Sharif Digital Repository

In this paper, a thorough investigation of response of a composite Timoshenko simply-supported beam with actuating layers, under the motion of a partially distributed mass is studied and a control system based on the feedback of beam's deflection velocity is applied to alleviate and suppress the vibration of the beam in either case when the mass is still traveling on the beam or departed the beam. The actuating layers are made up of Terfenol-D smart material which are sensitive to magnetic field (magnetostrictive materials) and this trait makes them very suitable to be used for vibration control. They introduce damping to the system through which the energy of system dissipates. The response... 

Free vibration response of a cylindrical shell closed with two hemispherical caps at the ends (hermit capsule) is analysed in this research. It is assumed that the system of joined shell is made from functionally graded materials (FGM). Properties of the shells are assumed to be graded through the thickness. Cylindrical and hemispherical shells are unified in thickness. To capture the effects of through-the-thickness shear deformations and rotary inertias, first order theory of shells is used. Donnell type of kinematic assumptions are adopted to establish the general equations of motion and the associated boundary and continuity conditions with the aid of Hamilton's principle. The resulting... 

This paper discusses the effects of substrate motions on the performance of a microgyroscope modeled as a suspended beam with a tip mass. These motions can be either along or around the three axes. Using the Extended Hamilton's Principle, the equations of motion are derived. In these equations, the effects of beam distributed mass, tip mass, angular accelerations, centripetal and coriolis accelerations are well apparent. The effect of electrostatic forces inducing the excitation vibrations are considered as linear functions of beam displacement. The response of the system to different inputs is studied and the system sensitivity to input parameter changes are examined. Finally, the sources... 

In this paper, the strain gradient theory, a non-classical continuum theory capable of capturing the size effect observed in micro-scale structures, is employed in order to investigate the size-dependent mechanical behavior of microbars. For a strain gradient bar, the governing equation of motion and classical and non-classical boundary conditions are derived using Hamilton's principle. Closed form solutions have been analytically obtained for static deformation, natural frequencies and mode shapes of strain gradient bars. The static deformation and natural frequencies of a clamped-clamped microbar subjected to a uniform axial distributed force are derived analytically and the results are... 

In this paper size-dependent static and dynamic behavior of nonlinear Euler-Bernoulli beams made of functionally graded materials (FGMs) is investigated on the basis of the strain gradient theory. The volume fraction of the material constituents is assumed to be varying through the thickness of the beam based on a power law. As a consequence, the material properties of the microbeam (including length scales) are varying in the direction of the beam thickness. To develop the model, the usual simplifying assumption which considers the length scale parameter to be constant through the thickness is avoided and equivalent length scale parameters are introduced for functionally graded microbeams... 

In this article, the dynamic responses of a Timoshenko beam subjected to a moving mass, and a moving sprung mass are analyzed. By making recourse to Hamilton's principle, governing differential equations for beam vibration are derived. By using the modal superposition method, the partial differential equations of the system are transformed into a set of Ordinary Differential Equations (ODEs). The resulted set of ODEs is represented in state-space form, and solved by means of a numerical technique. The accuracy of the results has been ascertained through comparing the results of our approach with those available from previous studies; moreover, a reasonable agreement has been obtained. The... 

In this paper axial and torsional vibrations of a drillstring are studied using cylindrical superelement. Drillstring vibration equation is derived by calculating kinetic and potential energy and work done by external forces on drillstring, and utilizing Hamilton's principle. The model is analyzed by implementing finite element technique with consideration drillstring weight, centrifugal force due to rotation of drillstring, axial force resulting from bit with the formation contact and torsional torque caused by the stick-slip phenomenon. To calculate the vibrational response of drillstring, a computational finite element scheme was developed. For a typical case of oil well drillstring, the... 

We apply Hamilton's principle and model the coupled in-plane and transverse vibrations of high-speed spinning disks, which are fiber-reinforced circumferentially. We search for eigenmodes in the linear regime using a collocation scheme, and compare the mode shapes of composite and isotropic disks. As the azimuthal wavenumber varies, the radial nodes of in-plane waves are remarkably displaced in isotropic disks while they resist such displacements in composite disks. The reverse of this phenomenon happens for transversal waves and the radial nodes move toward the outer disk edge as the azimuthal wavenumber is increased in composite disks. This result is in accordance with the predictions of... 

In this paper, chatter instability of micro end mill tools is studied by taking into account the process damping effect. The actual geometry of the micro tool including shank, taper part and fluted section is considered in the analysis. Timoshenko beam theory is utilized to consider the shear deformation and rotary inertia effects due to short and thick beam-type structures of each parts of the micro tool. The extended Hamilton's Principle is used to formulate a detailed dynamical model of the rotating micro end mill. The governing equations are solved by assumed mode model expansion. An exact dynamic stiffness method is developed to investigate modal characteristics of the tool including... 

This paper undertakes to facilitate appraisal of aeroelastic interaction of a locally distributed, flap-type control surface with aircraft wings operating in a subsonic potential flow field. The extended Hamilton's principle serves as a framework to ascertain the Euler-Lagrange equations for coupled bending-torsional-flap vibration. An analytical solution to this boundary-value problem is then accomplished by assumed modes and the extended Galerkin's method. The developed aeroelastic model considers both the inherent flexibility of the control surface displaced on the wing and the inertial coupling between these two flexible bodies. The structural deformations also obey the Euler-Bernoulli... 

In this paper, the coupled three-dimensional flexural vibration of micro-rotors is investigated by taking into account the small-scale effects utilizing the strain gradient theory, which is a powerful nonclassical continuum theory in capturing small-scale effects. A micro-rotor consists mainly of a flexible micro-rotating shaft and a disk. With the aid of Hamilton's principle, governing equations of motion are derived and then transformed to the complex form. By implementing the Galerkin's method, a coupled ordinary differential equation is attained for the system. Expressions for the first two natural frequencies of the spinning micro-rotors are obtained with truncated two-term equation.... 

In this paper, nonlinear dynamical behavior of a rectangular plate traveled by a moving mass as well as an equivalent concentrated force with non-constant velocity is studied. The nonlinear governing coupled partial differential equations (PDEs) of motion are derived by energy method using Hamilton's principle based on the large deflection theory in conjuncture with the von-Karman strain-displacement relations. Then Galerkin's method is used to transform the equations of motion into a set of three coupled nonlinear ordinary differential equations (ODEs) which then is solved in a semi-analytical way to get the dynamical response of the plate. Also, by using the Finite Element Method (FEM)... 

In this paper, the nonlinear transversal vibration of an axially moving viscoelastic string on a viscoelastic guide subjected to a mono-frequency excitation is considered. The model of the viscoelastic guide is a parallel combination of springs and viscous dampers. The governing equation of motion is developed using Hamilton's principle. Applying the method of multiple scales to the governing partial differential equation, the solvability condition and approximate solutions are derived. Three cases, namely primary, subharmonic and superharmonic resonances are studied and appropriate analytical solutions are obtained. The effect of mean value velocity, force amplitude, guide stiffness and... 

Nonlinear dynamics of an extensible cantilevered pipe conveying pulsating flow is considered in this paper. The fluid flow fluctuates harmonically and exhausts via a nozzle attached to the end of the pipe. Taking into account the extensibility assumption, the coupled nonlinear lateral–longitudinal equations of motion are derived using Hamilton's principle and discretized via Galerkin's method. The adaptive time step Adams algorithm is applied to extract the time response, and then the bifurcation, power spectral density and phase plane maps are plotted for some case studies. Effects of some geometrical parameters such as flow mass, pulsating flow frequency, gravity, nozzle mass and nozzle... 

In this paper, the planar maneuver of a flexible satellite with regard to its flexible appendages vibration has been studied. The flexible satellite translates and rotates in a plane; in addition, the flexible appendages can also vibrate in that plane. The system governing equations, which are coupled partial and ordinary differential equations, are obtained based on Hamilton's principle. Then the original system converts to three equivalent subsystems, two of which contains one partial differential equation and one ordinary differential equation along with four boundary conditions, by using change of variables. Employing control forces and one control torque which are applied to the central... 

This paper investigates the dynamic response of a clamped-free CNT-reinforced-MRE beam which is actuated by the combination of a constant and a harmonic time-dependent magnetic field. Using Hamilton's principle, the equation of motion has been obtained and discretized using the Galerkin method. This procedure transforms the governing PDE equation of motion into a nonlinear ODE equation in the form of the nonlinear Mathieu equation with cubic damping. Then, the method of multiple scales is employed to obtain the dynamic response of the system. Furthermore, a stability analysis is also performed and the effects of a magnetic field on the dynamic response and stability of the system is... 

A new beam theory different from the traditional first-order shear deformation beam theory is used to analyze free vibration of functionally graded beams. The beam properties are assumed to be varied through the thickness following a simple power law distribution in terms of volume fraction of material constituents. It is assumed that the lateral normal stress of the beam is zero and the governing equations of motion are derived using Hamilton's principle. Resulting system of ordinary differential equations of free vibration analysis is solved using an analytical method. Different boundary conditions are considered and comparisons are made among different beam theories. Also, the effects of... 

In this paper, a comprehensive assessment of design parameters for various beam theories subjected to a moving mass is investigated under different boundary conditions. The design parameters are adopted as the maximum dynamic deflection and bending moment of the beam. To this end, discrete equations of motion for classical Euler-Bernoulli, Timoshenko and higher-order beams under a moving mass are derived based on Hamilton's principle. The reproducing kernel particle method (RKPM) and extended Newmark-β method are utilized for spatial and time discretization of the problem, correspondingly. The design parameter spectra in terms of the beam slenderness, mass weight and velocity of the moving... 

Stability and dynamics of rotating coaxial cylindrical shells conveying incompressible and inviscid fluid are investigated. The interior shell is assumed to be flexible while the exterior cylinder is rigid. Using Sander's-Koiter theory assumptions and following Hamilton's principle, governing equations of motion are determined in their integral form. Employing the extended Galerkin method of solution, the integral equations of motion are projected to their equivalent system of algebraic equations. Fluid equations are fundamentally based on the linearized inviscid Navier-Stokes equations. Impermeability condition on the fluid and structure interface as well as the zero radial velocity... 

In this paper, the stability of pipes conveying fluid with viscoelastic fractional foundation is investigated. The pipe is fixed at the beginning while the pipe end is constrained with two lateral and rotational springs. The fluid flow effect is modeled as a lateral distributed force, containing the fluid inertia, Coriolis and centrifugal forces. The pipe is modeled using the Euler-Bernoulli beam theory and a fractional Kelvin-Voigt model is employed to describe the viscoelastic foundation. The equation of motion is derived using the extended Hamilton's principle. Presenting the derived equation in Laplace domain and applying the Galerkin method, a set of algebraic equations is extracted....