• Transactions of the Korean Society of Mechanical Engineers A
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• v.30 no.2 s.245
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• pp.171-178
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• 2006

Experimental and theoretical study of the non-planar response motions of a circular cantilever beam subject to base harmonic excitation has been presented in this paper work. Theoretical research is conducted using two non-linear coupled integral-differential equations of motion. These equations contain cubic linearities due do curvature term and inertial term. A combination of the Galerkin procedure and the method of multiple scales are used to construct a first-order uniform expansion for the case of one-to-one resonance. The results show that the non-linear geometric terms are very important for the low-frequency modes of the first and second mode. The non-linear inertia terms are also important for the high-frequency modes. We present the quantitative and qualitative results for non-planar motions of the dynamic behavior.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2005.11a
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• pp.690-695
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• 2005

Flexible circular cantilever beams when excited externally introduce a lot of dynamic characteristics. The non-linear elements that these flexible beams develop include non-linearity due to inertia terms, spring, and damping. They show different characteristics of motion from each other. In the modes of lower order, the non-linearity due to spring is prevalent, while the non-linearity due to inertia Is prevalent in the modes of higher order. To analyze these effects the non-linear phenomena are analyzed experimentally. When the response characteristics of non-linear vibration are analyzed using autospectrum, it is possible to analyze the subharmonic and superharmonic mot ion by comparison. The phase change is analyzed using the method of phase portrait and the non-linear characteristics of response characteristics that are developed in flexible structures can be predicted and applied to the stage of design.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2003.05a
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• pp.677-682
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• 2003

The non-linear dynamic characteristics of a semi-circular pipe conveying fluid are investigated when the pipe is clamped at both ends. To consider the geometric non-linearity for the radial and circumferential displacements, this study adopts the Lagrange strain theory for large deformation and the extensible dynamics based on the Euler-Bernoulli beam theory for slenderness assumption. By using the Hamilton principle, the non-linear partial differential equations are derived for the in-plane motions of the pipe, considering the fluid inertia forces as a kind of non-conservative forces. The linear and non-linear terms in the governing equations are compared with those in the previous study, and some significant differences are discussed. To investigate the dynamic characteristics of the system, the discretized equations of motion are derived form the Galerkin method. The natural frequencies varying with the flow velocity are computed fen the two cases, which one is the linear problem and the other is the linearized problem in the neighborhood of the equilibrium position. Finally, the time responses at various flow velocities are directly computed by using the generalized- method. From these results, we should to describe the non-linear behavior to analyze dynamics of a semi-circular pipe conveying fluid more precisely.

• Structural Engineering and Mechanics
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• v.24 no.5
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• pp.601-620
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• 2006

The paper presents an effective stiffness model for deformational analysis of reinforced concrete cracked members in bending throughout the short-term loading up to the near failure. The method generally involves the analytical derivation of an effective moment of inertia based on the smeared crack technique. The method, in a simplified way, enables us to take into account the non linear properties of concrete, the effects of cracking and tension stiffening. A statistical analysis has shown that proposed technique is of adequate accuracy of calculated and experimental deflections data provided for beams with small, average and normal reinforcement ratios.

• Structural Engineering and Mechanics
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• v.1 no.1
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• pp.87-102
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• 1993

A $C^{\circ}$ continuous finite element formulation of a higher order displacement theory is presented for predicting linear and geometrically non-linear in the sense of von Karman transient responses of composite and sandwich plates. The displacement model accounts for non-linear cubic variation of tangential displacement components through the thickness of the laminate and the theory requires no shear correction coefficients. In the time domain, the explicit central difference integrator is used in conjunction with the special mass matrix diagonalization scheme which conserves the total mass of the element and included effects due to rotary inertia terms. The parametric effects of the time step, finite element mesh, lamination scheme and orthotropy on the linear and geometrically non-linear responses are investigated. Numerical results for central transverse deflection, stresses and stress resultants are presented for square/rectangular composite and sandwich plates under various boundary conditions and loadings and these are compared with the results from other sources. Some new results are also tabulated for future reference.

• Structural Engineering and Mechanics
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• v.61 no.2
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• pp.193-207
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• 2017

In this study, the vibration of an electrostatically actuated micro cantilever beam is analyzed in which a viscoelastic layer covers a portion of the micro beam length. This proposed model is considered as the main element of mass and pollutant micro sensors. The nonlinear motion equation is extracted by means of Hamilton principle, considering nonlinear shortening effect for Euler-Bernoulli beam. The non-linear effects of electrostatic excitation, geometry and inertia have been taken into account. The viscoelastic model is assumed as Kelvin-Voigt model. The motion equation is discretized by Galerkin approach. The linear free vibration mode shapes of non-uniform micro beam i.e. the linear mode shape of the system by considering the geometric and inertia effects of viscoelastic layer, have been employed as comparison function in the process of the motion equation discretization. The discretized equation of motion is solved by the use of multiple scale method of perturbation theory and the results are compared with the results of numerical Runge-Kutta approach. The frequency response variations for different lengths and thicknesses of the viscoelastic layer have been founded. The results indicate that if a constant volume of viscoelastic layer is to be deposited on the micro beam for mass or gas sensor applications, then a modified configuration may be found by using the analysis of this paper.

• International Journal of Ocean System Engineering
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• v.1 no.3
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• pp.120-135
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• 2011

This paper proposes a model based trajectory tracking control scheme for under-actuated underwater robotic vehicles. The difficulty in stabilizing a non-linear system using smooth static state feedback law means that the design of a feedback controller for an under-actuated system is somewhat challenging. A necessary condition for the asymptotic stability of an under-actuated vehicle about a single equilibrium is that its gravitational field has nonzero elements corresponding to non-actuated dynamics. To overcome this condition, we propose a continuous time-varying control law based on the direct estimation of vehicle dynamic variables such as inertia, damping and Coriolis & centripetal terms. This can work satisfactorily under commonly encountered uncertainties such as an ocean current and parameter variations. The proposed control law cancels the non-linearities in the vehicle dynamics by introducing non-linear elements in the input side. Knowledge of the bounds on uncertain terms is not required and it is conceptually simple and easy to implement. The controller parameter values are designed using the Taguchi robust design approach and the control law is verified analytically to be robust under uncertainties, including external disturbances and current. A comparison of the controller performance with that of a linear proportional-integral-derivative (PID) controller and sliding mode controller are also provided.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2001.11b
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• pp.989-993
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• 2001

This paper deals with the free vibrations of horizontally curved beams supported by non-homogeneous elastic foundation. Taking into account the effects of rotatory inertia and shear deformation, differential equations governing the free vibrations of such beams are derived, in which the linear elastic foundation is considered as the non-homogeneous foundation. Differential equations are solved numerically to calculate natural frequencies. In numerical examples, the parabolic curved member is considered. The parametric studies are conducted and the lowest four frequency parameters are reported in tables and figures as the non-dimensional forms.

• Structural Engineering and Mechanics
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• v.34 no.4
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• pp.507-523
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• 2010

Parametric and forced non-linear vibrations of an axially moving rotor both in non-resonance and near-resonance cases have been investigated analytically in this paper. The axial speed is assumed to involve a mean value along with small harmonic fluctuations. Hamilton's principle is employed for this gyroscopic system to derive three coupled non-linear equations of motion. Longitudinal inertia is neglected under the quasi-static stretch assumption and two integro-partial-differential equations are obtained. With introducing a complex variable, the equations of motion is presented in the form of a single, complex equation. The method of multiple scales is applied directly to the resulting equation and the approximate closed-form solution is obtained. Stability boundaries for the steady-state response are formulated and the frequency-response curves are drawn. A number of case studies are considered and the numerical simulations are presented to highlight the effects of system parameters on the linear and nonlinear natural frequencies, mode shapes, limit cycles and the frequency-response curves of the system.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.14 no.12
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• pp.1314-1321
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• 2004

The non-linear responses of a slender rectangular cantilever beam subjected to lateral harmonic base-excitation are investigated by the 2-channel FFT analyzer. Both linear and nonlinear behaviors of the cantilever beam are compared with each other. Bending mode, torsional mode, and transverse mode are coupled in such a way that the energy transfer between them are observed. Especially, superharmonic, subharmonic, and chaotic motions which result from the unstable inertia terms in the transverse mode are analyzed by the FFT analyzer The aim is to give the explanations of the route to chaos, i.e., harmonic motion \longrightarrow superharmonic motion \longrightarrow subharmonic motion \longrightarrow chaos.