• Journal of the Korean Society of Industry Convergence
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• v.4 no.2
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• pp.133-139
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• 2001

The nonlinear response statistics of an spring-pendulum system with internal resonance under narrow band random excitation is investigated analytically- The center frequency of the filtered excitation is selected to be close to natural frequency of directly excited spring mode. The Fokker-Planck equations is used to generate a general first-order differential equation in the dynamic moment of response coordinates. By means of the Gaussian closure method the dynamic moment equations for the random responses of the system are reduced to a system of autonomous ordinary differential equations. The nonlinear phenomena, such as jump and multiple solutions, under narrow band random excitation were found by Gaussian closure method.

• Proceedings of the Earthquake Engineering Society of Korea Conference
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• 2001.09a
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• pp.243-250
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• 2001

Industrial machines are sometimes exposed to the danger of earthquake. In the design of a mechanical system, this factor should be accounted for from the viewpoint of reliability. A method to analyze a complex nonlinear structure system under random excitation is proposed. First, the actual random excitation, such as earthquake, is approximated to the corresponding Gaussian process far the statistical analysis. The modal equations of overall system are expanded sequentially. Then, the perturbed equations are synthesized into the overall system and solved in probabilistic way. Several statistical properties of a random process that are of interest in random vibration applications are reviewed in accordance with nonlinear stochastic problem. The obtained statistical properties of the nonlinear random vibration are evaluated in each substructure. Comparing with the results of the numerical simulation proved the efficiency of the proposed method.

• Structural Engineering and Mechanics
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• v.18 no.6
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• pp.791-806
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• 2004

The inverse pseudo excitation method is used in the identification of random loadings. For structures subjected to stationary random excitations, the power spectral density matrices of such loadings are identified experimentally. The identification is based on the measured acceleration responses and the structural frequency response functions. Numerical simulation is used in the optimal selection of sensor locations. The proposed method has been successfully applied to the loading identification experiments of three structural models, two uniform steel cantilever beams and a four-story plastic glass frame, subjected to uncorrelated or partially correlated random excitations. The identified loadings agree quite well with actual excitations. It is proved that the proposed method is quite accurate and efficient in addition to its ability to alleviate the ill conditioning of the structural frequency response functions.

• Structural Engineering and Mechanics
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• v.10 no.4
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• pp.359-369
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• 2000

Random loading identification has long been a difficult problem for Multi-Input-Multi-Output (MIMO) structure. In this paper, the Pseudo Excitation Method (PEM), which is an exact and efficient method for computing the structural random response, is extended inversely to identify the excitation power spectral densities (PSD). This identified method, named the Inverse Pseudo Excitation Method (IPEM), resembles the general dynamic loading identification in the frequency domain, and can be used to identify the definite or random excitations of complex structures in a similar way. Numerical simulations are used to reveal the the difficulties in such problems, and the results of some numerical analysis are discussed, which may be very useful in the setting up and processing of experimental data so as to obtain reasonable predictions of the input loading from the selected structural responses.

• Journal of Mechanical Science and Technology
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• v.16 no.10
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• pp.1229-1238
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• 2002

In this paper, a method to obtain the sensitivity of eigenvalues and the random responses of the structure with uncertain parameters is proposed. The concept of the proposed method is that the perturbed equation of each uncertain substructure is obtained using the finite element method, and the perturbed equation of the overall structure is obtained using the mode synthesis method. By this way, the reduced order perturbed equation of the uncertain system can be obtained. And the response of the uncertain system is obtained using probability method. As a numerical example, a simple piping system is considered as an example structure. The damping and spring constants of the support are considered as the uncertain parameters. Then the variations of the eigenvalues, the correlation function and the power spectral density function of the responses are calculated. As a result, the proposed method is considered to be useful technique to analyze the sensitivities of eigenvalues and random response against random excitation in terms of the accuracy and the calculation time.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.24 no.6
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• pp.437-443
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• 2014

Vibration testing is conducted for evaluate the fatigue resistance of responsible system over excitation situations and two kinds of vibration profiles, harmonic or random, are widely used in engineering fields. Harmonic excitation profile is adequate for the rotating machinery that is primarily exposed to the orderly excited force subjected for a rotating speed; Random profile is suitable for the non-stationary vibration input, that is a ground excitation for example. Recently, the sine on random(SOR) testing method was sometimes considered to represent the real excitation conditions since the measured response signals of a target system, expecially for moving mobility, shows usually a mixture of them. So, it is important to understand the accumulated fatigue damage over different excitation patterns, harmonic and/or random, to determine the efficient vibration profile of a target system. A uniaxial vibration testing with a notched simple beam was introduced to evaluate the fatigue damage for different excitation profiles and the best choice of vibration profile was concluded from those comparison of calculated fatigue damages.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2014.04a
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• pp.340-345
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• 2014

Vibration testing is conducted for evaluate the fatigue resistance of responsible system over excitation situations and two kinds of vibration profiles, harmonic or random, are widely used in engineering fields. Harmonic excitation profile is adequate for the rotating machinery that is primarily exposed to the orderly excited force subjected for a rotating speed; Random profile is suitable for the non-stationary vibration input, that is a ground excitation for example. Recently, the sine on random (SOR) testing method was sometimes considered to represent the real excitation conditions since the measured response signals of a target system, expecially for moving mobility, shows usually a mixture of them. So, it is important to understand the accumulated fatigue damage over different excitation patterns, harmonic and/or random, to determine the efficient vibration profile of a target system. A uniaxial vibration testing with a notched simple beam was introduced to evaluate the fatigue damage for different excitation profiles and the best choice of vibration profile was concluded from those comparison of calculated fatigue damages.

• Journal of the Korean Society of Industry Convergence
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• v.3 no.2
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• pp.141-147
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• 2000

The nonlinear response statistics of an autoparameteric system under broad-band random excitation is investigated. The specific system examined is a vibration absorber system with internal resonance, which is known to be a good model for a variety of engineering systems, including ship motions with nonlinear coupling between pitching and rolling motions. The Fokker-Planck equations is used to generate a general first-order differential equation in the dynamic moment of response coordinates. By means of the Gaussian closure method the dynamic moment equations for the random responses of the system are reduced to a system of autonomous ordinary differential equations. The jump phenomenon was found by Gaussian closure method under random excitation.

• Journal of KSNVE
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• v.8 no.3
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• pp.399-407
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• 1998

An investigation into the modal interaction of an autoparameteric systemunder broad-band random excitation is made. The specific system examined is a spring-pendulum system with internal resonance, which is known to be a good model for a variety of engineering systems, including ship motions with nonlinear coupling between pitching and rolling motions. By means of the Gaussian closure method the dynamic moment equations explaining the random responses of the system are reduced to a system of autonomous ordinanary differential equations of the first and second moments. In view of equilibrium solutions of this system and their stability we examine the system responses. The stabilizing effect of system damping is also examined.

• Structural Engineering and Mechanics
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• v.24 no.2
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• pp.213-225
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• 2006

The propagation of non-uniformly modulated, evolutionary random waves in viscoelastic, transversely isotropic, stratified materials is investigated. The theory is developed in the context of a multi-layered soil medium overlying bedrock, where the material properties of the bedrock are considered to be much stiffer than those of the soil and the power spectral density of the random excitation is assumed to be known at the bedrock. The governing differential equations are first derived in the frequency/wave-number domain so that the displacement response of the ground may be computed. The eigen-solution expansion method is then used to solve for the responses of the layers. This utilizes the precise integration method, in combination with the extended Wittrick-Williams algorithm, to obtain all the eigen-solutions of the ordinary differential equation. The recently developed pseudo-excitation method for structural random vibration is then used to determine the solution of the layered soil responses.