• Smart Structures and Systems
• /
• v.11 no.1
• /
• pp.87-102
• /
• 2013

Vibration-based damage detection methods are popular for structural health monitoring. However, they can only detect fairly large damages. Usually impact pulse, ambient vibrations and sine-wave forces are applied as the excitations. In this paper, we propose the method to use the chaotic excitation to vibrate structures. The attractors built from the output responses are used for the minor damage detection. After the damage is detected, it is further quantified using the Kalman Filter. Simulations are conducted. A 5-story building is subjected to chaotic excitation. The structural responses and related attractors are analyzed. The results show that the attractor distances increase monotonously with the increase of the damage degree. Therefore, damages, including minor damages, can be effectively detected using the proposed approach. With the Kalman Filter, damage which has the stiffness decrease of about 5% or lower can be quantified. The proposed approach will be helpful for detecting and evaluating minor damages at the early stage.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.27 no.6
• /
• pp.879-889
• /
• 2003

This research deals with the nonlinearities of rocking vibration associated with impact and sliding on the rocking behavior of rigid block under two dimensional sinusoidal excitation which has different frequencies in two excitation direction. The varied excitation direction influences not only the rocking response but also the sliding motion and the rocking response shape. Chaotic responses are observed in wider excitation amplitude region, when the frequencies in each excitation direction are different. The complex behavior of chaotic response, in the phase space, is related with the trajectory of base excitation and sliding motion.

• Journal of KSNVE
• /
• v.8 no.3
• /
• pp.408-419
• /
• 1998

Dynamic characteristics are investigated when a nonlinear system showing periodic and chaotic responses under harmonic excitation is exposed to random perturbation. Approach for both qulitative and quantitative analysis of the noise effect in a nonlinear system under harmonic excitation is presented. For the qualitative analysis, Lyapunov exponents are calculated and Poincar map is illustrated. For the quatitative analysis. Fokker-Planck equatin is solved numerical by means of a Path-integral solution procedure. Eigenvalue problem obtained from the numerical caculation is solved and the relation of eigenvalue, eigenvector and chaotic motion is investigated.

• Journal of KSNVE
• /
• v.7 no.3
• /
• pp.489-498
• /
• 1997

In this paper, chaotic motions of a curved pipe conveying oscillatory flow are theoretically investigated. The nonliear partial differential equation of motion is derived by Newton's method. The transformed nonlinear ordinary differential equation is a type of Hill's equation, which has the external and parametric excitation with a same frequency. Bifurcation curves of chaotic motion of the piping systems are obtained by applying Melnikov's method. Numerical simulations are performed to demonstrate theoretical results and show the strange attractor of the chaotic motion.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 1996.10a
• /
• pp.288-294
• /
• 1996

In this paper, Chaotic motions of a curved pipe conveying oscillatory flow are theoretically investigated. The nonlinear partial differential equation of motion is derived by Newton's method. The transformed nonlinear ordinary differential equation is a type of Hill's equation, which have the parametric and external excitation. Bifurcation curves of chaotic motion of the piping systems are obtained by applying Melnikov's method. Poincare maps numerically demonstrate theoretical results and show transverse homoclinic orbit of the chaotic motion.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 1997.10a
• /
• pp.154-159
• /
• 1997

In this paper, we describe the OGY method that convert the motion on a chaotic attractor to attracting time periodic motion by malting only small perturbations of a control parameter. The OGY method is illustrated by application to the control of the chaotic motion in chaotic attractor to happen at the famous Logistic map and Henon map and confirm it by making periodic motion. We apply it the chaotic motion at the behavior of the thin beam under periodic torsional base-excitation, and this chaotic motion is made the periodic motion by numerical experiment in the time evaluation on this chaotic motion. We apply the OGY method with the Jacobian matrix to control the chaotic motion to the periodic motion.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 2005.05a
• /
• pp.567-571
• /
• 2005

The slender rectangular cantilever beam has vef interesting to study dynamic behaviors of the harmonic base excitation of a cantilever beam shows many nonlinear dynamics due to unstability , energy transfer and mode coupling. Nonlinear phenomenon shows superharmonic, subharmonic, super subharmonic and chaotic motions of the cantilever beam. Experimental observation and verification of these phenomenon carry much importance for the theoretical study as well as in it self. In the experimental cantilever beam, the chaotic motions of the beam appear as a pink noise signal in FFT analysis and as a torus structure in the oscilloscope analyzed to eventually give information of chaotic motions of the cantilever beam.

• Journal of Mechanical Science and Technology
• /
• v.16 no.9
• /
• pp.1040-1053
• /
• 2002

This research deals with the influence of nonlinearities associated with impact and sliding upon the rocking behavior of a rigid block, which is subjected to two-dimensional horizontal and vertical excitation. Nonlinearities in the vibration were found to depend strongly on the effect of the impact between the block and the base, which involves an abrupt reduction in the system's kinetic energy. In particular, when sliding occurs, the rocking behavior is substantially changed. Response analysis using a non-dimensional rocking equation was carried out for a variety of excitation levels and excitation frequencies. The chaos responses were observed over a wide response region, particularly, in the cases of high vertical displacement and violent sliding motion, and the chaos characteristics appear in the time histories, Poincare maps, power spectra and Lyapunov exponents of the rocking responses. The complex behavior of chaotic response, in phase space, is illustrated by the Poincare map. The distribution of the rocking response is described by bifurcation diagrams and the effects of sliding motion are examined through the several rocking response examples.

• Steel and Composite Structures
• /
• v.6 no.2
• /
• pp.87-101
• /
• 2006

The deformation and dynamic behavior mechanism of submerged shell-like lattice structures with membranes are in principle of a non-conservative nature as circulatory system under hydrostatic pressure and disturbance forces of various types, existing in a marine environment. This paper deals with a characteristic analysis on quasi-periodic and chaotic behavior of a circular arch under follower forces with small disturbances. The stability region chart of the disturbed equilibrium in an excitation field was calculated numerically. Then, the periodic and chaotic behaviors of a circular arch were investigated by executing the time histories of motion, power spectrum, phase plane portraits and the Poincare section. According to the results of these studies, the state of a dynamic aspect scenario of a circular arch could be shifted from one of quasi-oscillatory motion to one of chaotic motion. Moreover, the correlation dimension of fractal dynamics was calculated corresponding to stochastic behaviors of a circular arch. This research indicates the possibility of making use of the correlation dimension as a stability index.

• International Journal of Automotive Technology
• /
• v.8 no.1
• /
• pp.33-38
• /
• 2007

Since it is difficult to analytically express the Melnikov function when a dynamic system possesses multiple saddle fixed points with homoclinic and/or heteroclinic orbits, this paper investigates a vehicle model with nonlinear suspension spring and hysteretic damping element, which exhibits multiple heteroclinic orbits in the unperturbed system. First, an algorithm for Melnikov integrals is developed based on the Melnikov method. And then the amplitude threshold of road excitation at the onset of chaos is determined. By numerical simulation, the existence of chaos in the present system is verified via time history curves, phase portrait plots and $Poincar{\acute{e}}$ maps. Finally, in order to further identify the chaotic motion of the nonlinear system, the maximal Lyapunov exponent is also adopted. The results indicate that the numerical method of estimating chaotic threshold is an effective one to complicated vehicle systems.