Characterization of dynamical systems remains a central challenge in real-world applications beca... more Characterization of dynamical systems remains a central challenge in real-world applications because, in most cases, governing equations of the systems cannot be obtained explicitly. Moreover, the behaviors of the systems are complex and possibly unpredictable, even when the system is deterministic. In this situation, nonlinear time series analysis provides an efficient tool for characterizing such dynamical systems. As one of the key techniques in nonlinear time series analysis, phase space reconstruction (PSR) can represent a univariate time series by a multidimensional phase space. Nevertheless, such representation relies on the conscientious selection of the time delay and embedding dimension. Although various algorithms have been developed to optimize these embedding parameters, there are still some limitations restricting their applicability, such as subjective effects, erratic results, and the consumption of time. Herein, we propose a novel Constant embedding parameters and Principal component analysis-based PSR (CPPSR) method, to characterize the low-dimensional ( $$ \le $$ 3) dynamical systems. The effectiveness and accuracy of the CPPSR method are numerically verified on various dynamical systems. The numerical results demonstrate that the CPPSR method can produce reconstructed attractors with precise correlation dimension and the largest Lyapunov exponent. The comparison with conventional and Hankel matrix-based PSR methods shows the superiority of the CPPSR method, demonstrating greater accuracy, higher efficiency, and stronger reliability. Moreover, the CPPSR method shows a high potential for the detection of singularity in applications such as structural health monitoring and abnormality diagnosis in ECG signals.
This study investigates the nonlinear dynamics of a cracked plate undergoing large-amplitude vibr... more This study investigates the nonlinear dynamics of a cracked plate undergoing large-amplitude vibration, aiming to show the influence of structural damage on the nonlinear characteristics of the plate. First, the governing equations of the cracked large-amplitude vibrating plate are derived by the von Kármán theory, with the central part-through crack being simulated by a modified line-spring model for characterizing the crack-induced reduction in stress values. Second, the acquired partial differential equations are discretized by the Galerkin method combined with a simply supported boundary condition. Third, the harmonic balance method and the fourth-order Runge–Kutta algorithm are used to obtain the analytical and numerical approximations of the structural responses, respectively. For cases of small harmonic loads, the plate shows a hardening nonlinear frequency response. Influences of various parameters on this hardening nonlinearity are presented, including crack stage, aspect ratio, plate thickness, excitation location, and excitation amplitude. In cases of large harmonic loads, the bifurcations and chaotic dynamics of the cracked plate are explored by considering the effects of excitation amplitude and excitation frequency. Both analytical and numerical results indicate that a thick plate with a large aspect ratio is more sensitive to damage, especially when the crack parallels to the long side of the plate. Besides, the excitation that occurs far from the plate center with a large amplitude is beneficial for the damage characterization. Particularly, the damage-induced periodic-chaotic transition provides a novel insight into characterizing structural damage from perspectives of chaotic dynamics.
Fatigue damage is a type of damage usually occurring to repeatedly loaded elements of structures ... more Fatigue damage is a type of damage usually occurring to repeatedly loaded elements of structures in various engineering fields. Accumulation of fatigue damage may cause failure of structural elements. Identification of incipient fatigue damage is essential to ensure safety of structures. Fatigue crack under repeated loads commonly behaves in a nonlinear dynamic manner, typically manifested by both occurrence of higher harmonic components and interaction of harmonic components. Interrogation of nonlinear dynamic manner provides a promising way to characterize structural fatigue damage. This study aims at developing a new method to interrogate nonlinear dynamic manner for fatigue damage identification. This method is based on bispectral analysis of structural vibrational responses. This method portrays fatigue damage by inspecting the presence of higher harmonic components and quantifying the interaction of these harmonic components. The method can precisely locate and quantify a smal...
Fatigue damage in engineering structures is universal. The occurrence of fatigue cracks brings un... more Fatigue damage in engineering structures is universal. The occurrence of fatigue cracks brings unpredictable hidden dangers to a structure in terms of safety and service performance. Traditional damage identification methods, such as power spectrum analysis, are mostly based on linear elasticity theory that cannot reflect the typical nonlinear characteristics of fatigue cracks and cannot meet the higher requirements of the signal analysis method put forward by current mass detection data. To solve this problem, a numerical model of a cantilever beam with a breathing crack is established in this study. A method for diagnosing fatigue damage is studied by combining bispectral analysis and a statistical normal cloud model, which characterize the nonlinear characteristics of the structure. This method can effectively describe the nonlinear characteristics of the structure and reasonably evaluate the degree of fatigue damage in the structure. The bispectrum-normal cloud model method prop...
International Journal of Mechanical Sciences, Apr 1, 2019
Abstract A nonlinear thermoelastic model of a circular plate is presented in the paper. The model... more Abstract A nonlinear thermoelastic model of a circular plate is presented in the paper. The model, based on the Mindlin plate theory, is extended by taking into account nonlinear geometrical terms. Partial differential equations of plate’s dynamics are derived for a fully coupled thermal and mechanical fields. Then the model is reduced to a set of ordinary differential equations taking into account the first three natural modes and assuming a constant thermal field. The influence of elevated temperature on the resonance curves and the mode involvement due to nonlinear and thermal couplings is presented. The analysis shows that the increased temperature may lead to various bifurcation scenarios. The buckling phenomenon and post-buckling nonlinear regular and chaotic oscillations are studied.
International Journal of Non-linear Mechanics, Sep 1, 1994
Abstract The dynamic behavior of moderately thick elastic-plastic circular plates has been invest... more Abstract The dynamic behavior of moderately thick elastic-plastic circular plates has been investigated within the context of the geometrical non-linear version of the Mindlin plate theory. For this purpose, an algorithm is developed based on the pseudo-normal mode superposition method. The plastic yielding is controlled by the von Mises yield criterion. In each time subinterval the non-linear terms are grouped together with external loads and the pseudo-loads so-obtained are interpolated by a quadratic polynomial of time and are ...
Collision between a moving ship and a bridge in inner rivers is a frequent occurrence that seriou... more Collision between a moving ship and a bridge in inner rivers is a frequent occurrence that seriously endanger the safety of the bridge. Existing studies mostly address the action of a ship colliding with a bridge pier that is used as a substitution of the associated whole bridge. Such a simplification necessarily induces errors in reflecting the mechanical mechanism and dynamic characteristics of ship–whole bridge collisions. To circumvent this problem, the mechanical behavior of collision between a barge and a whole bridge was studied via elaborating a delicate barge–whole bridge collision simulation underpinned by impact mechanics and materials theories. The main contributions of this study are fourfold: (i) the entire process of the collision between the barge and a whole bridge was fully inspected; (ii) the progressive evolution of collision-induced damage in the bridge pier as well as in the barge was investigated; (iii) the effect of impact velocity, impact angle and barge mas...
Characterization of dynamical systems remains a central challenge in real-world applications beca... more Characterization of dynamical systems remains a central challenge in real-world applications because, in most cases, governing equations of the systems cannot be obtained explicitly. Moreover, the behaviors of the systems are complex and possibly unpredictable, even when the system is deterministic. In this situation, nonlinear time series analysis provides an efficient tool for characterizing such dynamical systems. As one of the key techniques in nonlinear time series analysis, phase space reconstruction (PSR) can represent a univariate time series by a multidimensional phase space. Nevertheless, such representation relies on the conscientious selection of the time delay and embedding dimension. Although various algorithms have been developed to optimize these embedding parameters, there are still some limitations restricting their applicability, such as subjective effects, erratic results, and the consumption of time. Herein, we propose a novel Constant embedding parameters and Principal component analysis-based PSR (CPPSR) method, to characterize the low-dimensional ( $$ \le $$ 3) dynamical systems. The effectiveness and accuracy of the CPPSR method are numerically verified on various dynamical systems. The numerical results demonstrate that the CPPSR method can produce reconstructed attractors with precise correlation dimension and the largest Lyapunov exponent. The comparison with conventional and Hankel matrix-based PSR methods shows the superiority of the CPPSR method, demonstrating greater accuracy, higher efficiency, and stronger reliability. Moreover, the CPPSR method shows a high potential for the detection of singularity in applications such as structural health monitoring and abnormality diagnosis in ECG signals.
This study investigates the nonlinear dynamics of a cracked plate undergoing large-amplitude vibr... more This study investigates the nonlinear dynamics of a cracked plate undergoing large-amplitude vibration, aiming to show the influence of structural damage on the nonlinear characteristics of the plate. First, the governing equations of the cracked large-amplitude vibrating plate are derived by the von Kármán theory, with the central part-through crack being simulated by a modified line-spring model for characterizing the crack-induced reduction in stress values. Second, the acquired partial differential equations are discretized by the Galerkin method combined with a simply supported boundary condition. Third, the harmonic balance method and the fourth-order Runge–Kutta algorithm are used to obtain the analytical and numerical approximations of the structural responses, respectively. For cases of small harmonic loads, the plate shows a hardening nonlinear frequency response. Influences of various parameters on this hardening nonlinearity are presented, including crack stage, aspect ratio, plate thickness, excitation location, and excitation amplitude. In cases of large harmonic loads, the bifurcations and chaotic dynamics of the cracked plate are explored by considering the effects of excitation amplitude and excitation frequency. Both analytical and numerical results indicate that a thick plate with a large aspect ratio is more sensitive to damage, especially when the crack parallels to the long side of the plate. Besides, the excitation that occurs far from the plate center with a large amplitude is beneficial for the damage characterization. Particularly, the damage-induced periodic-chaotic transition provides a novel insight into characterizing structural damage from perspectives of chaotic dynamics.
Fatigue damage is a type of damage usually occurring to repeatedly loaded elements of structures ... more Fatigue damage is a type of damage usually occurring to repeatedly loaded elements of structures in various engineering fields. Accumulation of fatigue damage may cause failure of structural elements. Identification of incipient fatigue damage is essential to ensure safety of structures. Fatigue crack under repeated loads commonly behaves in a nonlinear dynamic manner, typically manifested by both occurrence of higher harmonic components and interaction of harmonic components. Interrogation of nonlinear dynamic manner provides a promising way to characterize structural fatigue damage. This study aims at developing a new method to interrogate nonlinear dynamic manner for fatigue damage identification. This method is based on bispectral analysis of structural vibrational responses. This method portrays fatigue damage by inspecting the presence of higher harmonic components and quantifying the interaction of these harmonic components. The method can precisely locate and quantify a smal...
Fatigue damage in engineering structures is universal. The occurrence of fatigue cracks brings un... more Fatigue damage in engineering structures is universal. The occurrence of fatigue cracks brings unpredictable hidden dangers to a structure in terms of safety and service performance. Traditional damage identification methods, such as power spectrum analysis, are mostly based on linear elasticity theory that cannot reflect the typical nonlinear characteristics of fatigue cracks and cannot meet the higher requirements of the signal analysis method put forward by current mass detection data. To solve this problem, a numerical model of a cantilever beam with a breathing crack is established in this study. A method for diagnosing fatigue damage is studied by combining bispectral analysis and a statistical normal cloud model, which characterize the nonlinear characteristics of the structure. This method can effectively describe the nonlinear characteristics of the structure and reasonably evaluate the degree of fatigue damage in the structure. The bispectrum-normal cloud model method prop...
International Journal of Mechanical Sciences, Apr 1, 2019
Abstract A nonlinear thermoelastic model of a circular plate is presented in the paper. The model... more Abstract A nonlinear thermoelastic model of a circular plate is presented in the paper. The model, based on the Mindlin plate theory, is extended by taking into account nonlinear geometrical terms. Partial differential equations of plate’s dynamics are derived for a fully coupled thermal and mechanical fields. Then the model is reduced to a set of ordinary differential equations taking into account the first three natural modes and assuming a constant thermal field. The influence of elevated temperature on the resonance curves and the mode involvement due to nonlinear and thermal couplings is presented. The analysis shows that the increased temperature may lead to various bifurcation scenarios. The buckling phenomenon and post-buckling nonlinear regular and chaotic oscillations are studied.
International Journal of Non-linear Mechanics, Sep 1, 1994
Abstract The dynamic behavior of moderately thick elastic-plastic circular plates has been invest... more Abstract The dynamic behavior of moderately thick elastic-plastic circular plates has been investigated within the context of the geometrical non-linear version of the Mindlin plate theory. For this purpose, an algorithm is developed based on the pseudo-normal mode superposition method. The plastic yielding is controlled by the von Mises yield criterion. In each time subinterval the non-linear terms are grouped together with external loads and the pseudo-loads so-obtained are interpolated by a quadratic polynomial of time and are ...
Collision between a moving ship and a bridge in inner rivers is a frequent occurrence that seriou... more Collision between a moving ship and a bridge in inner rivers is a frequent occurrence that seriously endanger the safety of the bridge. Existing studies mostly address the action of a ship colliding with a bridge pier that is used as a substitution of the associated whole bridge. Such a simplification necessarily induces errors in reflecting the mechanical mechanism and dynamic characteristics of ship–whole bridge collisions. To circumvent this problem, the mechanical behavior of collision between a barge and a whole bridge was studied via elaborating a delicate barge–whole bridge collision simulation underpinned by impact mechanics and materials theories. The main contributions of this study are fourfold: (i) the entire process of the collision between the barge and a whole bridge was fully inspected; (ii) the progressive evolution of collision-induced damage in the bridge pier as well as in the barge was investigated; (iii) the effect of impact velocity, impact angle and barge mas...
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Papers by Emil Manoach