Nonlinear structural dynamic system identification is often more a subjective art than it is a direct application of some particular method in systems theory. The nonlinear problem is subjective because although there are many analytical methods from which to choose, there is no general approach to detect, characterise, or model input-output relationships in nonlinear systems. This paper is a s...

A new semiorganic nonlinear optical crystal of bisthiourea nickel bromide (BTNB) was grown successfully by slow evaporation technique using water as solvent. The lattice parameters of the grown crystal have been determined by X-ray diffraction studies. Vibrational spectrum is recorded to determine symmetries of molecular vibrations. Optical absorbance spectrum recorded revealed that this crysta...

Travelling wave solutions are important in nonlinear science. These solutions describe phenomena such as vibrations, solitons and propagation with finite speed. In recent years, direct search for exact solutions of nonlinear partial differential equations (PDEs) has become more and more attractive, partly due to the availability of computer systems like Maple or Mathematica, which allow to perf...

Experimental measurements of nonlinear vibrations of a string are analyzed using new techniques of nonlinear modeling. Previous theoretical and numerical work suggested that the motions of a string can be chaotic and a Shil'nikov mechanism is responsible. We show that the experimental data is consistent with a Shil'nikov mechanism. We also reveal a period doubling cascade with a period three wi...

We study different types of manipulators’ attractors and propose a motion control method. In our analysis the manipulator’s motion is perturbed and its stability investigated using the nonlinear equations of perturbations and linearized equations for practical control. In order to realize a practical control the common areas of stability for nonlinear and linear models are identified. The maps ...

A historical introduction is given of the theory of normal forms for simplifying nonlinear dynamical systems close to resonances or bifurcation points. The specific focus is on mechanical vibration problems, described by finite degree-of-freedom second-order-in-time differential equations. A recent variant of the normal form method, that respects the specific structure of such models, is recall...

This paper discusses the use of nonlinear filters that are based on linear digital filters with input-signal-dependent coefficients in the context of digital waveguide synthesis models. It is proposed that the practical uses of such filters in music synthesis may be generalized to a time-varying fractional delay (TVFD) filter with signal-dependent coefficients. Three different cases are outline...

Mechanically nonlinear energy harvesters driven by broadband vibrations modeled as white noise are investigated. We derive an upper bound on output power versus load resistance and show that, subject to mild restrictions that we make precise, the upper-bound performance can be obtained by a linear harvester with appropriate stiffness. Despite this, nonlinear harvesters can have implementation-r...

We study the dynamics of a nonlinear oscillator near the critical point where period-two vibrations are first excited with the increasing amplitude of parametric driving. Above the threshold, quantum fluctuations induce transitions between the period-two states over the quasienergy barrier. We find the effective quantum activation energies for such transitions and their scaling with the differe...

We demonstrate that stable nonlinear localized modes can exist not only at a light-mass isotopic impurity, but also at a heavy-mass impurity, due to an interplay between discreteness and nonlinearity. This is in sharp contrast to the theory of linear lattice vibrations that an impurity mode is possible only at a light-mass defect. We determine the structure of the nonlinear impurity modes analy...