Scientia Iranica
Volume:20 Issue: 1, 2013

Thermo-elastic analysis of a functionally graded spherical shell with piezoelectric layers under the effect of thermo-electro-mechanical loading is carried out. Material properties of the shell are assumed to be graded in the radial direction according to a power law function, while the Poisson’s ratio is assumed to be constant. Governing differential equations are developed in terms of components of the displacement field, electric potential and temperature of each layer of the shell. These equations are then discretized using the polynomial differential quadrature method and numerical results of stress, displacement, temperature and electric fields are obtained. Convergence of the present method is studied and the results obtained are verified with results reported in the literature. Effects of the grading index of material properties, temperature difference and thickness of piezoelectric layers on stress, displacement and temperature fields are presented.

In this study, the extended finite element method was used for modeling dynamic fracture in Kirchhoff plate and shell problems. A new set of tip functions was extracted from analytical solutions of Kirchhoff plates. The semi-discrete method was used to simulate the dynamic behavior. An unconditionally stable implicit Newmark scheme was used for temporal discretization. The performance of the code in simulation of dynamic behaviors was proved by solving several benchmark problems and comparing the obtained results with other numerical and analytical solutions. Also, the problem of cracked thin tubes under gaseous detonation loading was simulated by the dynamic XFEM code. The results were compared with analytical and other numerical solutions and the obtained results showed that the method has good capability for simulation of these problems.

In this paper, free vibration of a simply supported rotating shaft with stretching nonlinearity is investigated. Rotary inertia and gyroscopic effects are included, but shear deformation is neglected. The equations of motion are derived with the aid of the Hamilton principle and then transformed to the complex form. To analyze the free vibration, the method of multiple scales is directly applied to the partial differential equation of motion. An analytical expression, as a function of system parameters, is derived, which describes the nonlinear free vibration of the rotating shaft in two transverse planes. The effects of rotary inertia, external damping and rotating speed on the forward and backward nonlinear natural frequencies are considered. It is shown that both forward and backward nonlinear natural frequencies are being excited. To validate the perturbation results, we use numerical simulation.

In supersonic two-phase flows of steam, under the influence of rapid expansion, the vapor becomes supersaturated. Following this condition, nucleation happens during the vapor phase; formed tiny droplets grow along the passage and, therefore, the condensation phenomenon occurs. The effects of the condensation phenomenon in power steam turbines include efficiency drop and mechanical damage. In the previous work of the authors, volumetric heating was introduced as an approach towards reducing the mentioned damage and loss. However, further investigations revealed that heating decreases the mass flow rate, which can be increased by adjusting the inlet stagnation pressure. In this paper, using a semi-analytical and a one-dimensional modeling approach, the simultaneous effects of volumetric heat transfer and inlet stagnation pressure variation are investigated in order to remedy the mass flow rate reduction. The results show that increasing the inlet stagnation pressure up to 5% can fix the mass flow rate of the non-adiabatic flow, compared to the adiabatic flow under the same conditions.

The unsteady viscous flow and heat transfer in the vicinity of an axisymmetric stagnation point of an infinite moving plate with transpiration are investigated when the axial velocity and wall temperature vary arbitrarily with time. The free stream is steady and with a strain rate of. An exact solution of the Navier–Stokes equations and energy equation is derived in this problem. A reduction of these equations is obtained by the use of appropriate transformations for the most general case when the transpiration rate is also time-dependent, but results are presented only for uniform values of this quantity. The general self-similar solution is obtained when the axial velocity of the plate and its wall temperature vary as specified time-dependent functions. For completeness, sample semi-similar solutions of the unsteady Navier–Stokes equations have been obtained numerically using a finite difference scheme. All the solutions above are presented for different values of dimensionless transpiration rate,, where is the kinematic viscosity of the fluid. The effects of the sundry parameters, including transpiration rate, Prandtl number, oscillation frequency and accelerating/decelerating parameter, on the velocity and temperature profiles, as well as surface shear stresses and heat transfer coefficient, are investigated and results are shown through graphs.

The mixing pattern of two parallel gas streams initially separated by a splitter plate is analyzed in this study. A recently proposed, two-fluid model is utilized for simulation of the flow field. The model provides separate balance equations for each component species of the system. As a consequence of the strong resemblance of the two-fluid model to the Navier–Stokes equations, the same numerical methods are applied to these new equations. The computations are undertaken for two-fluid systems; one with particles of about equal masses and another with particles of quite distinct masses, and the corresponding results are compared. This clarifies how the mass disparity of the constituents may affect the establishment of the flow field. The influence of molecular interaction descriptions in the model predictions is also examined by comparing the results of a hard-sphere model, the Maxwell repulsive potential, and the Lennard-Jones 12-6 potential.

In this paper, a two-link flexible manipulator is considered. For a prescribed motion, Timoshenko and Euler–Bernoulli beam models are considered. Using the Galerkin method, nonlinear equations of motion are solved. The Runge–Kutta method is employed for the time response integration method. A comparative study is made between the Euler–Bernoulli and Timoshenko beam models, with and without foreshortening effects. It is demonstrated that for two-link manipulators, both theories provide good models, and the results for both theories are very similar for all ranges of slenderness ratio. The findings suggest that for two-link manipulators with relatively high slenderness ratios, there is a remarkable difference between the models, considering the foreshortening effect and un-stiffened models. It is obvious that for high precisions applications, the stiffened Timoshenko model is recommended. It is interesting to note that joint torques for the entire range of slenderness ratios are the same.

This paper obtains the solitary wave solutions of two different forms of Boussinesq equations that model the study of shallow water waves in lakes and ocean beaches. The tanh method is applied to solve the governing equations. The travelling wave hypothesis is also utilized to solve the generalized case of coupled Boussinesq equations, and, thus, an exact 1-soliton solution is obtained. The results are also supported by numerical simulations.

Existing solutions of the problem of axisymmetric stagnation-point flow and heat transfer on either a cylinder or flat plate are for incompressible fluid. Here, fluid with temperature dependent density is considered in the problem of axisymmetric stagnation-point flow and heat transfer on a cylinder with constant heat flux. The impinging free stream is steady and with a constant strain rate,. An exact solution of the Navier–Stokes equations and energy equation is derived in this problem. A reduction of these equations is obtained by use of appropriate transformations introduced for the first time. The general self-similar solution is obtained when the wall heat flux of the cylinder is constant. All the solutions above are presented for Reynolds numbers,, ranging from 0.01 to 1000, selected values of compressibility factors, and different values of Prandtl number, where is cylinder radius and is the kinematic viscosity of the fluid. For all Reynolds numbers and surface heat flux, as the compressibility factor increases, both components of the velocity field, the heat transfer coefficient and the shear-stresses increase, and the pressure function decreases.

Piezoelectric microcantilevers (MCs) are types of MCs which can be used in Atomic Force Microscopy (AFM) as a micro-robot, sensor, and imaging actuator. In this paper, the vibrating motion of piezoelectric MCs in AFM application is analyzed. With respect to the geometrical discontinuities, due to the piezoelectric layer, as well as tip, a non-uniform beam model is chosen for analysis. At first, to determine the accuracy of the non-uniform beam model in simulating the vibrating motion of piezoelectric MC, the simulation results are compared with the experimental ones in the absence of the tip-sample force. Good agreement of these results indicates the ability of this model in modeling this type of MC. A numerical solution and a Multiple Time Scale (MTS) method are used to study the nonlinear response of the MC near the sample surface. Comparison of results, at the non-contact mode, shows good agreement between the two solving methods at normal equilibrium distances (). The effects of the angle of MC, the probe length, and the geometric dimensions of the piezoelectric layer on the nonlinearity of the system are studied and it then becomes clear that they can affect the frequency response curvature of the curve and the nonlinearity of the system.