Related papers: Reconstruction Harmonic Balance Method and its App…
Quasi-periodic responses composed of multiple base frequencies widely exist in science and engineering problems. The multiple harmonic balance (MHB) method is one of the most commonly used approaches for such problems. However, it is…
Periodic dynamical systems ubiquitously exist in science and engineering. The harmonic balance (HB) method and its variants have been the most widely-used approaches for such systems, but are either confined to low-order approximations or…
Combinig the harmonic balance method (HBM) and a continuation method is a well-known technique to follow the periodic solutions of dynamical systems when a control parameter is varied. However, since deriving the algebraic system containing…
In this paper, we extend the method proposed by Cochelin and Vergez [A high order purely frequency-based harmonic balance formulation for continuation of periodic solutions, Journal of Sound and Vibration, 324 (2009) 243-262] to the case of…
The harmonic balance method (HBM) was originally developed for finding periodic solutions of electronical and mechanical systems under a periodic force, but has later been adapted to self-sustained musical instruments. Unlike time-domain…
The harmonic balance (HB) method is widely used in the literature for analyzing the periodic solutions of nonlinear mechanical systems. The objective of this paper is to exploit the method for bifurcation analysis, i.e., for the detection…
The method of harmonic balance (HB) is a spectrally accurate method used to obtain periodic steady state solutions to dynamical systems subjected to periodic perturbations. We adapt HB to solve for the stress response of the Giesekus model…
Harmonic Balance is one of the most popular methods for computing periodic solutions of nonlinear dynamical systems. In this work, we address two of its major shortcomings: First, we investigate to what extent the computational burden of…
In some previous works, two of the authors introduced a technique to design high-order numerical methods for one-dimensional balance laws that preserve all their stationary solutions. The basis of these methods is a well-balanced…
We consider the harmonic balance method for finding approximate periodic solutions of the Lorenz system. When developing software that implements the described method, the math package Maxima was chosen. The drawbacks of symbolic…
Real applications in structural mechanics, where the dynamic behavior is linear, are rare. Usually, structures are made of components assembled together by means of joints whose behavior maybe highly nonlinear. Depending on the amount of…
Harmonic balance (HB) is a popular Fourier-Galerkin method used in the analysis of nonlinear vibration problems where dynamical systems are subjected to periodic forcing. We adapt HB to find the periodic steady-state response of nonlinear…
Computing accurate periodic responses in strongly nonlinear or even non-smooth vibration systems remains a fundamental challenge in nonlinear dynamics. Existing numerical methods, such as the Harmonic Balance Method (HBM) and the Shooting…
We consider the problem of reconstructing signals and images from periodic nonlinearities. For such problems, we design a measurement scheme that supports efficient reconstruction; moreover, our method can be adapted to extend to…
In some previous works, two of the authors have introduced a strategy to develop high-order numerical methods for systems of balance laws that preserve all the stationary solutions of the system. The key ingredient of these methods is a…
In numerical simulations of many charged systems at the micro/nano scale, a common theme is the repeated solution of the Poisson-Boltzmann equation. This task proves challenging, if not entirely infeasible, largely due to the nonlinearity…
Modern engineering structures exhibit nonlinear vibration behavior as designs are pushed to reduce weight and energy consumption. Of specific interest here, joints in assembled structures introduce friction, hysteresis, and unilateral…
This article describes a method for constructing approximations to periodic solutions of dynamic Lorenz system with classical values of the system parameters. The author obtained a system of nonlinear algebraic equations in general form…
Harmonic inversion has already been proven to be a powerful tool for the analysis of quantum spectra and the periodic orbit orbit quantization of chaotic systems. The harmonic inversion technique circumvents the convergence problems of the…
We propose a reformulation for the integral equations approach of Jain, Breunung \& Haller [Nonlinear Dyn. 97, 313--341 (2019)] to steady-state response computation for periodically forced nonlinear mechanical systems. This reformulation…