Sharif Digital Repository

In this article, OPSEM (Orthonormal Polynomial Series Expansion Method) is developed as a new computational approach for the evaluation of thin beams of variable thickness transverse vibration. Capability of the OPSEM in assessing the free vibration frequencies and mode shapes of an Euler-Bernoulli beam with varying thickness is discussed. Multispan continuous beams with various classical boundary conditions are included. Contribution of BOPs (Basic Orthonormal Polynomials) in capturing the beam vibrations is also illustrated in numerical examples to give a quantitative measure of convergence rate. Furthermore, OPSEM is adopted for the forced vibration of a thin beam caused by a moving mass.... 

In this paper, boundary control (BC) laws are designed to find a BC solution for a single-link nonlinear vertical manipulator to suppress the link’s transverse vibrations and control the rigid body nonlinear large rotating motion. The governing equations of motions and boundary conditions, which all consist of a set of PDEs and ODEs have been derived based on the Hamilton principle. It is desired to regulate large angular orientation, suppress the flexible link’s transverse vibrations and compensate the boundary disturbance simultaneously. The amount of elastic boundary vibration has remained within the constraint range. By considering novel Barrier-Integral Lyapunov functional in order to... 

This paper aims at investigating free vibrations and stability of double-walled carbon nanotube (DWCNT)-based spinning nanobearings. The so-called nanobearing consists of two coaxial carbon nanotubes (CNTs) where either of the two CNTs can be a rotor while the other takes the role of stator. Euler–Bernoulli beam model along with the Eringen’s nonlocal theory of elasticity are employed to obtain governing equations of transverse vibrations for the CNTs. The coupling of the two CNTs originates from the van-der-Waals (vdW) forcing present in the interface of the two CNTs. The coupling is taken into account as distributed spring foundation with an equivalent elastic stiffness. Based on the... 

In this article, transverse vibration of an Euler-Bernoulli beam carrying a series of traveling masses is analyzed. A semi-analytical approach based on eigenfunction expansion method is employed to achieve the dynamic response of the beam. The inertia of the traveling masses changes the fundamental period of the base beam. Therefore, a comprehensive parametric survey is required to reveal the resonance velocity of the traversing inertial loads. In order to facilitate resonance detection for engineering practitioners, a new simplified formula is proposed to approximate the resonance velocity  

Chaos control of a spinning disk having transverse vibration is considered in this article by stabilizing the system on its corresponding unstable periodic orbit (UPO). At the first step, the system continuous-time dynamic equations are quantized by utilizing a proper Poincare map. Then, using the regression method a linear description from the obtained cross points is achieved around the corresponding fixed point of the target UPO. Finally, through solving the Riccati equation, an optimal controller is introduced which stabilizes the system on its unstable fixed point. At the end, the effectiveness of the proposed control method is examined through numerical simulations. © SAGE Publications... 

Tapered piezoelectric beams, because of their more efficiency to generate power, are required to be analyzed by simple models. In this paper, single degree of freedom (SDOF) relations are used to model transvers vibration of an exponentially tapered piezoelectric beam. For this purpose, first, response of the damped cantilevered Euler–Bernoulli beam with base excitation is obtained. Then, lumped parameters of the beam are extracted in order to calculate the SDOF model response. Comparing the Euler-Bernoulli beam model with the SDOF model shows that the lumped parameter model is not accurate enough to predict the beam’s response. Therefore, a tapering parameter dependent correction factor is... 

An experimental setup has been developed to analyse the impact of cylinder transverse vibration caused by flow-induced vibration, and to improve wind energy harvesting from these vibrations. The setup consists of a cylinder mounted on four springs and is subjected to a uniform and steady flow of wind. In the first part, the effect of mounting a fixed cylinder as an obstacle with different diameters and distances from the downstream vibrating cylinder is investigated. It has been observed that the vibration amplitude on the wake of an unequal-sized obstacle is greatly amplified compared to the case of a single cylinder or an equal-sized cylinder. Numerical simulations has been conducted to... 

In this paper, boundary control (BC) laws are designed to find a BC solution for a single-link nonlinear vertical manipulator to suppress the link’s transverse vibrations and control the rigid body nonlinear large rotating motion. The governing equations of motions and boundary conditions, which all consist of a set of PDEs and ODEs have been derived based on the Hamilton principle. It is desired to regulate large angular orientation, suppress the flexible link’s transverse vibrations and compensate the boundary disturbance simultaneously. The amount of elastic boundary vibration has remained within the constraint range. By considering novel Barrier-Integral Lyapunov functional in order to... 

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, 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... 

Since the efficiency of non-classical continuum theories is strongly dependent on the recognition of the suitable values of small length scale parameters and there is still uncertainty about them, a novel approach, equivalent lattice stiffness method is developed here. This approach without the characteristic length scale parameter which arises in non-classical continuum theories, such as nonlocal theory and strain gradient theory, is capable to capture size effect more easily and accurately. This method is proposed based on the concept of lattice dynamics but a Taylor series expansion is involved to approximate the displacements of the continuous domain; accordingly, this approach is in... 

Since the efficiency of non-classical continuum theories is strongly dependent on the recognition of the suitable values of small length scale parameters and there is still uncertainty about them, a novel approach, equivalent lattice stiffness method is developed here. This approach without the characteristic length scale parameter which arises in non-classical continuum theories, such as nonlocal theory and strain gradient theory, is capable to capture size effect more easily and accurately. This method is proposed based on the concept of lattice dynamics but a Taylor series expansion is involved to approximate the displacements of the continuous domain; accordingly, this approach is in... 

This paper aims to develop a boundary control solution for complicated gantry crane coupled motions. In addition to the large angle sway motion, the crane cable has a flexural transverse vibration. The Hamilton principle has been utilized to derive the governing partial differential equations of motion. The control objectives which are sought include: moving the payload to the desired position; reducing the payload swing with large sway angle; and finally suppressing the cable transverse vibrations in the presence of boundary disturbances simultaneously. These simultaneous boundary control objectives make the problem challenging. The proposed control approach is based on the original... 

This paper presents a solution to the boundary stabilization of a FGM plate in free transverse vibration. The composite laminated plate dynamics is presented by a linear forth order partial differential equation (PDE). A linear control law is constructed to stabilize the plate. The control force consists of feedback of the velocity at the boundaries of plate. The novelty of this article is that it is possible to stabilize asymptotically a free transversely vibrating composite plate with simply supported or clamped boundary condition via boundary control without resorting to truncation of the model. © 2008 IEEE  

An experimental setup has been developed to analyse the impact of cylinder transverse vibration caused by flow-induced vibration, and to improve wind energy harvesting from these vibrations. The setup consists of a cylinder mounted on four springs and is subjected to a uniform and steady flow of wind. In the first part, the effect of mounting a fixed cylinder as an obstacle with different diameters and distances from the downstream vibrating cylinder is investigated. It has been observed that the vibration amplitude on the wake of an unequal-sized obstacle is greatly amplified compared to the case of a single cylinder or an equal-sized cylinder. Numerical simulations has been conducted to... 

In this paper, the Nonlinear Normal Modes (NNMs) analysis for the case of three-to-one (3:1) internal resonance of a slender simply supported beam in presence of compressive axial load resting on a nonlinear elastic foundation is studied. Using the Euler- Bernoulli beam model, the governing nonlinear PDE of the beam's transverse vibration and also its associated boundary conditions are extracted. These nonlinear motion equation and boundary condition relations are solved simultaneously using four different approximate-analytical solution techniques, namely the method of Multiple Time Scales, the method of Normal Forms, the method of Shaw and Pierre, and the method of King and Vakakis. The... 

Single-walled carbon nanotubes (SWCNTs) can be promising delivery nanodevices for a diverse range of applications, however, little is known about their dynamical interactions with moving nanoscale particles. In this paper, dynamic response of a SWCNT subjected to a moving nanoparticle is examined in the framework of the nonlocal continuum theory of Eringen. The inertial effects of the moving nanoparticle and the existing friction between the nanoparticle surface and the inner surface of the SWCNT are incorporated in the formulation of the problem. The equivalent continuum structure associated with the SWCNT is considered and modeled using nonlocal Rayleigh beam theory under simply supported...