Sharif Digital Repository

In this paper, a micro-polar continuum model is presented based on the Cosserat theory for 3D modeling of localization phenomena. Since the classical continuum model suffers from the pathological mesh-dependence in strain localization problem, the governing equations are regularized by adding the rotational degrees-of-freedom to conventional degrees-of-freedom. The fundamental relations in three-dimensional Cosserat continuum are presented and the internal length parameters are introduced in the elasto-plastic constitutive matrix to control the shear bandwidth. The mesh independency of Cosserat model in strain-softening problem is verified and the effect of internal parameters is... 

The present work aims at developing a boundary element method to determine the natural frequencies and mode shapes of liquid sloshing in 3D baffled tanks with arbitrary geometries. Green's theorem is used with the governing equation of potential flow and the walls and free surface boundary conditions are applied. A zoning method is introduced to model arbitrary arrangements of baffles. By discretizing the flow boundaries to quadrilateral elements, the boundary integral equation is formulated into a general matrix eigenvalue problem. The governing equations are then reduced to a more efficient form that is merely represented in terms of the potential values of the free surface nodes, which... 

There are hundreds models of reticulated structures including the squared reticulated cylindrical shells. It is considered as comprising of a number of circumferential and longitudinal rods. Analytical governing equation for natural frequencies has been derived for this type of structures and to verify the validity of solutions, Finite Element Method (FEM) is used. The comparison of results demonstrate close agreement between analytical and FE solutions. Also a comparison is preformed between a reticulated and equivalent solid hollow cylinder shell. The equivalent solid hollow cylinder has equal weight, length and outer diameter with the squared reticulated cylindrical shell. This comparison... 

A new characteristic-based method is developed and used for solving the mixed and forced convection problems. The nano-fluid flow with heat transfer is simulated with a novel characteristic-based scheme in closed domains with different aspect ratios. For this purpose, a FORTRAN code has been written and developed. Water as a pure fluid and water-titanium dioxide as a nano-fluid were considered. The governing equations are solved by the finite volume utilizing a characteristic-based scheme for the convective fluxes. The simulation is done at Grashof numbers from 100 to 104, Reynolds numbers from 100 to 1000, and volume fractions of nano-particles from 0% to 10%. Streamlines, isotherms,... 

In the present work, two cavitation modeling strategies, namely the barotropic cavitation model and the transport equation-based model are applied and assessed for the numerical simulation of inviscid cavitating flows over two-dimensional and axisymmetric geometries. The algorithm uses the preconditioned Euler equations employing the interface capturing method for both the cavitation models. A same numerical solution procedure is used herein for discretizing the governing equations resulting from these two cavitation modeling strategies for the assessment to be valid and reliable. A central difference finite-volume scheme employing the suitable dissipation terms to account for density jumps... 

In this paper, a continuous model for flexural vibration of beams with an edge crack perpendicular to the neutral plane has been developed. The model assumes that the displacement field 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 modified... 

In this paper a new continuous model for flexural vibration of rotors with an open edge crack has been developed. The cracked rotor is considered in the rotating coordinate system attached to it. Therefore, the rotor bending can be decomposed in two perpendicular directions. Two quasi-linear displacement fields are assumed for these two directions and the strain and stress fields are calculated in each direction. Then the final displacement and stress fields are obtained by composing the displacement and stress fields in the two directions. The governing equation of motion for the rotor has been obtained using the Hamilton principle and solved using a modified Galerkin method. The free... 

This study investigates acoustic energy harvesting via magnetic shape memory alloys (MSMA). The acoustic pressure impacts the neck of a Helmholtz resonator (HR) with a flexible face made of an elastic membrane. The design of the proposed energy harvester let radial force in the membrane be tunable. An MSMA is clamped to the membrane, and a proof mass is attached to the other end. The enhanced sound pressure vibrates the membrane and, therefore, excites the base of the MSMA specimen made of Ni-Mn-Ga to apply strain to it. Inserting strain onto the MSMA leads to variant reorientation and change of magnetization vectors, resulting in a change in flux passing through the pick-up coil. Therefore,... 

Mathematical simulation of non-isothermal multiphase flow in deformable unsaturated porous media is a complicated issue because of the need to employ multiple partial differential equations, the need to take into account mass and energy transfer between phases and because of the non-linear nature of the governing partial differential equations. In this paper, an analytical solution for analyzing a fully coupled problem is presented for the one-dimensional case where the coefficients of the system of equations are assumed to be constant for the entire domain. A major issue is the non-linearity of the governing equations, which is not considered in the analytical solution. In order to... 

Torsional aeroelastic analysis of a turbomachinery cascade comprised of three-layered sandwich blades embedded with Magnetorheological Elastomer (MRE) core layer is carried out in this paper. The MRE material is used as a constrained damping layer between two elastic skins in order to investigate its effects on the aeroelastic stability of a blade cascade. To formulate the structural dynamic of the blades, torsional theory of rectangular laminated plates is used and the unsteady Whitehead's aerodynamic theory is employed to model the aerodynamic loadings. Assumed modes method and the Lagrange's equations are used to derive the governing equations of motion of the coupled aeroelastic system.... 

Flight dynamics of the guided vehicle is modelled by the aid of linear and angular equations of motions using Lagrange's approach in this paper. Governing equations of the control system and the elastic behavior of the vehicle are added to the equations of dynamic states. Flexibility effect is modelled using the normal modes, generalized coordinates and forces. For validation of modified FORTRAN simulation code, the stability of specific vehicles is determined and compared with the same results in the literature. Using this code and by solving the governing equations for the desired flight vehicle, the aeroservoelasticity is analyzed and then the results are compared with the rigid cases and... 

With rapid development of methods for dynamic systems modeling, those with less computation effort are becoming increasingly attractive for different applications. This paper introduces a new form of Kane's equations expressed in the matrix notation. The proposed form can efficiently lead to equations of motion of multi-body dynamic systems particularly those exposed to large number of nonholonomic constraints. This approach can be used in a recursive manner resulting in governing equations with considerably less computational operations. In addition to classic equations of motion, an efficient matrix form of impulse Kane formulations is derived for systems exposed to impulsive forces.... 

A semi-analytical method is proposed to solve the equations governing a bi-directionally pumped Raman amplifier through continuous-spectrum radiation. The governing equations are systems of uncountable Nonlinear Ordinary Differential Equation (NODE). By applying the moment method, the uncountable system of NODE is reduced to a system of finite number of NODEs. This system of equations is solved numerically and the results are compared with that of the full numerical method. It was shown that the moment method is a powerful and efficient technique for the analysis of a bi-directionally pumped Raman amplifier through continuous-spectrum radiation  

The large amplitude free vibration of an unsymmetrically laminated composite beam (LCB) on a nonlinear elastic foundation subjected to axial load has been studied. The equation of motion for the axial and transverse deformations of a geometrically nonlinear LCB is derived. Using the Ritz method, the governing equation is reduced to a time-dependent Duffing equation with quadratic and cubic nonlinearities. The homotopy analysis method (HAM) is used to obtain exact expressions for the dynamic response of the LCB. This study shows that the third-order approximation of the HAM leads to highly accurate solutions that are valid for a wide range of vibration amplitudes. The effects of different... 

In this paper, the mechanical behavior of micro-rotating disks is investigated utilizing the strain gradient theory. The governing equation and boundary conditions are derived utilizing the variational method. The analytical solution for the derived equation is also presented. As a case study, some numerical results are presented to emphasize the importance of utilization of non-classical theories such as the strain gradient elasticity instead of the classical continuum theory in dealing with micro-rotating disks  

In this research, the developing turbulent swirling flow in the entrance region of a pipe is investigated analytically by using the boundary layer integral method. The governing equations are integrated through the boundary layer and obtained differential equations are solved with forth-order Adams predictor-corrector method. The general tangential velocity is applied at the inlet region to consider both free and forced vortex velocity profiles. The comparison between present model and available experimental data demonstrates the capability of the model in predicting boundary layer parameters (e.g. boundary layer growth, shear rate and swirl intensity decay rate). Analytical results showed... 

In this study, the authors present an analytical approach to find the axisymmetric buckling load of two joined isotropic conical shells under axial compression. The problem of two joined conical shells may be considered as the generalized form of joined cylindrical and conical shells with constant or stepped thicknesses. Thickness of each cone is constant; however it may be different from the thickness of the other cone. The boundary conditions are assumed to be simply supported with rigid rings. The governing equations for the conical shells are obtained and solved with an analytical approach. A simple closed-form expression is obtained for the buckling load of two joined truncated conical... 

In the present study, a simple analytical method is introduced for determination of natural frequencies of generally laminated conical and cylindrical shells with arbitrary boundary conditions. The governing equations of motion employed are those of thin-walled shell theory of Donnell. The free-vibration equations are solved using state space method and series solution in meridional direction. The results are compared and validated with the available especial results in the literature. The effects of bending-stretching coupling, semi-vertex angle, meridional length, shell thickness, fiber directions of composite plies, and lamination sequences on the natural frequency of conical and... 

this research chamber effective length, which is the minimum chamber length required for complete combustion, for a dilute monopropellant spray, constant area, one dimensional and fixed volume engine is analytically predicted. A new evaporation rate in the form of dk +1 relation, instead of d 2 law, is introduced. In case of controlling the vaporization by radiative heat transfer, k is equal to zero, and when molecular processes control the vaporization, k will be equal to unity and in some cases the vaporization data need the value of k greater than one to fit properly to related equation. Development of this approach can be used in design of combustion chambers with optimum length and with... 

In this research, effective length of one-dimensional combustion in a dilute monopropellant spray, constant area and fixed volume chamber is analytically predicted. A new evaporation rate in the form of d k+1 relation is introduced. In the case of controlling vaporization by radiative heat transfer, k is equal to zero, and when molecular processes control the vaporization, k will be equal to one and in some cases vaporization data need the value of k greater than one to fit properly to related equation. Development of this approach can be used in the design of combustion chambers with optimum length and with using vaporization rate of R = R0〈r〉 0 k/〈r〉k. Spray equation and distribution...