• Structural Engineering and Mechanics
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• 제34권4호
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• pp.491-505
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• 2010

A computational analysis of the nonlinear free vibration of corrugated annular plates with shallow sinusoidal corrugations under uniformly static ambient temperature is examined. The governing equations based on Hamilton's principle and nonlinear bending theory of thin shallow shell are established for a corrugated plate with a concentric rigid mass at the center and rotational springs at the outer edges. A simple harmonic function in time is assumed and the time variable is eliminated from partial differential governing equations using the Kantorovich averaging procedure. The resulting ordinary equations, which form a nonlinear two-point boundary value problem in spatial variable, are then solved numerically by shooting method, and the temperature-dependent characteristic relations of frequency vs. amplitude for nonlinear vibration of heated corrugated annular plates are obtained. Several numerical results are presented in both tabular and graphical forms, which demonstrate the accuracy of present method and illustrate the amplitude frequency dependence for the plate under such parameters as ambient temperature, plate geometry, rigid mass and elastic constrain.

• Steel and Composite Structures
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• 제45권5호
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• pp.641-652
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• 2022

Fluid-conveying tubes are widely used to transport oil and natural gas in industries. As an advanced composite material, functionally graded carbon nanotube-reinforced composites (FG-CNTRC) have great potential to empower the industry. However, nonlinear free vibration of the FG-CNTRC fluid-conveying pipe has not been attempted in thermal environment. In this paper, the nonlinear free vibration characteristic of functionally graded nanocomposite fluid-conveying pipe reinforced by single-walled carbon nanotubes (SWNTs) in thermal environment is investigated. The SWCNTs gradient distributed in the thickness direction of the pipe forms different reinforcement patterns. The material properties of the FG-CNTRC are estimated by rule of mixture. A higher-order shear deformation theory and Hamilton's variational principle are employed to derive the motion equations incorporating the thermal and fluid effects. A two-step perturbation method is implemented to obtain the closed-form asymptotic solutions for these nonlinear partial differential equations. The nonlinear frequencies under several reinforcement patterns are presented and discussed. We conduct a series of studies aimed at revealing the effects of the flow velocity, the environment temperature, the inner-outer diameter ratio, and the carbon nanotube volume fraction on the nature frequency.

• 한국소음진동공학회논문집
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• 제26권7호
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• pp.795-805
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• 2016

Nonlinear normal modes(NNMs) is a branch of periodic solution of nonlinear dynamic systems. Determination of stable periodic solution is very important in many engineering applications since the stable periodic solution can be an attractor of such nonlinear systems. Periodic solutions of nonlinear system are usually calculated by perturbation methods and numerical methods. In this study, numerical method is used in order to calculate the NNMs. Iteration of the solution is presented by multiple shooting method and continuation of solution is presented by pseudo-arclength continuation method. The stability of the NNMs is analyzed using Floquet multipliers, and bifurcation points are calculated using indirect method. Proposed analyses are applied to two nonlinear numerical models. In the first numerical model nonlinear spring-mass system is analyzed. In the second numerical model Jeffcott rotor system which has unstable equilibria is analyzed. Numerical simulation results show that the multiple shooting method can be applied to self excited system as well as the typical nonlinear system with stable equilibria.

• Structural Engineering and Mechanics
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• 제6권3호
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• pp.347-362
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• 1998

In this study an improved design method for the traditional A-type(or V-type) offshore template platform system was proposed to mitigate the vibration induced by the marine environmental loadings and the strong ground motions of earthquakes. A newly developed material model was combined into the structural system and then a nonlinear dynamic analysis in the time domain was carried out. The analysis was focused on the displacement and rotation induced by the input wave forces and ground motions, and the mitigation effect for these responses was evaluated when the viscoelastic damping devices were applied. The wave forces exerted on the offshore structures are based on Stokes fifth-order wave theory and Morison equation for small body. A step by step integration method was modified and used in the nonlinear analysis. It was found that the new design approach enhanced with viscoelastic dampers was efficient on the vibration mitigation for the structural system subjected to both the wave motion and the strong ground motion.

• 대한의용생체공학회:의공학회지
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• 제14권1호
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• pp.31-40
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• 1993

It is well known that nonlinear propagation characteristics of the wave in the tissue may give very useful information for the medical diagnoisis. In this paper, a new method to detect nonlinear propa gation characteristics of the internal vibration in the tissue for the low frequency mechanical vibra lion by using bispectral analysis is proposed. In the method, low frequency vibration of $f_0(=100Hz)$ is applied on the surface of the object, and the waveform of the internal vibration ${\times}{\;}(t)$ is measured from Doppler frequency modulation of silmultaneously transmitted probing ultrasonic waves. Then, the bispectra of the signal ${\times}{\;}(t.)$ at the frequencies ($f_0,{\;}f_0$) and ($f_0,{\;}2f_0$) are calculated to estimate the nonlinear propagation characteristics as their magnitude ratio, where since bispectrum is free from the gallssian additive noise we can get the value with high S/N. Basic experimental system is con structed by using 3.0 MHz probing ultrasonic waves and the several experiments are carried out for some phantoms. Results show the superiority of the proposed method to the conventional method using power spectrum and also its usefulness for the tissue characterization.

• 대한기계학회논문집A
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• 제20권4호
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• pp.1251-1262
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• 1996

In this paper, a mathematical model for a belt driven system is proposed to analyse the vibration characteristics of the driving units with belts and the free and forced vibraiton anlyses are carried out. The mathematical model for a belt-driven system includes belts, pulleys, spindle and bearings. By using Hamilton's principle, four nonlinear governing equations and twelve nonlinear boundary conditions are derived. To linearize and discretize the nonlinear governing equations and boundary conditions, the perturbation method and Galerkin method are used. Also, the free vibration analyses for various parameters of a belt driven system, which are the tension of a belt, the length of a belt, the material properties of belts, the velocity of a velt and the mass of pulley are made. The forced vibration analyses of the system are performed and the dynamic responses for main parameters are anlysed with a belt driven system.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2000년도 추계학술대회논문집
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• pp.287-290
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• 2000

An efficient dynamic response analysis method of structures supported by nonlinear resilient mounts when subjected to the transient base excitations is presented by using the structural synthesis method in time domain. Through a numerical example, the validity of the presented method is verified by comparison of the results with those of the 'traditional' analysis method.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2012년도 추계학술대회 논문집
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• pp.225-226
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• 2012

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2013년도 추계학술대회 논문집
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• pp.848-849
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• 2013

• 한국공작기계학회논문집
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• 제17권1호
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• pp.71-76
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• 2008

Nonlinear dynamic system under random excitation was analyzed by using stochastic method. A linearization method was used in order to linearize non-linear structural characteristics but the parametric excitation was used as it was given. An equivalent energy method which equalizes the expectation value of energy of the original nonlinear system and that of quasi-linearized system was proposed. Ito's differential rule was applied to obtain steady state moments. Quasi-linearization coefficients can be obtained the iterative calculation of linearization scheme and steady state moments. Monte Carlo simulation was used to verify the results of the proposed method. Nonlinear vibration of a slender beam was analyzed in this research. The analysis results were compared with Monte Carlo simulation result and showed good agreement. As the spectral density of the given excitation increased, the analysis results showed the better agreement with Monte Carlo simulation.