• 대한기계학회논문집A
• /
• 제26권12호
• /
• pp.2511-2518
• /
• 2002

Dynamic behaviors and stability of an optical disk drive coupled with an automatic ball balancer (ABB) are analyzed by a theoretical approach. The feeding system is modeled a rigid body with six degree-of-freedom. Using Lagrange's equation, we derive the nonlinear equations of motion for a non -autonomous system with respect to the rectangular coordinate. To investigate the dynamic stability of the system in the neighborhood of the equilibrium positions, the monodromy matrix technique is applied to the perturbed equations. On the other hand, time responses are computed by the Runge -Kutta method. We also investigate the effects of the damping coefficient and the position of ABB on the dynamic behaviors of the system.

• 한국소음진동공학회:학술대회논문집
• /
• 한국소음진동공학회 2001년도 추계학술대회논문집 II
• /
• pp.983-988
• /
• 2001

Dynamic behaviors and stability of an optical disk drive coupled with an automatic ball balancer(ABB) are analyzed by a theoretical approach. The feeding system is modeled a rigid body with six degree-of-freedom. Using Lagrange's equation, we derive the nonlinear equations of motion for a non-autonomous system with respect to the rectangular coordinate. To investigate the dynamic stability of the system in the neighborhood of the equilibrium positions, the monodromy matrix technique is applied to the perturbed equations. On the other hand, time responses are computed by the Runge-Kutta method. We also investigate the effects of the damping coefficient and the position of ABB on the dynamic behaviors of the system.

• Advances in nano research
• /
• 제13권3호
• /
• pp.285-295
• /
• 2022

Creation of plastic deformation under seismic loads, is one of the most serious subjects in RC structures with steel bars which reduces the life threatening risks and increases dissipation of energy. Shape memory alloy (SMA) is one of the best choice for the relocating plastic hinges. In a challenge to study the seismic response of concrete moment resisting frame (MRF), this article investigates numerically a new type of concrete frames with nano fiber reinforced polymer (NFRP) and shape memory alloy (SMA) hinges, simultaneously. The NFRP layer is containing carbon nanofibers with agglomeration based on Mori-Tanaka model. The tangential shear deformation (TASDT) is applied for modelling of the structure and the continuity boundary conditions are used for coupling of the motion equations. In SMA connections between beam and columns, since there is phase transformation, hence, the motion equations of the structure are coupled with kinetic equations of phase transformation. The Hernandez-Lagoudas theory is applied for demonstrating of pseudoelastic characteristics of SMA. The corresponding motion equations are solved by differential cubature (DC) and Newmark methods in order to obtain the peak ground acceleration (PGA) and residual drift ratio for MRF-2%. The main impact of this paper is to present the influences of the volume percent and agglomeration of nanofibers, thickness and length of the concrete frame, SMA material and NFRP layer on the PGA and drift ratio. The numerical results revealed that the with increasing the volume percent of nanofibers, the PGA is enhanced and the residual drift ratio is reduced. It is also worth to mention that PGA of concrete frame with NFRP layer containing 2% nanofibers is approximately equal to the concrete frame with steel bars.

• Structural Engineering and Mechanics
• /
• 제39권6호
• /
• pp.861-875
• /
• 2011

The aim of the present article is to study the micropolar thermoelastic interactions in an infinite Kelvin-Voigt type viscoelastic thermally conducting plate. The coupled dynamic thermoelasticity and generalized theories of thermoelasticity, namely, Lord and Shulman's and Green and Lindsay's are employed by assuming the mechanical behaviour as dynamic to study the problem. The model has been simplified by using Helmholtz decomposition technique and the resulting equations have been solved by using variable separable method to obtain the secular equations in isolated mathematical conditions for homogeneous isotropic micropolar thermo-viscoelastic plate for symmetric and skew-symmetric wave modes. The dispersion curves, attenuation coefficients, amplitudes of stresses and temperature distribution for symmetric and skew-symmetric modes are computed numerically and presented graphically for a magnesium crystal.

• Coupled systems mechanics
• /
• 제9권6호
• /
• pp.539-562
• /
• 2020

In this paper the linear elastic coupling between a 2 degree of freedom shear-type frame system and a rigid block is analytically and experimentally investigated. As demonstrated by some of the authors in previous papers, it is possible to choose a coupling system able to guarantee advantages, whatever the mechanical characteristics of the frame. The main purpose of the investigation is to validate the analytical model. The nonlinear equations of motion of the coupled system are obtained by a Lagrangian approach and successively numerically integrated under harmonic and seismic excitation. The results, in terms of gain graphs, maps and spectra, represent the ratio between the maximum displacements or drifts of the coupled and uncoupled systems as a function of the system's parameters. Numerical investigations show the effectiveness of the nonlinear coupling for a large set of parameters. Thus experimental tests are carried out to verify the analytical results. An electro-dynamic long-stroke shaker sinusoidally and seismically forces a shear-type 2 d.o.f frame coupled with a rigid aluminium block. The experimental investigations confirm the effectiveness of the coupling as predicted by the analytical model.

• 한국소음진동공학회논문집
• /
• 제13권8호
• /
• pp.598-604
• /
• 2003

In this paper a general solution method is presented to obtain the unbalance response orbit from the finite element based equations of motion of a gear-coupled two-shaft rotor-bearing system, whose shafts rotate at their different speeds from each other. Particularly, are proposed analytical solutions of the maximum and minimum radii of the orbit. The method has been applied to analyze the unbalance response of a 800 refrigeration-ton turbo-chiller rotor-bearing system having a bull-pinion speed increasing gear. Bumps in the unbalance response of the driven high speed compressor rotor system have been observed at the first torsional natural frequency due to the coupling effect of lateral and torsional dynamics. Further, the proposed analytical solutions have agreed well with those obtained by a full numerical approach. The proposed analytical solutions can be generally applied to obtain the maximum and minimum radii of the unbalance response orbits of dual-shaft rotor-bearing systems coupled by bearings as well.

• Structural Engineering and Mechanics
• /
• 제66권5호
• /
• pp.595-608
• /
• 2018

This paper deals with the lateral - torsional motion of bridges provided with external cables acting as dampers under the action of horizontal dynamic loads or of walking human crowd loads. A three dimensional analysis is performed for the solution of the bridge models. The theoretical formulation is based on a continuum approach, which has been widely used in the literature to analyze bridges. The resulting equations of the uncoupled motion are solved using the Laplace Transformation, while the case of the coupled motion is solved through the use of the potential energy. Finally, characteristic examples are presented and useful results are obtained.

• Structural Engineering and Mechanics
• /
• 제88권5호
• /
• pp.405-417
• /
• 2023

This paper reveals theoretical research to the nonlinear dynamic response and initial geometric imperfections sensitivity of the spinning graphene platelets reinforced metal foams (GPLRMF) cylindrical shell under different boundary conditions in thermal environment. For the theoretical research, with the framework of von-Karman geometric nonlinearity, the GPLRMF cylindrical shell model which involves Coriolis acceleration and centrifugal acceleration caused by spinning motion is assumed to undergo large deformations. The coupled governing equations of motion are deduced using Euler-Lagrange principle and then solved by a combination of Galerkin's technique and modified Lindstedt Poincare (MLP) model. Furthermore, the impacts of a set of parameters including spinning velocity, initial geometric imperfections, temperature variation, weight fraction of GPLs, GPLs distribution pattern, porosity distribution pattern, porosity coefficient and external excitation amplitude on the nonlinear harmonic resonances of the spinning GPLRMF cylindrical shells are presented.

• Advances in Computational Design
• /
• 제9권1호
• /
• pp.73-80
• /
• 2024

The aim of this paper is to remove the rigid body motion in the interior boundary value problem (BVP) of plane elasticity by solving the interior and exterior BVPs simultaneously. First, we formulate the interior and exterior BVPs simultaneously. The tractions applied on the contour in two problems are the same. After adding and subtracting the two boundary integral equations (BIEs), we will obtain a couple of BIEs. In the coupled BIEs, the properties of relevant integral operators are modified, and those integral operators are generally invertible. Finally, a unique solution for boundary displacement of interior region can be obtained.

• Structural Engineering and Mechanics
• /
• 제73권3호
• /
• pp.319-330
• /
• 2020

This paper investigates the free vibrations of cylindrical shells made of time-dependent materials for different viscoelastic models under various boundary conditions. During the extraction of equations, the displacement field is estimated through the first-order shear deformation theory taking into account the transverse normal strain effect. The constitutive equations follow Hooke's Law, and the kinematic relations are linear. The assumption of axisymmetric is included in the problem. The governing equations of thick viscoelastic cylindrical shell are determined for Maxwell, Kelvin-Voigt and the first and second types of Zener's models based on Hamilton's principle. The motion equations involve four coupled partial differential equations and an analytical method based on the elementary theory of differential equations is used for its solution. Relying on the results, the natural frequencies and mode shapes of viscoelastic shells are identified. Conducting a parametric study, we examine the effects of geometric and mechanical properties and boundary conditions, as well as the effect of transverse normal strain on natural frequencies. The results in this paper are compared against the results obtained from the finite elements analysis. The results suggest that solutions achieved from the two methods are ideally consistent in a special range.