• Steel and Composite Structures
• /
• v.33 no.2
• /
• pp.307-318
• /
• 2019

This is the first attempt to consider the nonlinear bending analysis of porous functionally graded (FG) thick annular and circular nanoplates resting on Kerr foundation. The size effects are captured based on modified couple stress theory (MCST). The material properties of the porous FG nanostructure are assumed to vary smoothly through the thickness according to a power law distribution of the volume fraction of the constituent materials. The elastic medium is modeled by Kerr elastic foundation which consists of two spring layers and one shear layer. The governing equations are extracted based on Hamilton's principle and two variables refined plate theory. Utilizing generalized differential quadrature method (GDQM), the nonlinear static behavior of the nanostructure is obtained under different boundary conditions. The effects of various parameters such as material length scale parameter, boundary conditions, and geometrical parameters of the nanoplate, elastic medium constants, porosity and FG index are shown on the nonlinear deflection of the annular and circular nanoplates. The results indicate that with increasing the material length scale parameter, the nonlinear deflection is decreased. In addition, the dimensionless nonlinear deflection of the porous annular nanoplate is diminished with the increase of porosity parameter. It is hoped that the present work may provide a benchmark in the study of nonlinear static behavior of porous nanoplates.

• Transactions of the Korean Society for Noise and Vibration Engineering
• /
• v.18 no.5
• /
• pp.558-563
• /
• 2008

Vibration/shock affects biggest taking a train subtraction of vehicle and durability decline. Therefore, absorber is used for vibration/shock isolation and various qualities of the material and design are applied to isolation. This paper proposes vibration/shock absorber that applies 'Disc' spring. Through comparison with 'Disc' spring that has nonlinearity and coil spring that is having linearity, see effect that nonlinearity of isolation gets in vibration/shock Isolation. Coil spring and 'Disc' spring are non-linear numerical analysis and simulation through theory for this, get and investigate comparison result through an experiment finally. Expressed and formulated shock through 'Runge-Kutta' method/impact response to nonlinear-vibration-equation of 1 degree of freedom for numerical analysis. Double half sine pulse of excitation used and analyzed result through spectrum response analysis here. Response of disc spring is compared to response of coil spring by changing $h_o/t$ ratio with computer simulation and the usage of disc spring is increased through analysis of effect of design factors. The purpose of this paper is that the shock response of disc spring is calculated through numerical simulation and to design the optimal absorber under the limited condition. And then, the isolation effect was analyzed through the shock test.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 2008.04a
• /
• pp.990-993
• /
• 2008

Vibration/shock affects biggest taking a train subtraction of vehicle and durability decline. Therefore, absorber is used for vibration/shock isolation and various qualities of the material and design are applied to isolation. This paper proposes vibration/shock absorber that applies 'Disc'spring. Through comparison with 'Disc' spring that has nonlinearity and coil spring that is having linearity, see effect that nonlinearity of isolation gets in vibration/shock isolation. Coil spring and 'Disc' spring are non-linear numerical analysis and simulation through theory for this, get and investigate comparison result through an experiment finally. Expressed and formulated shock through 'Runge-Kutta' method/impact response to nonlinear-vibration-equation of 1 degree of freedom for numerical analysis. Double half sine pulse of excitation used and analyzed result through spectrum response analysis here. Response of disc spring is compared to response of coil spring by changing ho/t ratio with computer simulation and the usage of disc spring is increased through analysis of effect of design factors. The purpose of this paper is that the shock response of disc spring is calculated through numerical simulation and to design the optimal absorber under the limited condition. And then, the isolation effect was analyzed through the shock test.

• Journal of applied mathematics & informatics
• /
• v.8 no.2
• /
• pp.613-625
• /
• 2001

In this paper, we investigate a simplified model of a particle suspended elastically from two towers by two nonlinear elastic springs, with a restoring force similar to Hooke’s law under extension and with no resistance to compression. Numerical results are presented, showing the solutions can be either of the same period oscillation the forcing term, can be a subharmonic response of multiple period, or can be noisy periodic which is apparently chaotic. Multiplicity of periodic solutions for certain physical parameters are demonstrated.

• Korean Journal of Mathematics
• /
• v.14 no.1
• /
• pp.113-123
• /
• 2006

The arches may buckle in a symmetrical snap-through mode or in an asymmetry bifurcation mode if the load reaches a certain value. Each bifurcation curve develops as pressure increases. The governing equation is derived according to the bending theory. The balance of forces provides a nonlinear equilibrium equation. Bifurcation theory near trivial solution of the equation is developed, and the buckling pressures are investigated for various spring constants and opening angles.

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.12 no.2
• /
• pp.193-199
• /
• 1988

The forced vibrations of nondissipative nonlinear two-degree-of-freedom system, subjected to periodic forcing functions, are investigated by use of the method of slowly changing phase and amplitude. The first order differential equations are derived for nonrationally solutions and the coupled nonlinear algebraic equations for stationary solutions. Through investigating the response curves of the system, which are obtained numerically by using Newton-Raphson method, it is found that the resonances can occur at more than the number of degree-of-freedom of the system depending on the relation between the nonlinear spring parameters, which has no counterpart in linear systems.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 2005.05a
• /
• pp.424-429
• /
• 2005

In this paper, the response characteristics of one to one resonance on the rectangular cantilever beam in which basic harmonic excitations are applied by nonlinear coupled differential integral equations are studied. This equations have 3-dimensional non-linearity of nonlinear inertia and nonlinear curvature. Galerkin and multi scale methods are used for theoretical approach to one to one internal resonance. Nonlinear response characteristics of 1st, 2nd, 3rd modes are measured from the experiment for basic harmonic excitation. From the experimental result, geometrical terms of nonlinearity display light spring effect and these terms play an important role in the response characteristics of low frequency modes. Dynamic behaviors in the out of plane are also studied.

• International Journal of Precision Engineering and Manufacturing
• /
• v.3 no.4
• /
• pp.87-93
• /
• 2002

In this study, basic concepts of magnet were introduced, and dynamic characteristics of magnet coupling were explored. Based on these characteristics, it was proposed how to analyze transverse and torsional vibrations of a spindle system with magnet coupling. Proposed theoretical approaches were applied to a precision power transmission system machined for this study, and the transverse and torsional vibrations were simulated. The force on magnet coupling was shown as a form of nonlinear function of the gap and the eccentricity. Also, the form of torque transmitted by magnet coupling was considered as a sinusoidal function. Main spindle connected to a coupling of a follower part was assumed to be a rigid body. Nonlinear partial differential equation was derived to be as a function of angular displacement. By using the equation, torsional vibration analysis of a spindle system with magnet coupling was performed. Free and forced vibration analyses of a spindle system with magnetic coupling were explored by using FEM.

• Proceedings of the Korean Geotechical Society Conference
• /
• 2005.03a
• /
• pp.25-32
• /
• 2005

Modeling techniques of piled pier were reviewed and the influences of pile cap's boundary conditions were analyzed in this study. Among various modeling techniques, equivalent cantilever method seems relatively simple for modeling pile groups and it has some problems to determine the virtual fixed points. Through the analyses, it was found that the method of nonlinear p-y model with soil springs was more appropriate than equivalent cantilever method. The method modeling a pile group using stiffness matrix seems useful for practical design, which can represent the nonlinear three-dimensional behavior of a piled pier. In this study, the stiffness matrix of a pile group could be estimated efficiently and precisely using three-dimensional nonlinear analysis programs of pile groups (FBPier 3.0, YSGroup).

• Proceedings of the KSR Conference
• /
• 2010.06a
• /
• pp.1478-1485
• /
• 2010

In this paper, the nonlinear dynamic response of Vehicle-Bridge interaction with the coupled equations of motion including nonlinear Hertzian contact is presented. The moving train model is chosen to have 10 degrees of freedom (DOF). The bridge is modeled as 2D Euler-Bernoulli beam element with 4 DOF for each element, two for rotations and another two for translations. The nonlinear Hertzian contact is used to simulate the interaction between vehicle and bridge. Base on the relationship of wheel displacement of the vehicle and the vertical displacement of the bridge in Hertzian contact, the coupled equations of motion of the whole system is derived. The convenient formulation was encoded into a computer program. The contact forces, contact area and stress of the rail surface were also computed. The accuracy and efficiency of the proposed program are verified and compared with exact analytical solution and other previous studies. Various numerical examples and parametric studies have demonstrated the versatility and applicability of the proposed program.