... equations that govern vibration of the gear transmission system are formulated by employing the Newton's second law. Analytical results reveal abundant interesting phenomena, including jumps, bifurcations, softening-spring behaviors, and primary, super-harmonic, and subharmonic resonances, which have...

... problem, and a stability analysis is performed to study the governing bifurcations. In addition, we build a machine learning framework where neural net (NN) simulators are trained to predict the performance measures of the gated waveguide in terms of certain transmissibility and nonreciprocity measures...

.... The dynamic behavior of a rotor supported by an NSAB system was studied using spectral response, bifurcation, Poincaré map, and the maximum Lyapunov exponent. The numerical results showed that chaos in an NSAB system occurred within specific ranges of rotor mass and bearing number. For example, the chaotic...

...Zechang Zheng; Zhongrong Lu; Guang Liu; Yanmao Chen A twice harmonic balance (THB) method is proposed to compute and analyze quasi-periodic (QP) responses of nonlinear dynamical systems, with emphasis on the stability and bifurcation of QP responses. In the first harmonic balancing, the original...

... the system's robustness to perturbations in the initial conditions. We use the method of multiple scales and harmonic balance to obtain the global bifurcation diagram in the space of the applied frequency and the amplitude of the response. Numerical simulations verify our analytical expressions. Study...

...Hany A. Hosham; Noha M. Hafez The paper provides an analysis of dynamic behavior of peristaltic transport of non-Newtonian fluid in a nonuniform diverging channel with various waveforms. The canonical object of the study is the bifurcation techniques of the physical parameters, from which...

... cables with some differences between their parameters can exhibit either softening or hardening characteristics. 17 11 2020 02 06 2021 11 08 2021 cable-stayed bridge internal resonance external resonance stability bifurcation National Natural Science Foundation...

... to study the various responses of the system. The system is subjected to hard excitation and hence the subharmonic and superharmonic resonance conditions have been studied. The second-order method of multiple scales (MMS) has been used to find the response, stability, and bifurcations of the system...

..., and input power on bifurcation, and chaos properties of the system are analyzed. The numerical results indicate that the system performs a chaotic motion after several frequency jumps as the mesh frequency increases. When the backlash increases, the frequency region of double-side impact and chaos tends...

... of the branches we have unstable nonhyperbolic fixed point. In the present study, stability and bifurcational behavior of a microbeam driven by asymmetrically located upper and lower electrodes were studied. Equation of static deflection using a distributed and a lumped 2-DOF was studied and positions...

... vibration and chaotic motion of the axially moving current-conducting thin plate under external harmonic force in magnetic field is studied. Improved multiple-scale method is employed to derive the strongly nonlinear subharmonic resonance bifurcation-response equation of the strip thin plate in transverse...

... structures are introduced to describe different periodic and chaotic motions. Analytical prediction of complex periodic motion of the ball in the periodically shaken impact pair is completed, and the corresponding stability and bifurcation analysis are also carried out. Numerical illustrations of periodic...

... dynamically unstable, due to both e ff ects of friction and mode coupling. Furthermore, the amplitude of the vibration in the unstable region is determined through nonlinear analysis. The obtained results show that this unstable vibration is a bifurcation classified as a supercritical Hamiltonian-Hopf...

... system is an archetypal model of modal interaction in stability theory representing a large class of structural problems. When the system displays coincident buckling loads, several post-buckling paths emerge from the bifurcation point (critical load) along the fundamental path. This leads to a complex...

... function determines the stability of these equilibria, and bifurcation diagrams are constructed to demonstrate the co-existence of several equilibrium configurations of the vessel. To validate the results, a vessel of rectangular cross section was built. The results of the experiments agree well...

...Wei Huang; Andrew J. Dick In this paper, a study of the characteristics of period-doubling bifurcations in the dynamic behavior of an atomic force microscope probe for off-resonance excitation is presented. Using a three-mode approximation and excitation at two-and-a-half times the fundamental...

... of the semidiscretization method applied for the corresponding time-periodic delay system. Predictor-corrector method is developed to continue the periodic solutions as the bifurcation parameter, that is, the axial immersion is varied. It is observed that the influence of the state dependent delay on linear stability can...

... settings. This paper argues for exploiting nonsmooth fold bifurcations in the design of ultrafast and robust, resettable, electromechanical limit switches. Specifically, the discussion emphasizes the dramatic changes in system response associated with the onset of near-grazing, low-velocity contact...

... and auxiliary toolboxes, including the continuation of families of periodic orbits in a hybrid dynamical system with impacts and friction as well as the detection and constrained continuation of selected degeneracies characteristic of such systems, such as grazing and switching-sliding bifurcations...

... in calculating the frequency response curves that pitchfork bifurcation can occur followed by “localization phenomenon” for a specific excitation frequency range. During this range, sloshing occurs at different amplitudes in the two tanks, even if the dimensions of both tanks are identical. Furthermore, Hopf...