This work concerns the computation of the nonlinear solutions of forced vibration of damped plates. In a recent work [1], a numerical method coupling an Asymptotic Numerical Method (ANM), harmonic balance method and Finite Element method was proposed to resolve this type of problem. The harmonic balance method transforms the dynamic equations to equivalent static ones which are solved by using ...

To predict nonlinear circuit behaviour, harmonic balance (HB) is a popular and useful frequency-domain technique. But given its mathematical nature, it can only converge to mathematical solutions being harmonically related to the input sources into the circuit. Nevertheless, the mathematical solutions to a nonlinear system do not necessarily need to be harmonically related to the input signals ...

in this paper, newton harmonic balance method (nhbm) is applied to obtain the analytical solution for an electron beam injected into a plasma tube where the magnetic field is cylindrical and increases towards the axis in inverse proportion to the radius. periodic solution is analytically verified and consequently the relation between the natural frequency and the amplitude is obtained in an ana...

Abstract Quasi-periodic (QP) solutions of a damped nonlinear QP Mathieu equation with cubic nonlinearity are investigated by using the incremental harmonic balance (IHB) method two time scales. The contains incommensurate excitation frequencies, one is small frequency while other nearly equals twice linear natural frequency. It found that Fourier spectra consist uniformly spaced sidebands due t...

Circuit simulation is a fundamental enabler for the design of integrated circuits. As the design complexity increases, there has been a long lasting interest in speeding up transient circuit simulation using paralellization (Dong et al., 2008; Dong & Li, 2009b;c; Reichelt et al., 1993; Wever et al., 1996; Ye et al., 2008). On the other hand, Harmonic Balance (HB), as a general frequency-domain ...

In rotors supported on a squeeze-film damper (SFD) with static eccentricity, subharmonic and quasi-periodic vibrations are generated by rotor unbalance. this paper, in Jeffcott an SFD analyzed using the modified incremental harmonic balance (IHB) method. Oil film forces calculated π theory short bearing approximation. These first time domain then transformed into frequency Fourier transformatio...

An efficient semi-numerical framework is used in this paper to analyze the dynamic model of an axially moving beam with a nonlinear attachment composed energy sink and piezoelectric device. The governing equations motion system are derived by using Hamilton’s principle von Karman strain-displacement relation Euler - Bernoulli theory. modeled as lumped mass point mass, spring cubic stiffness lin...

Abstract: In this paper, new front-end structures (smart) are proposed to improve vehicle frontal impact. The work carried out in this paper includes developing and analysing mathematical models of vehicle-to-rigid barrier offset frontal impact using fixed and extendable smart front-end structures with piecewise linear characteristics. In these models, vehicle components are modelled by lumped ...