Sharif Digital Repository

The current study is dedicated to free vibration analysis of a thin cylindrical shell with an oblique end. To this end, governing equations of motion and the corresponding boundary conditions are derived using Hamiltonian formulations. The differential form of equations is obtained by applying by part integration to the integral form of equations of motion. Equations of motions have been solved by Galerkin method for two different kinds of boundary conditions. Convergence process for different kinds of conditions has been done and results compared with papers. The effect of different parameters such as, length of cylinder, oblique angle, thickness etc. on the fundamental frequencies has been... 

Here the differential equations of a Graphene sheet deformation is determined by making use of the most general form of first Strain Gradient Elasticity (SGE) theory. In order to derive the equations of in-plane and out-of-plane deformations, the matrix representation of Strain Gradient constitutive law is used. Vibration of the nano-plate is studied by modeling the plate based on Kirchhoff theory and application of variation of energy, therefor the in-plane and out-of-plane vibration of the nano-plate is found through Navier analytical solution. After all natural frequencies are obtained based on SGE parameters. SGE parameters are determined by calculating the potential of a representative... 

In this project, vibration and stability condition of a pipe conveying flow has been studied for use in firefighting plane. The Plane is a multi-rotor that carries the pipe to a certain height and it does the washing work there, bassed on the fluid flow from the nozzle embedded in the end of the pipe. Due to the flexibility of the pipe in this application, structure modeling is based on cable without bending stiffness. The Galerkin method is used to solve equations by considering the assumed mode shape for structure. At first, by analyzing free vibrations, different boundary conditions were considered for the pipe and the natural frequencies and natural shape modes were extracted in... 

Nanotechnology with the tools, materials and their applications in areas such as engineering mechanics, materials, electronics, computers, and machines at the nanoscale is dealing. The Fnarvy, atoms and molecules as building materials, engineering bricks counts. In mechanical engineering branch, two aspects are discussed in view of nanotechnology, nano-scale structures and analyzing the behavior of phenomena that occur at the nanoscale. In this project, methods to analyze the behavior of nanoscale materials has been studied.
The present thesis examines the natural frequencies of nano graphene sheets on elastic foundation deals. The elastic foundation modeled with two springs.At first The... 

In this study, the nonlinear vibrations of an elastic rotor that is under the elastic support and under the follower force caused by the airflow passing through the rotating plane are investigated. The elastic shaft is modeled by the Timoshenko beam theory, which is connected to a motor through a flexible coupling and the motor increases the rotational speed of the rotor by applying torque. Gibbons’ equations have been used to model the misalignment forces. First, the kinetic energy of the rotating system is calculated nonlinearly to take into account the effect of nonlinear terms due to the rotational inertia of the system, and then the potential energy and The work of external forces on... 

In the current study, stability and nonlinear vibration of bending-torsional extensible beams conveying internal pulsatile and uniform external flow are studied. The internal and external fluid flows are assumed to be incompressible and frictionless. Applying the extensibility to the pipe along its length and using the nonlinear Euler-Bernoulli beam model and including some appropriate additional assumptions, the 3D nonlinear equations of motion of a cantilevered composite pipe is obtained. In order to derive the equations governing the fluid-structure interaction, the internal flow effect is modeled as a distributed load along the pipe which contains the inertia, Coriolis and centrifugal... 

This study presents the aeroelastic stability and vibration analysis of a sandwich circular cylindrical shells with a constrained viscoelastic layer. Based on the Donnell-Moshtari theory, the structural formulation of the cylinder is obtained using Lagrange method. The Rayleigh-Ritz method is implemented to solve the discretized governing equations. To describe the mechanical properties of the viscoelastic layer, the fractional order standard solid model is applied. The effects of variation of the governing parameters such as the length to radius ratio, radius to total thickness ratio and ratio of core to facing thickness on the stability margins and frequencies of sandwich cylindrical... 

The present study investigates the vibrational behavior of a special type of nano-motor based on a thin cylindrical shell model and the nonlocal elasticity theory of Eringen. The presumed nano-motor is comprised of three single walled carbon nanotubes (CNT), where two of them are cantilevered and the third one is located in the middle. The CNT in the middle will suspend due to the Van-der-Waals forces generated from the interaction by the cantilevered CNT pair. Some proper chirality arrangements can conduct electricity and make the middle CNT rotate in extremely high speeds. In fact, the middle CNT rotates on a frictionless elastic foundation. In the present study, the nano-motor is modeled... 

In this M.Sc. thesis dynamics of a system of 3-D fluid (internal) and solid interaction hase been studied. Structure (shell) filled with dense fluid (liquid) and it is under large amplitude vibrations excitations. Shell is analized using geometrical nonlinear general shells formulations. The nonlinear analysis includes large displacements, large rotations and large strains without considering material nonlinearity. Based on the potential flow assumption the governing equations of fluid are derived. And using boundary elements formulations fluid hydrodynamic pressure in each step is drived. In order to simultaneous and mutual influence of fluid and structure, numerical model of combined... 

This thesis deals with developing and applying reduced order modeling techniques for fluid and structure interaction problems. First, the basis and formulations of reduced order modeling technique in the function space are reviewed. Then the governing equations of structural dynamics as well as incompressible flow are reviewed and some simplifications are applied. Based on the modal analysis technique along with the finite element model of the structure and the boundary element model for flow field, some reduced order models are represented. The represented models are developed for liquid sloshing in moving and elastic tanks, fluid structure interaction in flexible shells conveying flow,... 

This study aims at investigating the vibration analysis and stability of Graphene Nano-Ribbon (GNR) under a magnetic field using continuum mechanics approach and an efficient hybrid modal-molecular dynamics method. The force distribution on the GNR due to the magnetic field is determined by Maxwell's equations, Biot-savart law, magnetic dipoles and Lorentz force law.
Using the continuum mechanics model, the vibration of the GNR in a magnetic field is investigated by some problems and the resonance frequencies, stability boundaries and critical load are studied.
Furthermore, in this present study, an efficient hybrid modal-molecular dynamics method is developed for the vibration... 

Because the structural stability is directly related with structural damage, it is considered one of the most important issues in the industry. One of the applied cases in the stability issue discuss about the stability of the beam under follower loads. Follower loads obtained from aerodynamic pressure, rocket’s thrust, dry friction of the rotating disk, drilling and etc. Because the follower loads are always perpendicular to the beam cross section, thus with changing the angle of their location, their directions are changed. Spatial dependence makes a non-conservative and dynamic problem. So these loads causes dynamic instability that say flutter. In this study, the stability of a... 

In this study, an analytical investigation of the hydrodynamic damping due to vertical baffles in circular cylindrical storage tanks is investigated. A lot of research about damping characteristics of different types of baffles has been done but because of specific applications of vertical baffles, studies are limited in this case. For analytical approach the average rate of energy dissipation is obtained with using the solution of Laplace’s equation by estimation the rate of the work done by baffles drag force to the oscillatory flow. The analytical solution validate by a series of experiments that conducted at the Langley Research Center of the National Aeronautics and Space... 

In static floating structures such as floating bridges and offshore runways that are in contact with the water surface from the floor and with the open air from the top, three types of interactions occur: the interaction of the structure with air, the interaction of the structure with water and Interaction of air with water. Due to the long length of such structures and approaching their natural frequencies to the standing wave frequencies (seiche frequencies), the analysis of the elastic behavior of the structure alone is not enough, but the structure-air-water interaction must be evaluated simultaneously in a system. Leading research addresses this issue and examines the behavior of an... 

The dry friction and its effect on the dynamics and vibrations of structures have always been one of the remarkable engineering issues. In the structures of engineering, dry friction mostly exists at the joints of structures and substrates and dry friction can lead to the nonlinearity and even chaos in the vibration of structures. There are different theories for the friction modeling and the most famous theory is the relation between the proportional ratio of the force of friction and perpendicular force to the surface. The main characteristic of friction as a damper force is the change of direction along with change in the direction of velocity. In the present study, at first, the nature... 

Long thin rectangular beams are used in many industrial engineering including railways, aerospace and etc. Beam subjected to moving mass is one of the classic problems in mechanics and vibrations of beams and have been studied by many researchers. In most of done works, the moving mass was assumed to be small compared to beam mass and only acceleration effect of mass was considered. Also in many of researches only bending of beams was studied. Moving mass imposes 2 type of force in the supporting beam, first one is weight and the other is due to motion of mass and contains lateral, coriolis and centrifugal acceleration effects. In addition, due to the particular geometry considered (narrow... 

In this thesis, effects of bending and torsional elasticity of a flapping wing on its average lift and input power are studied, using a semi-analytic method. Bending stiffness and torsional rigidity of wing spar, wing mass ratio and chordwise and spanwise center of gravity, also spar location are considered as variables for controlling elastic behavior of the wing.Governing integral equation is derived using Hamilton principle via modified quasi aerodynamic and linear Green-Lagrange strain tensor. Also an idealized flapping pattern is used to maximize average acceleration during each cycle. Next, integral equation is converted to a set of ordinary differential equations by means of Galerkin... 

In this thesis, sloshing of a rectangular container with perforated baffle is being analysed. Employing the linear sloshing theorem, we construct an accurate numerical and analytical approximation of natural sloshing mode in rectangular container with perforated baffle. Two dimensional irrotational flow of an ideal incompressible liquid is assumed. Finally the dissipated energy is being measured and equal viscous damping was calculated. So the perforation in which the damping is being maximized is determined and finally the results being compared with some experimental and analytical results from journal paper  

At high speeds, cavitation bubbles form at the sharp edges of the submerged body or in situations where the pressure falls below the fluid vapor pressure. By placing a suitable cavitator in the nose of the body, the cavitation bubbles are cobined by increasing the speed and the whole body is placed inside the cavity. The formation of a supercavity leads to a significant reduction in the drag force of the vehicle. The submersible device is in contact with the fluid at two points, the cavitator and the fins, and due to the location of the cavitator in the nose of the body, the forces acting on it play an important role in the stability and control of the device.The main goal of current...