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Fluid mechanics seminars

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Some advances in the formulation of analytical methods for linear and nonlinear dynamics
15:10 Tue 20 Nov, 2018 :: EMG07 :: Dr Vladislav Sorokin :: University of Auckland

In the modern engineering, it is often necessary to solve problems involving strong parametric excitation and (or) strong nonlinearity. Dynamics of micro- and nanoscale electro-mechanical systems, wave propagation in structures made of corrugated composite materials are just examples of those. Numerical methods, although able to predict systems behavior for specific sets of parameters, fail to provide an insight into underlying physics. On the other hand, conventional analytical methods impose severe restrictions on the problem parameters space and (or) on types of the solutions. Thus, the quest for advanced tools to deal with linear and nonlinear structural dynamics still continues, and the lecture is concerned with an advanced formulation of an analytical method. The principal novelty aspect is that the presence of a small parameter in governing equations is not requested, so that dynamic problems involving strong parametric excitation and (or) strong nonlinearity can be considered. Another advantage of the method is that it is free from conventional restrictions on the excitation frequency spectrum and applicable for problems involving combined multiple parametric and (or) direct excitations with incommensurate frequencies, essential for some applications. A use of the method will be illustrated in several examples, including analysis of the effects of corrugation shapes on dispersion relation and frequency band-gaps of structures and dynamics of nonlinear parametric amplifiers.