scholarly journals Nonlinear periodic response analysis of mooring cables using harmonic balance method

2019 ◽  
Vol 438 ◽  
pp. 402-418 ◽  
Author(s):  
Lin Chen ◽  
Biswajit Basu ◽  
Søren R.K. Nielsen
Keyword(s):  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Balance Method ◽  
Response Analysis ◽  
Periodic Response

Periodic Response of a Duffing Oscillator Under Combined Harmonic and Random Excitations

2015 ◽  
Vol 137 (4) ◽  
Author(s):  
Hai-Tao Zhu ◽  
Siu-Siu Guo
Keyword(s):  
Harmonic Balance ◽  
Duffing Oscillator ◽  
Harmonic Balance Method ◽  
Solution Procedure ◽  
Balance Method ◽  
Periodic Response ◽  
Coupled Equations ◽  
The Mean ◽  
Closure Method ◽  
Gaussian Closure

This paper presents a solution procedure to investigate the periodic response of a Duffing oscillator under combined harmonic and random excitations. The solution procedure consists of an implicit harmonic balance method and a Gaussian closure method. The implicit harmonic balance method, previously developed for the case of harmonic excitation, is extended to the present case of combined harmonic and random excitations with the help of the Gaussian closure method. The amplitudes of the periodic response and the steady variances can be automatically found by the proposed solution procedure. First, the response process is separated into the mean part and the random process part. Then the Gaussian closure method is adopted to reformulate the original equation into two coupled differential equations. One is a deterministic equation about the mean part and the other is a stochastic equivalent linear equation. In terms of these two coupled equations, the implicit harmonic balance method is used to obtain a set of nonlinear algebraic equations relating to amplitudes, frequency, and variance. The resulting equations are not explicitly determined and they can be implicitly solved by nonlinear equation routines available in most mathematical libraries. Three illustrative examples are further investigated to show the effectiveness of the proposed solution procedure. Furthermore, the proposed solution procedure is particularly convenient for programming and it can be extended to obtain the periodic solutions of the response of multi degrees-of-freedom systems.

Nonlinear Frequency Response Analysis of a Multistage Clutch Damper With Multiple Nonlinearities

2014 ◽  
Vol 9 (3) ◽  
Author(s):  
Jong-Yun Yoon ◽  
Hwan-Sik Yoon
Keyword(s):  
Frequency Response ◽  
Harmonic Balance ◽  
Piecewise Linear ◽  
Dynamic Performance ◽  
Harmonic Balance Method ◽  
Balance Method ◽  
Response Analysis ◽  
Nonlinear Frequency ◽  
System Equation ◽  
Nonlinear Frequency Response

This paper presents the nonlinear frequency response of a multistage clutch damper system in the framework of the harmonic balance method. For the numerical analysis, a multistage clutch damper with multiple nonlinearities is modeled as a single degree-of-freedom torsional system subjected to sinusoidal excitations. The nonlinearities include piecewise-linear stiffness, hysteresis, and preload all with asymmetric transition angles. Then, the nonlinear frequency response of the system is numerically obtained by applying the Newton–Raphson method to a system equation formulated by using the harmonic balance method. The resulting nonlinear frequency response is then compared with that obtained by direct numerical simulation of the system in the time domain. Using the simulation results, the stability characteristics and existence of quasi-harmonic response of the system are investigated. Also, the effect of stiffness values on the dynamic performance of the system is examined.

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