Scientia Iranica
Volume:17 Issue: 3, 2010

This paper considers the scattering of an in nite plane acoustic wave from a long immersed, solid, transversely isotropic cylinder. The mathematical model which has already been developed for this problem does not work in the case of a normally incident wave. Modi cations to the mathematical model are proposed in order to make it applicable to all incidence angles, including = 0. Numerical results are used to demonstrate the correctness of the modi ed equations. Moreover, using a mathematical discussion, it is shown that at normal incidence, the whole displacement eld is constrained within the isotropic plane of the cylinder (cylinder cross section) and only the two elastic constants characterizing this plane appear in the remaining equations. A perturbation study on the ve elastic constants of the transversely isotropic cylinder con rms this result.

Circulation is created in some parts of settling tanks. It can increase the mixing level, decrease the effective settling, and create a short circuiting from the inlet to the outlet. All above-mentioned phenomena act in such a way to decrease the tank''s hydraulic efficiency, which quantitatively shows how ow within the tank is uniform and quiet. So, the main objective of the tank design process is to avoid forming the circulation zone, which is known as the dead zone. Prediction of the ow field and size of the recirculation zone is the first step in the design of settling tanks. In the present paper, the non-linear k - e " turbulence model is used for predicting the length of the reattachment point in the separated ow of a Karlsruhe tank. Then, the recirculation bubble size, which is out of the capability of standard turbulence models, is determined. Also, the effect of the separation zone size on the tank''s hydraulic efficiency is investigated.

In this investigation, the Flexible String Algorithm (FSA) used before for the inverse design of 2D subsonic ducts is developed and applied for the inverse design of subsonic and supersonic ducts with and without normal shock waves. In this method, the duct wall shape is changed under a novel algorithm based on the deformation of a virtual exible string in a ow. Deformation of the string due to the local ow conditions resulting from changes in the wall geometry is performed until the target shape satisfying the prescribed walls pressure distribution is achieved. The ow eld at each shape modi cation step is analyzed using an Euler equation solution by the AUSM method. Some validation test cases and design examples in subsonic and supersonic regimes are presented here, which show the robustness and exibility of the method in handling the complex geometries in various ow regimes. In the case of unsymmetrical ducts with two unknown walls, the FSA is modi ed to increase the convergence rate signi cantly. Also, the e ect of duct inlet and outlet boundary conditions on the convergence of the FSA is investigated. The FSA is a physical and quick converging approach and can eciently utilize ow analysis codes as a black box.

In this paper, a continuous model for exural vibration of beams with an edge crack perpendicular to the neutral plane has been developed. The model assumes that the displacement eld is a superposition of the classical Euler-Bernoulli beam''s displacement and of a displacement due to the crack. The additional displacement is assumed to be a product between a function of time and an exponential function of space. The unknown functions and parameters are determined based on the zero stress conditions at the crack faces and the concept of J-integral from fracture mechanics. The governing equation of motion for the beam has been obtained using the Hamilton principle and solved using a modi ed Galerkin method. The results have been compared with nite element results and an excellent agreement is observed.

The geometrically non-linear behavior of unsymmetrical, ber-reinforced, laminated, annular sector composite plates is studied. The rst order shear deformation theory is applied to the von Karman type non-linear behavior of unsymmetrically, laminated, annular sector composite plates. Five equilibrium equations, ve stress-displacement relations, three curvature-displacement relationships, together with eight stress resultants, stress couples and shear force relationships are solved. The nonlinear nature of the problem prohibits the application of a closed form solution method. Consequently, the Dynamic Relaxation (DR) numerical method is chosen for solving the system of 21 simultaneous equations. The in-plane and out-of-plane displacements are reported for di erent con gurations of annular sector plates. Di erent sector angles, ber orientations and plate thicknesses are considered. For better observation of the numerical methods, they are illustrated graphically. The correlations of the present results and the corresponding nite element generated results are very satisfactory.

In this paper, the problem of attitude control of a 1D non-linear exible spacecraft is investigated. Three controllers are presented. The rst is a non-linear dynamic inversion, the second is a linear -synthesis and the third is a composition of dynamic inversion and a -synthesis controller. It is assumed only one reaction wheel is used. Actuator saturation is considered in the design of controllers. The performances of the proposed controllers are compared in terms of nominal performance, robustness to uncertainties, vibration suppression of panels, sensitivity to measurement noise, environment disturbance and non-linearity in large maneuvers. To evaluate the performance of the proposed controllers, an extensive number of simulations on a non-linear model of the spacecraft are performed. Simulation results show the ability of the proposed controller in tracking the attitude trajectory and damping panel vibration. It is also veri ed that the perturbations, environment disturbance and measurement errors have only slight e ects on the tracking and damping responses.

In this paper, the general dynamic equation of motion of Cable Driven Robots (CDRs) is obtained from Lagrangian formulation. A computational technique is developed for obtaining an optimal trajectory to maximize the dynamic load carrying capacity for a given point-to-point task. Dynamic equations are organized in a closed form and are formulated in the state space form. In order to nd the Dynamic Load Carrying Capacity (DLCC) of CDRs, joint actuators torque, and robot workspace constraints for obtaining the positive tension in cables are considered. The problem is formulated as a trajectory optimization problem, which fundamentally is a constrained nonlinear optimization problem. Then, the Iterative Linear Programming (ILP) method is used to solve the optimization problem. Finally, a numerical example involving a 6 d.o.f CDR is presented and, due to validation, the results of the ILP method are compared with the optimal control method.