scholarly journals An adaptive harmonic balance method for predicting the nonlinear dynamic responses of mechanical systems—Application to bolted structures

2010 ◽  
Vol 329 (19) ◽  
pp. 4048-4067 ◽  
Author(s):  
V. Jaumouillé ◽  
J.-J. Sinou ◽  
B. Petitjean
Keyword(s):  
Nonlinear Dynamic ◽  
Harmonic Balance ◽  
Mechanical Systems ◽  
Harmonic Balance Method ◽  
Balance Method ◽  
Dynamic Responses

Finding Periodic Solutions of Forced Systems With Local Nonlinearities: A Mixed Shooting Harmonic Balance Method

2015 ◽  
Author(s):  
Frederic Schreyer ◽  
Remco Leine
Keyword(s):  
Dynamical Systems ◽  
Periodic Solutions ◽  
Harmonic Balance ◽  
Shooting Method ◽  
Mechanical Systems ◽  
Harmonic Balance Method ◽  
Nonlinear Effects ◽  
Balance Method ◽  
Pros And Cons ◽  
Numerical Approaches

Several numerical approaches have been developed to capture nonlinear effects of dynamical systems. In this paper we present a mixed shooting-harmonic balance method to solve large mechanical systems with local nonlinearities efficiently. The Harmonic Balance Method as well as the shooting method have both their pros and cons. The proposed mixed shooting-HBM approach combines the efficiency of HBM and the accuracy of the shooting method and has therefore advantages of both.

scholarly journals Nonlinear Dynamic Behaviour Analysis of a Clutch System with Uncertainties Using Polynomial Chaos and the Constrained Harmonic Balance Method

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
M.-H. Trinh ◽  
S. Berger ◽  
E. Aubry
Keyword(s):  
Limit Cycles ◽  
Nonlinear Dynamic ◽  
Harmonic Balance ◽  
Dynamic Behaviour ◽  
Polynomial Chaos ◽  
Equilibrium Points ◽  
Harmonic Balance Method ◽  
Unstable Equilibrium ◽  
Balance Method ◽  
Clutch System

The study of the nonlinear dynamic behaviour of friction systems in general and of clutch systems in particular remains an open problem. Noise and vibrations induced by friction in the sliding phase of a clutch are very sensitive to design parameters. The latter have significant dispersions. In the study of the system stability, the problem is not only to know if the parameter values lead to the appearance of unstable equilibrium points; the real challenge lies in estimating the vibration levels when such unstable equilibrium points occur. This estimation is analyzed using the limit cycles. This article aims to study the ability of robust approaches based on developments in nonintrusive generalized polynomial chaos and a constrained harmonic balance method to estimate the vibration levels through the limit cycles of a clutch system in the presence of uncertainty. The purpose is to provide a low-cost, high precision approach, compared to the classic Monte Carlo method.

scholarly journals Multi-level residue harmonic balance method for nonlinear vibration of the beam

2021 ◽  
pp. 146134842110384
Author(s):  
Abu SMZ Hasan ◽  
M S Rahman
Keyword(s):  
Dynamic System ◽  
Nonlinear Vibration ◽  
Nonlinear Dynamic ◽  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Nonlinear Dynamic System ◽  
Balance Method ◽  
Simply Supported Beam ◽  
Simply Supported ◽  
Multi Level

This study presents the nonlinear vibration and chaotic response of a beam subjected to harmonic excitation. The multi-level residue harmonic balance method is applied to solve the geometrically cubic nonlinear vibration of the simply supported beam. The obtained results agree well with those of the numerical integration method. The amplitude frequency response curves are presented to illustrate the nonlinear dynamic system response both for a damping and without damping model. Also, the chaotic response is examined for a simply supported beam with a nonlinear dynamic system.

Dynamical analysis of vibratory feeder and feeding parts considering interactions by an improved increment harmonic balance method

2014 ◽  
Vol 229 (6) ◽  
pp. 1029-1040 ◽  
Author(s):  
Xiangxi Kong ◽  
Xueliang Zhang ◽  
Qinliang Li ◽  
Bangchun Wen
Keyword(s):  
Discrete Element Method ◽  
Nonlinear Dynamic ◽  
Dynamic Problem ◽  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Balance Method ◽  
Dynamical Analysis ◽  
Simplified Model ◽  
Vibratory Feeder ◽  
Nonlinear Dynamic Problem

Vibratory feeder is known as one of major machines in various industries. The feeding parts in a vibratory feeder are experiencing repeated discontinuous friction that can be considered as a typical strong nonlinear dynamic problem. It is very significant to obtain the motion of parts under different alternating loads for the design of vibratory feeder. An analytical model of parts’ motion in sliding regime was constructed and verified with a simplified model based on discrete element method. An improved increment harmonic balance method was proposed to obtain the dynamic behaviors of vibratory feeder and the motion of feeding parts. In contrast to previous researches, we considered the interactions between vibratory feeder and parts in detail, not only containing the effects of the dynamics of vibratory feeder on the motion of parts but also the motion of parts on vibratory feeder. Finally, studying the interactions for various parts’ masses in different frequencies, the motion of parts had a significant effect on the dynamics of vibratory feeder. In reverse, the alterations of the dynamics of vibratory feeder influenced the motion of parts and conveying speed. In the design of vibratory feeder, the interactions between vibratory feeder and parts should not be neglected.

Dynamic vibratory motion analysis of a multi-degree-of-freedom torsional system with strongly stiff nonlinearities

2014 ◽  
Vol 229 (8) ◽  
pp. 1399-1414 ◽  
Author(s):  
Jong-yun Yoon ◽  
Hyeongill Lee
Keyword(s):  
Numerical Simulation ◽  
Nonlinear Dynamic ◽  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Degree Of Freedom ◽  
Balance Method ◽  
Nonlinear Frequency ◽  
Dynamic Behaviors ◽  
Resonance Frequencies ◽  
Torsional System

Physical driveline systems have inherent nonlinearities such as multiple piecewise linear springs, gear backlashes, and drag torques. The multi-staged clutch dampers, in particular, cause severe problems in simulating the nonlinear dynamic behaviors of multi-degree-of-freedom systems. In order to analyze the nonlinear dynamic behaviors of the system, the harmonic balance method has been employed. This study suggests a method to overcome the convergence problems with strong nonlinearities by employing two distinct smoothening factors for stiffness and hysteresis. First, the dynamic behaviors of the multi-degree-of-freedom torsional system are investigated by employing multi-staged clutch dampers subjected to a sinusoidal excitation. Second, the effects of system parameters are examined with respect to dynamic characteristics of torsional vibration. The regimes of resonance frequencies along with the relevant parameters of the system are investigated by calculating backbone curves, which reduce the calculation time significantly. In order to validate harmonic balance method simulation, the simulated results are compared with those of numerical simulation. Harmonic balance method is shown to be more efficient than numerical simulation in calculating the nonlinear frequency response, as well as in simulating the steady-state responses without transient response effect.

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