This book treats nonlinear dynamics in both Hamiltonian and dissipative systems. The emphasis is on the mechanics for generating chaotic motion, methods of calculating the transitions from regular to chaotic motion, and the dynamical and statistical properties of the dynamics when it is chaotic. The book is intended as a self consistent treatment of the subject at the graduate level and as a reference for scientists already working in the field. It emphasizes both methods of calculation and results. It is accessible to physicists and engineers without training in modern mathematics. The new edition brings the subject matter in a rapidly expanding field up to date, and has greatly expanded the treatment of dissipative dynamics to include most important subjects. It can be used as a graduate text for a two semester course covering both Hamiltonian and dissipative dynamics.

Regular and Chaotic Dynamics

Nonlinear Oscillations: Exact Solutions and their Approximations

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Introduction To Perturbation Techniques

Analytical Methods in Vibrations

Nonlinear dissipative devices in structural vibration control: A review

Vibration attenuation of a continuous rotor-blisk-journal bearing system employing smooth nonlinear energy sinks

Primary resonances of a nonlinear in-extensional rotating shaft

Primary and parametric resonances of asymmetrical rotating shafts with stretching nonlinearity

This paper studies the efficiency of a number of smooth non-linear energy sinks (NESs) on the vibration attenuation of a rotor system under mass eccentricity force. The non-linear energy sinks have a linear damping, linear stiffness and a cubic stiffness. To reduce the number of equations of motion, the modal coordinates and complex transformations are used. For analytical solution, the Multiple Scales-Harmonic Balance Method (MSHBM) is used. The most important parameters to examine NES efficiency is the range of happening of the SMR in the detuning parameter range. For different parameters of the system, the SMR, the WMR, the low amplitude periodic motion, and the high amplitude periodic motion happen in the system. It is shown that, the linear stiffness of the NES is canceled out by the stiffness which is created by the centrifugal force and therefore, by changing the linear stiffness of the NESs, the collection of the NESs to the desired rotational speed of the rotor can be tuned. It should be noted that after this cancellation, the remained stiffness is essentially non-linear (non-linearizable) stiffness. In addition, when the external force reaches its medium magnitude, the area of the occurrence of the SMR in the domain of the system parameters would be larger and the collection of the NESs demonstrates an impressive effect.

Lateral vibration attenuation of a rotor under mass eccentricity force using non-linear energy sink

In this paper, the performance of a smooth nonlinear energy sink (NES) to mitigate vibration of a rotating beam under an external force is investigated. The rotating beam is modeled using the Euler-Bernoulli beam theory, and the centrifugal stiffening effect is considered. It is assumed that the nonlinear energy sink has a linear damping and an essentially nonlinear (nonlinearizable or cubic) stiffness. Required conditions for occurring Hopf bifurcation, saddle-node bifurcation and strongly modulated responses (SMR) in the system are investigated. The most important parameter to study NES performance is SMR occurrence range in the detuning parameter span. Effects of position and damping of the NES and magnitude of the external force on the vibration mitigation of the rotating beam are studied. The Complexification-Averaging and the Runge Kutta methods are employed for analytical and numerical investigations, respectively. Finally, the efficiency of an optimal linear absorber and an optimal NES in the vibr...

https://mediatum.ub.tum.de/doc/1308079/file.pdf

Majid Shahgholi

Papers

Vibration attenuation of a continuous rotor-blisk-journal bearing system employing smooth nonlinear energy sinks

Primary resonances of a nonlinear in-extensional rotating shaft

Primary and parametric resonances of asymmetrical rotating shafts with stretching nonlinearity

Lateral vibration attenuation of a rotor under mass eccentricity force using non-linear energy sink

Vibration mitigation of a rotating beam under external periodic force using a nonlinear energy sink (NES)