• Structural Engineering and Mechanics
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• v.19 no.5
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• pp.535-550
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• 2005

The non-linear static and dynamic response of doubly curved thin isotropic shells has been studied for the step and sinusoidal loadings. Dynamic analogues Von Karman-Donnel type shell equations are used. Clamped immovable and simply supported immovable boundary conditions are considered. The governing nonlinear partial differential equations of the shell are discretized in space and time domains using the harmonic differential quadrature (HDQ) and finite differences (FD) methods, respectively. The accuracy of the proposed HDQ-FD coupled methodology is demonstrated by the numerical examples. Numerical examples demonstrate the satisfactory accuracy, efficiency and versatility of the presented approach.

• Structural Engineering and Mechanics
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• v.31 no.4
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• pp.383-392
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• 2009

The static and dynamic analyses of simply supported beams are studied by using the U-transformation method and the finite difference method. When the beam is divided into the mesh of equal elements, the mesh may be treated as a periodic structure. After an equivalent cyclic periodic system is established, the difference governing equation for such an equivalent system can be uncoupled by applying the U-transformation. Therefore, a set of single-degree-of-freedom equations is formed. These equations can be used to obtain exact analytical solutions of the deflections, bending moments, buckling loads, natural frequencies and dynamic responses of the beam subjected to particular loads or excitations. When the number of elements approaches to infinity, the exact error expression and the exact convergence rates of the difference solutions are obtained. These exact results cannot be easily derived if other methods are used instead.

• Proceedings of the KSR Conference
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• 2002.10a
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• pp.721-726
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• 2002

The topic on today is dynamic response analysis of curved bridge-AGT(Automated Guide-way Transit) vehicle interaction system. Rubber wheel type AGT vehicle is adopted in this study, and the vehicle is idealized as three dimensional eleven DOF model. Three types of composited steel box girder bridges are modelized with F.E. method. And three types of artificially generated surface roughnesses are adopted for analysis. The dynamic equations of curved bridge, AGT vehicle and surface roughness are derived by using Lagrange's equation of motion. And the equations are solved by Newmark-${\beta}$ method. As a result, The dynamic increasement factor is inverse proportional to radius curvature.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.28 no.5
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• pp.511-516
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• 2004

The dynamic behavior of an automatic ball balancer (ABB) is studied considering the effects of gravity and angular velocity profiles. In this study, a physical model for an ABB installed on the Jeffcott rotor is adopted in order to investigate the effects of gravity and angular acceleration. The equations of motion for the rotor with ABB are derived by using Lagrange's equation. Based on derived equations, dynamic responses for the rotor are computed by using the generalized-o method. From the computed responses, the effects of gravity and angular velocity profiles on the dynamic behavior are investigated. It is found that the balancing of the rotor with ABB can be achieved regardless of gravity. It Is also shown that a smooth velocity profile yields relatively smaller vibration amplitude than a non-smooth velocity profile.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.12 no.12
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• pp.979-985
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• 2002

The paper presents the dynamic stability of a vertical cantilevered pipe conveying fluid and haying translational linear spring supports. Real pipe systems may have some elastic hanger supports or other mechanical attached parts. which can be regarded as attached spring supports. Governing equations are derived by energy expressions, and numerical technique using Galerkin's method is applied to the equations of small motion of the pipe. Effects of spring supports on the dynamic stability of a vortical cantilevered pipe conveying fluid are fully investigated for various locations and spring constants of elastic supports.

• Journal of KSNVE
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• v.9 no.2
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• pp.355-362
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• 1999

Vibration reduction of an optical disk drive is achieved by an automatic ball balancer and dynamic behaviors of the drive are studied by theoretical approaches. Using Lagrange's equation, we derive 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 equilibrium positions, the Floquet theory is applied to the perturbed equations. On the other hand, time responses are computed by an explicit time integration method. We also investigate the effects of mass center and the position of the ABB on the dynamic behaviors of the system.

• Structural Engineering and Mechanics
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• v.22 no.1
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• pp.107-130
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• 2006

The paper deals with the numerical solution of the dynamic problem of masonry structures. Masonry is modelled as a non-linear elastic material with zero tensile strength and infinite compressive strength. Due to the non-linearity of the adopted constitutive equation, the equations of the motion must be integrated directly. In particular, we apply the Newmark or the Hilber-Hughes-Taylor methods implemented in code NOSA to perform the time integration of the system of ordinary differential equations obtained from discretising the structure into finite elements. Moreover, with the aim of evaluating the effectiveness of these two methods, some dynamic problems, whose explicit solutions are known, have been solved numerically. Comparisons between the exact solutions and the corresponding approximate solutions obtained via the Newmark and Hilber-Hughes-Taylor methods show that in the cases under consideration both numerical methods yield satisfactory results.

• Structural Engineering and Mechanics
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• v.87 no.2
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• pp.129-136
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• 2023

In this paper, dynamic buckling of truncated conical shell made of carbon nanotubes (CNTs) composite is studied. In aerospace industries, this category of structures is utilized extensively due to wide range of engineering applications. To calculate the effective material properties of the nanocomposite, The Mori-Tanaka model is applied. Also, the motion equations are derived with the assistance of the first order shear deformation theory (FSDT), Hamilton's principle and energy method. Besides, In order to solve motion equations and analyze dynamic instability region (DIR) of the structure, mixed model of differential quadrature method (DQM) and Bolotin's method is used. Moreover, investigation of the different parameters effects such as geometrical parameters and volume fraction of CNTs on the analysis of the DIR of the structure is done. In accordance with the obtained results, the DIR will occur at higher frequencies by increasing the volume fraction of CNTs.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.28 no.9
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• pp.1359-1367
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• 2004

The purpose of this study is to predict the dynamic transmission error of the helical gear system. To do so, the equations of motion in the helical gear system which consists of motor, coupling, gear, torque sensor, and brake are derived. As the input parameters, the mass moment of inertia by a 3D CAD software and the equivalent stiffness of the bearings and shaft are calculated and the coupling stiffness is measured. The static transmission error as an excitation is calculated by in-house program. Dynamic transmission error is predicted by solving the equations of motion. Mode shape, the dynamic mesh force and the bearing force are also calculated. In this analysis, the relationship between the dynamic mesh force and the bearing force and mode shape behavior in gear mesh are checked. As a result, the magnitude of mesh force is highly related with the gear mesh behavior in mode shape. The finite element analysis is conducted to find out the natural frequency of gear system. The natural frequencies by finite element analysis have a good agreement with the results by equation of motion. Finally, dynamic transmission error is measured by the specially designed experiment and the results by equation of motion are validated.

• Structural Engineering and Mechanics
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• v.67 no.6
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• pp.659-669
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• 2018

The Dynamic equations in the polar coordinates are drawn out using the MLPG method for the non-symmetric FG cylindrical shell. To simulate the mechanical properties of FGM, the nonlinear volume fractions for radial direction are used. The shape function applied in this paper is a form of the radial basis functions, by using this function all the requirements for an effective and suitable shape function are established. Hence in this study, the multiquadrics (MQ) radial basis functions are exploited as the shape function governing the problem. The MLPG method is combined with the the Newmark time approximation scheme to solve dynamic equations in the time domain. The obtained results by the MLPG method to be verified are compared with the analytical solution and the FEM. The obtained results through the MLPG method show a good agreement in comparison to other results and the MLPG method has high accuracy for dynamic analysis of the non-symmetric FG cylindrical shell. To demonstrate the capability of the present method to dynamic analysis of the non-symmetric FG cylindrical shell, it is analyzed dynamically with different volume fraction exponents under harmonic and rectangular shock loading. The present method shows high accuracy, efficiency and capability to dynamic analysis of the non-symmetric FG cylindrical shell with nonlinear grading patterns.