This work investigates the effects of system nonlinearities on degenerate parametric amplifiers. A simple, Duffing-type nonlinearity is appended to a representative equation of motion for a mechanical or electromechanical parametric amplifier, and classical perturbation methods are used to characterize the resulting effects on the amplifier’s frequency response and performance. Ultimately, the ...

We propose a new approach to the multiple–scale analysis of difference equations, in the context of the finite operator calculus. We derive the transformation formulae that map any given dynamical system, continuous or discrete, into a rescaled discrete system, by generalizing a classical result due to Jordan. Under suitable analytical hypotheses on the function space we consider, the rescaled ...

This work is concerned with the performance of a single degree of freedom electromagnetic energy harvester when subjected to a broadband white noise base acceleration. Firstly, using the Fokker-Planck-Kolmogorov equation, it is shown that Duffing-type nonlinearities can be used to reduce the size of energy harvesting devices without affecting their power output. This is then verified using the ...

Identification and control problems for unknown chaotic dynamical systems are considered. Our aim is to regulate the unknown chaos to a fixed point or a stable periodic orbit. This is realized by following two contributions. First, a dynamic neural network is used as identifier. The weights of the neural networks are adjusted by the sliding mode technique. Second, we derive a local optimal cont...

has been studied by many authors from the pioneering work of Picard 1 , who proved the existence of a solution by an application of the well-known method of successive approximations under a Lipschitz condition on g and a smallness condition on T . Sharper results were obtained by Hamel 2 in the special case of a forced pendulum equation see also 3, 4 . The existence of periodic solutions for t...

In this brief, we deal with the open problem of controlling the periodically forced Duffing equation with uncertainty in all parameters. To date, several control schemes have been proposed to adapt for the linearly appearing unknown parameters but no solution exists for the case when the frequency of the periodic forcing is also unknown. We prove for the state feedback control case, global asym...

‎A numerical technique based on the collocation method using Legendre multiwavelets are‎ ‎presented for the solution of forced Duffing equation‎. ‎The operational matrix of integration for ‎Legendre multiwavelets is presented and is utilized to reduce the solution of Duffing equation‎ ‎to the solution of linear algebraic equations‎. ‎Illustrative examples are included to demonstrate‎ ‎the valid...

The renormalization group method of Goldenfeld, Oono and their collaborators is applied to asymptotic analysis of vector fields. The method is formulated on the basis of the theory of envelopes, as was done for scalar fields. This formulation actually completes the discussion of the previous work for scalar equations. It is shown in a generic way that the method applied to equations with a bifu...

A period-doubling cascade is often seen in numerical studies of those smooth (one-parameter families of) maps for which as the parameter is varied, the map transitions from one without chaos to one with chaos. Our emphasis in this paper is on establishing the existence of such a cascade for many maps with phase space dimension 2. We use continuation methods to show the following: under certain ...

The need for better aircraft performance is increasingly prompting designers towards the realisation of morphing or shape-adaptable structural systems. One way to achieve this is to employ multistable composites elements. In this paper a square, curved bistable plate is studied. The finite element analysis provides the load-deflection characteristic of the bistable plate. A cubic expression is ...