using Hamilton’s principle and Euler-Bernoulli theory, equation of motion of the system is obtained. It is shown that the load type (distributed or concentrated) applied to the micro beam from the piezoelectric layer, depends on the shape of the actuator layer (E.g. rectangle, triangular). Finite element method is implemented for evaluation of displacement field in the micro beam and dynamic response of the micro beam under electric force is calculated using finite difference method. Effect of squeeze film damping on pull-in voltage and time-response of the system is considered using nonlinear Reynolds equation. Effect of several parameters such as gain value between piezoelectric sensor and actuator layer, profile of functionally material, and geometry of the system is considered on dynamic behavior of the micro beam especially on pull-in instability. Results are verified for simple cases with previous related studies in the literature and good agreements were achieved. Results indicate that increasing gain value between sensor and actuator enhances stiffness of the system and will raise pull-in voltage. Also, dependency of dynamic properties of the system such as amplitude and frequency of vibration on functionally graded material profile is shown. The material distribution of the functionally graded material is designed in such a way that results in a specific pull-in voltage. تفاصيل المقالة

Embryogenesis, regeneration and cell differentiation in microbiological entities are influenced by mechanical forces. Therefore, development of mechanical properties of these materials is important. Neural network technique is a useful method which can be used to obtain cell deformation by the means of force-geometric deformation data or vice versa. Prior to insertion in the needle injection process, deformation and geometry of cell under external point-load is a key element to understand the interaction between cell and needle. In this paper, the goal is the prediction of cell membrane deformation under a certain force and to visually estimate the force of indentation on the membrane from membrane geometries. The neural network input and output parameters are associated to a three dimensional model without the assumption of the adherent affects. The neural network is modeled by applying error back propagation algorithm. In order to validate the strength of the developed neural network model, the results are compared with the experimental data on mouse oocyte and mouse embryos that are captured from literature. The results of the modeling match nicely the experimental findings. تفاصيل المقالة