• 한국소음진동공학회:학술대회논문집
• /
• 한국소음진동공학회 2006년도 춘계학술대회논문집
• /
• pp.666-671
• /
• 2006

This paper proposes a method to calculate the stiffness and the damping coefficients of the coupled journal and thrust bearings. The Reynolds equations and their perturbation equations are transformed to the finite element equations by considering the continuity of pressure and flow at the interface between bearings. The Reynolds boundary condition is used in the numerical analysis to simulate the cavitation phenomena. The dynamic coefficients of the proposed method are compared with those of the numerical differentiation of the loads with respect to finite displacements and velocities of bearing center. It shows that the proposed method is more accurate and efficient than the differentiation method.

• Steel and Composite Structures
• /
• 제41권6호
• /
• pp.821-829
• /
• 2021

Nonlinear dynamic response of a sandwich beam considering porous core and nano-composite face sheet on nonlinear viscoelastic foundation with temperature-variable material properties is investigated in this research. The Hamilton's principle and beam theory are used to drive the equations of motion. The nonlinear differential equations of sandwich beam respect to time are obtained to solve nonlinear differential equations by Homotopy perturbation method (HPM). The effects of various parameters such as linear and nonlinear damping coefficient, linear and nonlinear spring constant, shear constant of Pasternak type for elastic foundation, temperature variation, volume fraction of carbon nanotube, porosity distribution and porosity coefficient on nonlinear dynamic response of sandwich beam are presented. The results of this paper could be used to analysis of dynamic modeling for a flexible structure in many industries such as automobiles, Shipbuilding, aircrafts and spacecraft with solar easured at current time step and the velocity and displacement were estimated through linear integration.

• Structural Engineering and Mechanics
• /
• 제82권2호
• /
• pp.191-204
• /
• 2022

A three-mass vehicle model including one rigid mass and two unsprung masses is adopted to predict the vehicle-bridge interaction (VBI) and to establish the nonlinear coupled governing equations. To overcome the numerical instability and large computation problems concerning the vehicle-bridge system, the perturbation method is used to convert the nonlinear coupled governing equations into a set of linear uncoupled equations. Formulas for bridge's natural frequencies considering both the VBI and the dynamic responses of bridge and vehicle are proposed. Compared with the numerical results obtained by the Newmark-β method, the theoretical solutions for natural frequencies and dynamic responses are validated. The effects of the important factors of unsprung mass, vehicle damping, surface irregularity on the natural frequencies and dynamic responses of bridge and vehicle are discussed, based on the theoretical solutions.

• Structural Engineering and Mechanics
• /
• 제62권5호
• /
• pp.607-618
• /
• 2017

In this paper, an analytical procedure based on the perturbation technique is presented to study the free vibrations of annular viscoelastic plates by considering the first order shear deformation theory as the displacement field. The viscoelastic properties obey the standard linear solid model. The equations of motion are extracted for small deflection assumption using the Hamilton's principle. These equations which are a system of partial differential equations with variable coefficients are solved analytically with the perturbation technique. By using a new variable change, the governing equations are converted to equations with constant coefficients which have the analytical solution and they are appropriate especially to study the sensitivity analysis. Also the natural frequencies are calculated using the classical plate theory and finite elements method. A parametric study is performed and the effects of geometry, material and boundary conditions are investigated on the vibrational behavior of the plate. The results show that the first order shear deformation theory results is more closer than to the finite elements with respect to the classical plate theory for viscoelastic plate. The more results are summarized in conclusion section.

• 대한기계학회논문집A
• /
• 제26권4호
• /
• pp.764-774
• /
• 2002

Dynamic behaviors are analyzed for an automatic ball balancer (ABB) with triple races, which is a device to reduce the unbalanced mass of optical disk drives (ODD) such as CD-ROM or DVD drives. The nonlinear equations of motion are derived by using Lagrange's equations with the polar coordinate system. It is shown that the polar coordinate system provides the complete stability analysis while the rectangular coordinate system used in other previous studies has limitations on the stability analysis. For the stability analysis, the equilibrium positions and the linearized perturbation equations are obtained by the perturbation method. Based on the linearized equations, the stability of the system is analyzed around the equilibrium positions; furthermore, to confirm the stability, the time responses for the nonlinear equations of motion are computed by using a time integration method and experimental analyses are performed. Theoretical and experimental results show a superiority of the ABB with triple races.

• Structural Engineering and Mechanics
• /
• 제40권5호
• /
• pp.689-703
• /
• 2011

A new perturbation method is introduced to study the undamped free vibration of a non-prismatic Timoshenko beam for its natural frequencies and vibration modes. For simplicity, the natural modes of vibration of its corresponding prismatic Euler-Bernoulli beam with the same length and boundary conditions are used as Ritz base functions with necessary modifications to account for shear strain in the Timoshenko beam. The new method can transform two coupled partial differential equations governing the transverse vibration of the non-prismatic Timoshenko beam into a set of nonlinear algebraic equations. It significantly simplifies the solution process and is applicable to non-prismatic beams with various boundary conditions. Three examples indicated that the new method is more accurate than the previous perturbation methods. It successfully takes into account the effect of shear deformation of Timoshenko beams particularly at the free end of cantilever structures.

• 한국소음진동공학회:학술대회논문집
• /
• 한국소음진동공학회 2002년도 추계학술대회논문집
• /
• pp.994-999
• /
• 2002

The Pendulum Automatic Dynamic Balancer is a device to reduce the unbalanced mass of rotors. For the analysis of dynamic stability and behavior, the nonlinear equations of motion for a system including the Pendulum Balancer are derived with respect to polar coordinate by Lagrange's equations. And the perturbation method is applied to find the equilibrium positions and to obtain the linear variation equations. Based on the linearized equations, the dynamic stability of the system around the equilibrium positions is investigated by the eigenvalue problem. Furthermore, in order to confirm the stability, the time responses for the system are computed from the nonlinear equations of motion.

• 소음진동
• /
• 제7권3호
• /
• pp.387-392
• /
• 1997

This paper concerns a SCARA robot with the flexible forearm linked to the rigid upper arm. The equations of motion are derived by the Lagrangian mechanics. For controller design, the perturbation approach is taken to separate the original equations of motion into linear equations describing small perturbed motions and nonlinear equations describing purely rigid motion of the robot. To effect the desired payload motion, open loop control inputs are determined based on the inverse dynamics of the latter. In order to reduce the positional error during maneuver, an active vibration suppression is done. To this end, a feedback control is designed for robustness against disturbance on the basis of the linear equations and the LQR theory modified to have a prescribed degree of stability. The proposed control scheme shows satisfactory performances in experiments as well as in numerical simulations.

• 제어로봇시스템학회:학술대회논문집
• /
• 제어로봇시스템학회 1996년도 한국자동제어학술회의논문집(국내학술편); 포항공과대학교, 포항; 24-26 Oct. 1996
• /
• pp.225-228
• /
• 1996

This paper concerns a SCARA type robot with the second arm flexible. Its equations of motion are derived by the Lagrangian mechanics. For controller design, the perturbation approach is taken to separate the original equations of motion into linear equations describing small perturbed motions and nonlinear equations describing purely rigid motion of the robot. To effect the desired payload motion, open loop control inputs are first determined based on the inverse dynamics of the latter. Next, in order to reduce the positional error during maneuver, an active vibration suppression is done. To this end, a feedback control is designed for robustness against disturbance on the basis of the linear equations and the LQR theory modified with a prescribed degree of stability. The numerical simulations results show the satisfactory control performance.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• 제13권2호
• /
• pp.109-121
• /
• 2009

In this paper, we use He's polynomials for solving higher order integro differential equations (IDES) by converting them to an equivalent system of integral equations. The He's polynomials which are easier to calculate and are compatible to Adomian's polynomials are found by using homotopy perturbation method. The analytical results of the equations have been obtained in terms of convergent series with easily computable components. Several examples are given to verify the reliability and efficiency of the proposed method.