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Dynamics of Nonlinear Oscillators with Discontinuous Nonlinearities Subjected to Harmonic and Stochastic Excitations
- Source :
- Journal of The Institution of Engineers (India): Series C. 102:1321-1363
- Publication Year :
- 2021
- Publisher :
- Springer Science and Business Media LLC, 2021.
-
Abstract
- Dynamics of nonlinear oscillators with discontinuous nonlinearities subjected to harmonic and random excitations is investigated. Impact, dry friction and Hertzian type compliant contact nonlinearities are considered. Stochastic bifurcations like the P-bifurcation and D-bifurcation are discussed. P and D bifurcations are characterized respectively by the joint probability density functions (jpdf) of the response and the largest Lyapunov exponent. The jpdf is obtained by the solution of the corresponding Fokker–Planck equation by the finite element and path integral methods. The results are verified by Monte Carlo simulation methods. Adaptive time step integration procedure (ATSP) is adopted which accurately determines the point of discontinuity. A bisection method and a Brownian tree approach are used in this process and direct the solution along the correct Brownian path. Numerical results are also obtained using non-smooth coordinate transformations like the Zhuvarlev and Ivanov transformations converting the discontinuous systems to equivalent smooth systems and compared with the results of the ATSP. The Filippov convex transformation is used in the case of the dry friction nonlinearity in the integration near the discontinuity. The results are discussed with respect to some examples like the Duffing and Van der Pol oscillators with impact and dry friction.
- Subjects :
- Physics
Van der Pol oscillator
Mechanical Engineering
Numerical analysis
Monte Carlo method
Mathematical analysis
Aerospace Engineering
Ocean Engineering
Lyapunov exponent
Industrial and Manufacturing Engineering
Discontinuity (linguistics)
symbols.namesake
Nonlinear system
Bisection method
symbols
Fokker–Planck equation
Subjects
Details
- ISSN :
- 22500553 and 22500545
- Volume :
- 102
- Database :
- OpenAIRE
- Journal :
- Journal of The Institution of Engineers (India): Series C
- Accession number :
- edsair.doi...........0ed3d2d8bf82c23764d0527b0bd6acf8