• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2005.05a
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• pp.983-986
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• 2005

Free vibration characteristics of a curved pipe conveying fluid is studied when the pipe is clamped at both ends. Using the perturbation method, the non-linear governing equations divided into two parts; the steady state non-linear equilibrium equations and the linearized equations of motion in the neighborhood of the equilibrium position. The natural frequencies are computed from the linearized equations of motion. In this study, the equilibrium positions are determined by two types of equations, i.e., (1) the non-linear equations, and (2) the equations obtained by neglecting the non-linear terms. The natural frequencies obtained from the non-linear equilibrium equations are compared to those obtained from the linearized equilibrium equations. From the results, as the fluid velocity increases, the equilibrium position should be determined from the nonlinear equations for the vibration analysis of the curved pipe conveying fluid.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2001.11a
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• pp.319-324
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• 2001

Free non-linear vibration of a rotating thin ring with a constant speed is analyzed when the ring has both the in-plane and out-of-plane motions. The geometric non-linearity of displacements is considered by adopting the Lagrange strain theory for the circumferential strain. By using Hamilton's principle, the coupled non-linear partial differential equations are derived, which describe the out-of-plane and in-plane bending, extensional and torsional motions. The natural frequencies are calculated from the linearized equations at various rotational speeds. Finally, the computation results from three non-linear models are compared with those from a linear model. Based on the comparison, this study recommends which model is appropriate to describe the non- linear behavior more precisely.

• Structural Engineering and Mechanics
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• v.88 no.5
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• pp.439-449
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• 2023

Non-linear vibration characteristics of functionally graded CNT-reinforced composite (FG-CNTRC) cylindrical shell panel on elastic foundation have not been sufficiently examined. In this situation, this study aims at the profound numerical investigation of the non-linear vibration response of FG-CNTRC cylindrical panels on Winkler-Pasternak foundation by introducing an accurate and effective 2-D meshfree-based non-linear numerical method. The large-amplitude free vibration problem is formulated according to the first-order shear deformation theory (FSDT) with the von Karman non-linearity, and it is approximated by Laplace interpolation functions in 2-D natural element method (NEM) and a non-linear partial derivative operator H_NL. The complex and painstaking numerical derivation on the curved surface and the crucial shear locking are overcome by adopting the geometry transformation and the MITC3+ shell elements. The derived nonlinear modal equations are iteratively solved by introducing a three-step iterative solving technique which is combined with Lanczos transformation and Jacobi iteration. The developed non-linear numerical method is estimated through the benchmark test, and the effects of foundation stiffness, CNT volume fraction and functionally graded pattern, panel dimensions and boundary condition on the non-linear vibration of FG-CNTRC cylindrical panels on elastic foundation are parametrically investigated.

• Steel and Composite Structures
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• v.15 no.4
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• pp.439-449
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• 2013

In this study simply supported nonlinear Euler-Bernoulli beams resting on linear elastic foundation and subjected to the axial loads is investigated. A new kind of analytical technique for a non-linear problem called He's Energy Balance Method (EBM) is used to obtain the analytical solution for non-linear vibration behavior of the problem. Analytical expressions for geometrically non-linear vibration of Euler-Bernoulli beams resting on linear elastic foundation and subjected to the axial loads are provided. The effect of vibration amplitude on the non-linear frequency and buckling load is discussed. The variation of different parameter to the nonlinear frequency is considered completely in this study. The nonlinear vibration equation is analyzed numerically using Runge-Kutta $4^{th}$ technique. Comparison of Energy Balance Method (EBM) with Runge-Kutta $4^{th}$ leads to highly accurate solutions.

• Structural Engineering and Mechanics
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• v.8 no.6
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• pp.547-560
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• 1999

In this paper an asymptotic iteration method is adopted to analyze non-linear free vibration of reticulated circular plates composed of beam members placed in two orthogonal directions. For the resulting linear ordinary differential equations in the process of iteration, the power series with rapid convergence has been applied to obtain an analytical solution for non-linear characteristic relation between the amplitude and frequency of the structure. Numerical examples are given, and the phenomena indicating hardening of such structures have been presented for the (immovable or movable) simply-supported and clamped circular plates.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 1996.10a
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• pp.282-287
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• 1996

The non-linear torsional vibrations of the propulsion shafting system with viscous damper are considered. The motion is modeled by non-linear differential equations of second order. the equivalent system is modeled by two mass softening system with Duffing's oscillator. The steady state response of a equivalent system is analyzed for primary resonance only. Harmonic balance method as a non-linear vibration analysis technique is used. Jump phenomena are explained. The primary unstable region obtained by the Mathieu equation is investigated. Both theoretical and measured results of the propulsion shafting system are compared with and evaluated. As a result of comparisons with both data, it was confirmed that Duffing's oscillator can be used as a analysis method in the modeling of the propulsion shafting system attached viscous damper with non-linear stiffness.

• Steel and Composite Structures
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• v.32 no.4
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• pp.509-519
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• 2019

In this paper, an analytical approach for the free vibration analysis of spiral stiffened functionally graded (SSFG) cylindrical shells is investigated. The SSFG shell is resting on linear and non-linear elastic foundation with damping force. The elastic foundation for the linear model is according to Winkler and Pasternak parameters and for the non-linear model, one cubic term is added. The material constitutive of the stiffeners is continuously changed through the thickness. Using the Galerkin method based on the von $K\acute{a}rm\acute{a}n$ equations and the smeared stiffeners technique, the non-linear vibration problem has been solved. The effects of different geometrical and material parameters on the free vibration response of SSFG cylindrical shells are adopted. The results show that the angles of stiffeners and elastic foundation parameters strongly effect on the natural frequencies of the SSFG cylindrical shell.

• 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.

• Journal of Advanced Marine Engineering and Technology
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• v.24 no.6
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• pp.7-14
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• 2000

Nowadays, the viscous damper using high viscosity oil was much to be used for engine shafting system to reduce the excessive additional stress by torsional vibration. In general, it was assumed that the viscous damper could be modelled having only damping coefficient, that is to say, whose stiffness be ignored. But it is found that there exists a jump phenomenon, as a kind of non-linear vibration, in the actual engine shafting system with a damper of high viscosity. Therefore the damper ring and the casing are modelled as two mass elastic system with a complex viscosity. Also, to analyze a non-linear phenomenon, it is assumed that the viscous damper has a linear stiffness coefficient in proportion to the angular amplitude and a non-linear stiffness coefficient in proportion to cube of the angular amplitude. For the analysis, Quasi-Newton method with BFGS(Broyden-Fletcher-Goldfarb-Shanno) formula is used. Both calculated and measured values are provided in this paper which confirm the possibility of applying non-linear theory to engine shafting system with viscous damper.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2008.11a
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• pp.192-194
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• 2008