The objective of this study is to extend the concept analogous piezoelectric networks vibration mitigation multiple nonlinear resonances. First, undamped linear part electrical network designed so as possess similar modal characteristics those underlying mechanical structure. Then, components possessing same mathematical form that nonlinearities are added network. Because both and analogies enf...

We study the nonlinear-damping continuation of singular solutions of the critical and supercritical NLS. Our simulations suggest that for generic initial conditions that lead to collapse in the undamped NLS, the solution of the weakly-damped NLS iψt(t, x) + ∆ψ + |ψ |p−1ψ + iδ|ψ |q−1ψ = 0, 0 < δ ≪ 1, is highly asymmetric with respect to the singularity time, and the post-collapse defocusing velo...

The current paper presents the first treatment to obtain solution of a complex Helmholtz–Duffing oscillator. This model has described elevation surface waves in fluid mechanics. non-perturbative approach is used convert nonlinear oscillator linear derive opened path for new way study more waves.

The principal goal of this research is developing physics-based, reduced-order, analytical models of nonlinear fluid-structure interactions associated with offshore structures. Our primary focus is to generalize the Hamilton's variational framework so that systems of flow-oscillator equations can be derived from first principles. This is an extension of earlier work that led to a single energy ...

The fractal Toda oscillator with an exponentially nonlinear term is extremely difficult to solve; Elias-Zuniga et al. (2020) suggested the equivalent power-form method. In this paper, first, variational theory used show basic property of oscillator, and a new form obtained free exponential term, which similar Jerk oscillator. homotopy perturbation method solve analytical solution examined using...

Westervelt's equation is a nonlinear wave that widely used to model the propagation of sound waves in compressible medium, with one important application being ultra-sound human tissue. Two fundamental aspects this -- symmetries and conservation laws are studied present work by modern methods. Numerous results obtained: new conserved integrals; potential systems yielding hidden nonlocal laws; m...

This paper deals with the application of a linear dynamic vibration absorber (DVA) to a piecewise linear beam system to suppress its first harmonic resonance. Both the undamped and the damped DVAs are considered. Results of experiments and simulations are presented and show good resemblance. It appears that the undamped DVA is able to suppress the harmonic resonance, while simultaneously many s...

This paper describes the physical relationships that exist between the Fourier transform and the response spectrum of a strong-motion accelerogram. By developing the new concept of the "Damped Fourier Spectrum" (D.F.S.), we show that the velocity and displacement of the damped oscillator can be represented by a linear combination of the real and imaginary parts of the D.F.S. and by the initial ...

We consider a beam-string-beam transmission problem, where two structurally damped or undamped beams are coupled with frictionally string by conditions. show that for this structure, the dissipation produced frictional part is strong enough to produce exponential decay of solution no matter how small its size. For stability in damped-damped-damped situation we use energy method. undamped-damped...