An analytical method is proposed to get the amplitude-frequency and the phase-frequency characteristics of free/forced oscillators with nonlinear restoring *** from different points as the conventional methods,in this...
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An analytical method is proposed to get the amplitude-frequency and the phase-frequency characteristics of free/forced oscillators with nonlinear restoring *** from different points as the conventional methods,in this approach the nonlinear restoring force is written as a product of the displacement and the stiffness coefficient that is dependent on *** the stationary response,namely,the restoring force is formally written as That is,for given stationery vibration,the restoring force linearly varies along with the displacement within the amplitude,but the varying rate of the restoring force,so-called stiffness here referring to linear spring,is dependent on the vibration *** the stiffness is constructed according to the characters of the restoring force function;the characters of the restoring force are described with its averaged first and second derivatives respect to the *** this stiffness is used to calculate the frequency of free vibration and the amplitude frequency characteristics for forced *** examples show that this method can be applied to extensive oscillators with nonlinear restoring force,and that the solving process is extremely simple.
Hamiltonian system is a special case of dynamical *** of time it has been used for potential shaping to stabilize the mechanical *** this research article we have used Hamiltonian system to study and control the fuel ...
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Hamiltonian system is a special case of dynamical *** of time it has been used for potential shaping to stabilize the mechanical *** this research article we have used Hamiltonian system to study and control the fuel slosh in a tank of *** is produced by the movement of free liquid surface inside a *** kind of movement may cause a large structural damage if the period of tank motion is close to the natural period of the fluid inside *** general sloshing depends on the amplitude,frequency,law of tank's motion,tank's geometry,liquid depth inside the tank and the liquid *** effect of sloshing can be equally represented by the equivalent mechanical model of pendulum or a mass attached with *** kind of slosh is because of external forces,and in such case Hamiltonian formulation of problem is more difficult than for a free oscillation *** a free oscillation system,the Hamiltonian is simply defined as the sum of kinetic and potential energy of the system but for a forced system defining the Hamiltonian requires the Legendre transform to be carried out on the system's Lagrangian,which can be very difficult from a computational point of view for a system with infinite degree of *** have used equivalent mechanical model of sloshing,coupled with spacecraft,to derive the equations for Hamiltonian *** attached with spring has considered as sloshing of liquid and another fixed mass has taken as the rest of mass of spacecraft to apply the Hamiltonian theory on the model.
By introducing time-dependent power source,a periodically excited piecewise linear circuit with double-scroll is *** the absence of the excitation,all possible equilibrium points as well as the stability conditions ar...
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By introducing time-dependent power source,a periodically excited piecewise linear circuit with double-scroll is *** the absence of the excitation,all possible equilibrium points as well as the stability conditions are *** analysis of the corresponding characteristic equations with perturbation method,Hopf bifurcation conditions associated with the equilibria are derived,which can be proved by the numerical *** Hopf bifurcations of the two symmetric equilibrium points may cause two symmetric periodic orbits,which lead to single-scroll chaotic attractors via sequences of period-doubling bifurcations,*** two chaotic attractors expand to interact with each other to form an enlarged chaotic attractor with *** behavoirs on the switching boundaries are investigated through the generalized Jacobian *** periodic excitation is applied to work on the circuit,three periodic orbits with the frequnecy of the excitation may exist,which can be called as generalized equilibrium points(GEPs)with the same characteristic polynomials as those of the corresponding equlibrium points for the autonomous *** is shown that when the trajectories do not pass across the switching boundaries,the soultions are the same as the ***,when the trajectories pass across the switching boundaries,complicated behaviors take *** forms of chaotic attractors via different bifurcations can be observed and the influence of the switching boundaries on the phase portraits is discussed to explore the mechanism of the dynamical evolution.
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