Search

The investigation of global bifurcation behaviors the vibrating structures of micro-electromechanical systems (MEMS) has received substantial attention. This paper considers the vibrating system of a typical bilateral MEMS resonator containing fractional functions and multiple potential wells. By introducing new variations, the Melnikov method is applied to derive the critical conditions for global bifurcations. By engaging in the fractal erosion of safe basin to depict the phenomenon pull-in instability intuitively, the point-mapping approach is used to present numerical simulations which are in close agreement with the analytical prediction, showing the validity of the analysis. It is found that chaos and pull-in instability, two initial-sensitive phenomena of MEMS resonators, can be due to homoclinic bifurcation and heteroclinic bifurcation, respectively. On this basis, two types of delayed feedback are proposed to control the complex dynamics successively. Their control mechanisms and effect are then studied. It follows that under a positive gain coefficient, delayed position feedback and delayed velocity feedback can both reduce pull-in instability; nevertheless, to suppress chaos, only the former can be effective. The results may have some potential value in broadening the application fields of global bifurcation theory and improving the performance reliability of capacitive MEMS devices. [ABSTRACT FROM AUTHOR]

Jump and excessive motion are undesirable phenomena in relative rotation systems, causing a loss of global integrity and reliability of the systems. In this work, a typical relative rotation system is considered in which jump, excessive motion, and their suppression via delayed feedback are investigated. The Method of Multiple Scales and the Melnikov method are applied to analyze critical conditions for bi-stability and initial-sensitive excessive motion, respectively. By introducing the fractal of basins of attraction and the erosion of the safe basin to depict jump and initial-sensitive excessive motion, respectively, the point mapping approach is used to present numerical simulations which are in agreement with the theoretical prediction, showing the validity of the analysis. It is found that jump between bistable attractors can be due to saddle–node bifurcation, while initial-sensitive excessive motion can be due to heteroclinic bifurcation. Under a positive coefficient of the gain, the types of delayed feedback can both be effective in reducing jump and initial-sensitive excessive motion. The results may provide some reference for the performance improvement of rotors and main bearings. [ABSTRACT FROM AUTHOR]

Abstract Concepts and tools of global dynamics play a meaningful role in enhancing the engineering design and safety of multistable structural systems in a dynamic environment. Basins of attraction topology can vary meaningfully as a function of system parameters, and the basin boundaries can be smooth or fractal. Fractal boundaries have important practical consequences as they lead to uncertainty with respect to the outcome of a given initial condition, thus reducing the system safety, which can be quantified through different dynamic integrity measures and their variation with a control parameter. In the present paper two key issues influencing the integrity measures and basins' erosion profiles are addressed: transient escape and added random noise. Transient escape is a significant issue in many structural systems since it may lead to unwanted stresses and strains or exceed some safe design requirements in terms of maximum displacements and velocities. In turn, the random noise may increase the uncertainty of the systems, thus decreasing their practical safety and escape load. As a case study, the bistable von Mises truss is considered and the effects of transient escape and added random noise on the global dynamics of the harmonically excited truss are investigated in detail, clarifying their influence on the system safety as evaluated with different integrity measures. Highlights • Influence of transient escape and added random noise on bifurcation diagrams. • Evolution of safe basins under deterministic and non-deterministic loads. • Influence of transient escape and added random noise on dynamic integrity measures. • The use of dynamic integrity measures to access the robustness of safe solutions. [ABSTRACT FROM AUTHOR]

In this paper, the chaotic motion of ship roll in stochastic beam seas, which is regarded as a bounded noise is investigated in detail. The stochastic Melnikov approach is applied to the model and the criterion for the chaos in the mean-square sense is derived. The chaotic thresholds of noise parameters obtained by means of the stochastic Melnikov process are verified by the numerical safe basin. Besides of the factors of noise disturbances, the effects of the other parameters in the system on safe basin are also discussed systematically. The varieties of coefficients of the restoring moment can also induce the erosion of safe basin and lead to the occurrence of the chaos. On the other hand, the increase of damping coefficients can enhance the safe domain of ship sailing. [ABSTRACT FROM AUTHOR]

In this paper, the nonlinear dynamic characteristics and bifurcation of Al-doped graphene are studied. The nonlinear dynamic model of Al-doped graphene impacted by hydrogen atoms is developed where the nonlocal effect of a graphene is considered. The natural frequency of the system is obtained, the system's drift coefficient and diffusion coefficient are verified, and the stationary probability density function of the system's dynamic response is given. The condition of stochastic bifurcation is determined, and the fractal boundary of the safe basin is provided. Finally, the reliability function of the system is solved, and the probability density of the first-passage time is determined. Theoretical analysis and numerical simulation show that stochastic bifurcation occurs in the variation of parameters; the area of safe basin decreases when the intensity of the atom's impact increases. The results of this paper are helpful for the application of Al-doped graphene in hydrogen storage. [ABSTRACT FROM AUTHOR]

The nonlinear dynamic characteristics of Fe-Ga cantilever nanobeam subjected to stochastic excitation are studied in this paper where the nonlocal effect is considered. Nonlinear differential terms are introduced to explain the hysteretic phenomena of the Fe-Ga alloy's strain-magnetic field intensity curves, and the nonlinear dynamic model of Fe-Ga cantilever composite nanobeam subjected to stochastic excitation is developed. The system's nonlinear dynamic characteristics are discussed, and the optimal control strategy is proposed to enhance the system's reliability. Numerical simulations show that the nonlocal effect can influence the system's stochastic Hopf bifurcation; the boundary of the system's safe basin has fractal characteristics, the area of safe basin decreases when the intensity of the noise increases, and it increases again through stochastic optimal control. The results of this study are helpful for the application of Fe-Ga composite nanobeam in engineering fields. [ABSTRACT FROM AUTHOR]

In this article, the thermodynamic characteristics and bifurcation of MWCNTs impacted by hydrogen atoms were studied. The impact between MWCNTs and hydrogen atoms was regarded as white noise. Nonlinear differential items were introduced to explain the hysteretic phenomena of MWCNTs stiffness, and a nonlinear dynamic model of MWCNTs impacted by hydrogen atoms was developed where the nonlocal effect is considered. The conditions of stochastic Hopf bifurcation were identified, and the fractal boundary of the safe basin was provided. The reliability function of the system was solved, and the probability density of the first-passage time was determined. Theoretical analysis and numerical simulation show that stochastic Hopf bifurcation occurs in the variation of parameters; the boundary of safe basin has fractal characteristics, the area of safe basin decreases when the intensity of the noise increases; the hysteretic nonlinearity of MWCNTs stiffness can affect the system's stability and safe basin, which decides the actual hydrogen storage capacity of MWCNTs. [ABSTRACT FROM AUTHOR]

In this article, stochastic nonlinear dynamic characteristics of a Li-doped graphene considering nonlocal effect are studied. The interaction of Li atoms and graphene is regarded as standard Gauss white noise. The nonlinear dynamic model of a Li-doped graphene is developed, in which the nonlocal effect of Li atoms on graphene's stiffness is considered. The dynamic response of the system is obtained by stochastic dynamical theory and transition sets theory, and the bifurcation characteristics and safe basin of the system are analyzed. The results of numerical simulation and experiments show that the stochastic noise intensity has important influence on the system's dynamical response. The stochastic resonance phenomenon occurs with the stochastic noise intensity variety which decides the graphene's actual hydrogen storage capacity. The results of this paper are helpful for the graphene's application in hydrogen storage fields. [ABSTRACT FROM AUTHOR]

In this article, stochastic nonlinear dynamic characteristics and safe basin of a Li-doped graphene impacted by hydrogen atoms are studied. The interaction of hydrogen atoms to a graphene is regarded as Gauss white noise excitation. The nonlinear dynamic model of a Li-doped graphene impacted by hydrogen atoms is developed, in which the effect of Li atoms on graphene's stiffness is considered. The local and global stability of the system are analyzed, and the system's safe basin is obtained. The reliability function of the system is solved, and the probability of the first-passage time is determined. Theoretical analysis and numerical simulation show that the safe basin's boundary has fractal characteristics, which means chaos induced by noise; the safe basin's area decreases when the noise's intensity increases; the inhomogeneity of the graphene's stiffness can affect the system's safe basin, which decides the graphene's actual hydrogen storage capacity. Finally, the phenomena of the graphene's stiffness changing with the temperature are explained. [ABSTRACT FROM AUTHOR]

Abstract: The focus of this study is to examine the transverse stability of BSRA trawlers in beam seas using both numerical and analytical safe basin concepts and also shows how the concept of safe basin can be utilized for the assessment of the stability of trawlers. In the first part of this study, the nonlinear ship roll motion equation and the main parameters that induce ship capsizing in beam seas are analyzed using the concept of numeric safe basin. Then, the safe operating conditions of trawlers such as maximum allowable wave height and wind velocity are obtained for given loading conditions. In the second part of this study, analytic safe basins of nonlinear rolling motion are determined for given operating and loading conditions using the Lyapunov direct method. It is observed from the comparisons of analytically and numerically obtained safe basins that the analytically obtained safe basins are coherent with numerically obtained safe basins but beside this coherency analytically obtained safe basins are more conservative. [Copyright &y& Elsevier]

Abstract: The aim of this study is to examine both the stochastic rolling motion of ships in following seas by using analytical and numerical safe basin concept and to show how the concept of safe basin can be utilized for the assessment of the stability of ships. First, the boundary of the analytic safe basins of stochastic rolling motion is obtained by using the Lyapunov function used by . Second, the safe basins of stochastic rolling motion are obtained numerically by using stochastic Euler (Euler–Maruyama) method. It is concluded that the analytically and numerically obtained safe basins are coherent. Lastly, the practical intact stability criterion for ships in following seaway is developed by proposing a formula given for the maximum width of analytic safe basin. [Copyright &y& Elsevier]

Abstract: The purpose of this paper is to analyze the nonlinear ship roll motion equation and the main parameters that induce ship capsizing in beam seas, estimate the survival probability of a ferry in random seas and to find out a risk assessment method for the ship’s intact stability. A single degree of freedom (1-DOF) dynamic system of ship rolling in beam seas is investigated and the nonlinear differential equation is solved in the time domain by the fourth order Runge–Kutta algorithm. The survival probability of a ferry in beam seas is investigated using the theory of “safe basin”. The survival probability is calculated by estimating erosion of “safe basin” during ship rolling motion by Monte Carlo simulations. From the results it can be concluded that the survival probability of a ship in beam sea condition can be predicted by combining Monte Carlo simulations and the theory of “safe basin”. [Copyright &y& Elsevier]

Abstract: The erosion curves for the Helmholtz, the Duffing and rigid block oscillators are constructed to investigate the loss of integrity in different mechanical systems. Various definitions of safe basin and integrity measures are reviewed, compared with each other and applied to the considered cases. A control method aimed at shifting the erosion profiles towards larger excitation amplitudes is considered, too, and its main features are discussed in depth. [Copyright &y& Elsevier]

Abstract: In this paper a statistical methodology is extended to the nonlinear multi-degree of freedom vessel capsize problem in random seas. It is demonstrated that the study of transient motions, through analysis of the erosion of the vessel''s safe basin mapped in the space of initial conditions [Soliman, M.S. Thompson, J., 1991. Transient and steady state analysis of capsize phenomena. Applied Ocean Research 13, 2], leads to significantly less conservative and potentially more accurate predictions of ultimate dynamic stability. The work presented herein pairs this approach with a statistical framework to yield feasible stability criteria. [Copyright &y& Elsevier]

In this paper, a kind of single-walled carbon nanotube nonlinear model is developed and the strongly nonlinear dynamic characteristics of such carbon nanotubes subjected to random magnetic field are studied. The nonlocal effect of the microstructure is considered based on Eringen’s differential constitutive model. The natural frequency of the strongly nonlinear dynamic system is obtained by the energy function method, the drift coefficient and the diffusion coefficient are verified. The stationary probability density function of the system dynamic response is given and the fractal boundary of the safe basin is provided. Theoretical analysis and numerical simulation show that stochastic resonance occurs when varying the random magnetic field intensity. The boundary of safe basin has fractal characteristics and the area of safe basin decreases when the intensity of the magnetic field permeability increases. [ABSTRACT FROM AUTHOR]