Reliability of Strongly Nonlinear Single Degree of Freedom Dynamic Systems by the Path Integration Method

2008 ◽  
Vol 75 (6) ◽  
Author(s):  
Daniil Iourtchenko ◽  
Eirik Mo ◽  
Arvid Naess
Keyword(s):  
Path Integration ◽  
Integration Method ◽  
First Passage Time ◽  
Degree Of Freedom ◽  
First Passage ◽  
Controlled System ◽  
Single Degree Of Freedom ◽  
Strongly Nonlinear ◽  
Single Degree ◽  
Path Integration Method

This paper presents a first passage type reliability analysis of strongly nonlinear stochastic single-degree-of-freedom systems. Specifically, the systems considered are a dry friction system, a stiffness controlled system, an inertia controlled system, and a swing. These systems appear as a result of implementation of the quasioptimal bounded in magnitude control law. The path integration method is used to obtain the reliability function and the first passage time.

Passive Targeted Energy Transfers and Strong Modal Interactions in a Thin Plate With Strongly Nonlinear End Attachments of Different Configurations

2007 ◽  
Author(s):  
F. Georgiades ◽  
A. F. Vakakis
Keyword(s):  
Wavelet Transforms ◽  
Degree Of Freedom ◽  
Vibration Energy ◽  
Modal Interactions ◽  
Single Degree Of Freedom ◽  
Strongly Nonlinear ◽  
Single Degree ◽  
Energy Transfers ◽  
Parametric Studies ◽  
Underlying Mechanisms

In this paper we examine Targeted Energy Transfers (TETs) and nonlinear modal interactions occurring in a thin cantilever plate lying on an elastic foundation with strongly nonlinear lightweight attachments of different configurations. Under shock excitation of the plate we systematically study, nonlinear modal interactions and passive broadband targeted energy transfer phenomena between the plate and attachments of the following configurations: a single ungrounded, strongly (essentially) nonlinear single-degree-of-freedom (SDOF) NES; multiple SDOF attachments attached at different points of the plate; and a single multi-degree-of-freedom (MDOF) attachment with multiple essential stiffness nonlinearities. We perform parametric studies by varying the parameters and location of the attachments, in order to optimize TETs from the plate to the NES. We examine in detail the underlying mechanisms influencing TETs by means of Hilbert-Huang Transforms in combination with Wavelet Transforms. These transforms enable one to systematically study the strong modal interactions between the essentially nonlinear attachments and different plate modes. The efficacy of using this type of essentially nonlinear attachments as passive absorbers of broadband vibration energy is discussed.

An Averaging Approach for Noisy Strongly Nonlinear Periodically Forced Systems

2002 ◽  
Author(s):  
Seunggil Choi ◽  
N. Sri Namachchivaya
Keyword(s):  
Stochastic Averaging ◽  
External Noise ◽  
Degree Of Freedom ◽  
Periodic Force ◽  
Single Degree Of Freedom ◽  
Strongly Nonlinear ◽  
Single Degree ◽  
Periodically Driven ◽  
Statistical Measures ◽  
Stochastic Bifurcations

The purpose of this work is to develop a unified approach to study the dynamics of single degree of freedom systems excited by both periodic and random perturbations. The near resonant motion of such systems is not well understood. We will study this problem in depth with the aim of discovering a common geometric structure in the phase space, and to determine the effects of noisy perturbations on the passage of trajectories through the resonance zone. We consider the noisy, periodically driven Duffing equation as a prototypical single degree of freedom system and achieve a model-reduction through stochastic averaging. Depending on the strength of the noise, reduced Markov process takes its values on a line or on graph with certain gluing conditions at the vertex of the graph. The reduced model will provide a framework for computing standard statistical measures of dynamics and stability, namely, mean exit times, probability density functions, and stochastic bifurcations. This work will also explain a counter-intuitive phenomena of stochastic resonance, in which a weak periodic force in a nonlinear system can be enhanced by the addition of external noise.

Sign in / Sign up

Export Citation Format

Share Document