1,721,257 research outputs found
Exact solutions for coupled Duffing oscillators
Full text linkThe exact analytical solution of a system made of two coupled Duffing oscillators is obtained. The mathematical solution is illustrated by means of some examples aimed at showing the dynamical phenomena occurring in the considered system. Frequency response curves are reported for different value of the parameters, highlighting the effects of the linear and nonlinear coupling between the two variables. The presence of various solution branches, up to four coexisting attractors, is reported
Propagation of periodic waves in beams on a bilinear foundation
No full textThe propagation of periodic flexural waves in an Euler-Bernoulli beam resting on a bilinear elastic foundation is investigated. Although the problem is nonlinear, the closed form solution is obtained thanks to its piecewise linear nature. The dependence of the phase velocity on the two stiffnesses of the substrated is investigated in depth, and it is shown that a very complex behaviour is observed when the stiffnesses are large. Veering-like phenomena has been discovered, apparently for the first time. It is shown that some branches end with cusp points, not related to classical bifurcations. The stability of the considered waves is also addressed, in a restricted class of perturbations
An asymptotic approach for large amplitude motions of generic nonlinear systems
No full textStarting from the observation that classical asymptotic methods fail to correctly describe the resonance peak of the frequency response curve of a nonlinear oscillator under moderate and large excitation amplitudes, an alternative approach is proposed to overcome this problem. The differences between the multiple time scale method (one of the most performant classical methods) and numerical simulations are initially shown with reference to on the paradigmatic Duffing equation. They are also shown some characteristics of the near peak behavior. Then, the proposed asymptotic approach is illustrated. The basic idea is that of having the zero-order problem nonlinear, while in classical methods it is linear. Thanks to the energy conservation, the zero-order problem is solved exactly. Also, the exact solution of the higher-order problems is obtained in closed-form, thus providing a fully analytical approach. Although the proposed method is valid for any kind of motion, special attention is dedicated to periodic nonlinear oscillations, because of their interest in practical applications. A simple formula for determining the exact intersection of the frequency response and backbone curves is obtained, and it is shown that it can be computed without the need of solving explicitly not even the zero-order problem. Some illustrative examples are finally reported
An impact model of a ball bouncing on a flexible beam
No full textIn this work we investigate a model for the description of the impact of a ball with a flexible beam. The coupling of the kinematic parameters of the ball (the velocity components) with the vibration modes of the beam are taken into account by using the Hertz theory of impact. We solve the model equations numerically in a few physically relevant cases and illustrate the variation of the modal coefficients of the beam and of the velocity components of the ball during the impact. The restitution coefficient, the size of the deformation region and the impact duration are also reported as functions of the impact velocity and of the impact location
Attractor-basin and bifurcation analysis in an impact system: chaotic uncontrolled versus controlled steady response
No full textOverturning threshold of a rocking block subjected to harmonic excitation: computer simulations and analytical treatment
No full textCD-Ro
Homoclinic and heteroclinic solutions for a class of two dimensional Hamiltonian systems
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Effects of shear stiffness, rotatory and axial inertia, and interface stiffness on free vibrations of a two-layer beam
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