Chaotic dynamics of flexible beams driven by external white noise (original) (raw)
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Chaotic vibrations of flexible infinitely length plates
In this paper chaotic vibrations of flexible infinitely length plates are studied. In particular, various wavelets are applied in order to achieve the reliable and validated results. In addition, charts of vibrational regimes including regular, chaotic and bifurcational dynamics are constructed.
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Dynamic Response of Non-linear Beam Structures in Deterministic and Chaos Perspective
Indonesian Journal of Physics, 2019
The behavior of large deformation beam structures can be modeled based on non-linear geometry due to geometricnonlinearity mid-plane stretching in the presence of axial forces, which is a form a nonlinear beam differential equationof Duffing equation type. Identification of dynamic systems from nonlinear beam differential equations fordeterministic and chaotic responses based on time history, phase plane and Poincare mapping. Chaotic response basedon time history is very sensitive to initial conditions, where small changes to initial terms leads to significant change inthe system, which in this case are displacement x (t) and velocity x’(t) as time increases (t). Based on the phase plane, itshows irregular and non-stationary trajectories, this can also be seen in Poincare mapping which shows strange attractorand produces a fractal pattern. The solution to this Duffing type equation uses the Runge-Kutta numerical method withMAPLE software application.
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Stochastic free vibration of orthotropic plates using generalized polynomial chaos expansion
Journal of Sound and Vibration, 2012
This paper presents the theory and application of the generalized polynomial chaos expansion for the stochastic free vibration of orthotropic plates. Specifically, the stochastic analysis of orthotropic plates under the uncertainties in elasticity moduli is investigated. The uncertain moduli, eigen-frequencies and eigen-modes of the plates are represented by truncated polynomial chaos expansions with arbitrary random basis. The expansions are substituted in the governing differential equations to calculating the polynomial chaos coefficients of the eigen-frequencies and the eigen-modes. Distribution functions of the uncertain moduli are derived from experimental data where the Pearson model is used to identify the type of density functions. This realization then is employed to construct random orthogonal basis for each uncertain parameter. Because of available experimental modal analysis data, this paper provides a useful practical example on the efficacy of polynomial chaos where the statistical moments and the probability distributions of modal responses are compared with experimental results.
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