Dual frequency parametric excitation of a nonlinear, multi degree of freedom mechanical amplifier with electronically modified topology

The Response of Two-Degree of Freedom Self-Sustained Systems with Quadratic Nonlinearities to a Parametric Excitation (RESEARCH NOTE)

In this study the interaction between self-excited and paramet rically excited oscillations in two-degree-of-freedom systems with quadratic nonlinearities is investigated. The fundamental parametric resonance of the first mode and 3:1 internal resonance is considered, followed by 1:2 internal and parametric resonances of the second mode. The method of multiple time scales is applied to derive f...

Relationships between the Nonlinear Output Frequency Response Functions of Multi- Degree-of-Freedom Nonlinear Systems

Sliding Mode Control for Single-degree-of-freedom Nonlinear Structures

The occurrence of catastrophic earthquakes necessitates further researches in the structure engineering for retrofitting construction structures. In this paper, the application of the active control in the structures’ seismic response has been addressed. A single degree of freedom nonlinear structure has been studied. The nonlinear dynamic of the structure is considered in which, the nonlinear ...

Nonlinear model identification and spectral submanifolds for multi-degree-of-freedom mechanical vibrations

In a nonlinear oscillatory system, spectral submanifolds (SSMs) are the smoothest invariant manifolds tangent to linear modal subspaces of an equilibrium. Amplitude-frequency plots of the dynamics on SSMs provide the classic backbone curves sought in experimental nonlinear model identification. We develop here, a methodology to compute analytically both the shape of SSMs and their corresponding...

Stability of Multi-Degree of Freedom Stochastic Nonlinear Systems

Melnikov's method for nding necessary conditions for homoclinic chaos is extended to a class of stochastically forced multi-degree of freedom nonlinear systems. The stochastic forcing induces a stochastic Melnikov process, and simple zeros of this process imply transversal intersection of appropriate stable and unstable manifolds. This process can also provide information on probabilities of es...