Analytic solution of transversal oscillation of quintic non-linear beam with energy balance method and global residue harmonic balance method

2017 ◽  
Vol 72 (2) ◽  
pp. 157-162
Author(s):  
M. Akbarzade ◽  
A. Farshidianfar
Keyword(s):  
Energy Balance ◽  
Harmonic Balance ◽  
Analytic Solution ◽  
Harmonic Balance Method ◽  
Balance Method ◽  
Energy Balance Method ◽  
Non Linear

An analytical technique for solving quadratic nonlinear oscillator

2017 ◽  
Vol 13 (3) ◽  
pp. 424-433 ◽  
Author(s):  
Md. Helal Uddin Molla ◽  
Md. Abdur Razzak ◽  
M.S. Alam
Keyword(s):  
Energy Balance ◽  
Harmonic Balance ◽  
Nonlinear Oscillator ◽  
Design Methodology ◽  
Harmonic Balance Method ◽  
Balance Method ◽  
Energy Balance Method ◽  
Content Type ◽  
Analytical Technique ◽  
Present Technique

Purpose The purpose of this paper is to present an analytical technique, based on the He’s energy balance method (an improved version recently presented by Khan et al.), to obtain the approximate solution of quadratic nonlinear oscillator (QNO). Design/methodology/approach This oscillator (QNO) is used as a mathematical model of the human eardrum oscillation. Findings It has been shown that the results by the present technique are very close to the numerical solution. Originality/value The results obtained in this paper are compared with those obtained by Hu (harmonic balance method) and Khan et al. The result shows that the method is more accurate and effective than harmonic balance as well as improved energy balance methods.

Simulations of Unsteady Blade Row Interactions Using Linear and Non-Linear Frequency Domain Methods

2015 ◽  
Author(s):  
Christian Frey ◽  
Graham Ashcroft ◽  
Hans-Peter Kersken
Keyword(s):  
Frequency Domain ◽  
Harmonic Balance ◽  
Measurement Data ◽  
Harmonic Balance Method ◽  
Balance Method ◽  
Frequency Domain Methods ◽  
Blade Row ◽  
Non Linear ◽  
Rotor Stator Interaction ◽  
Unsteady Simulation

This paper compares various approaches to simulate unsteady blade row interactions in turbomachinery. Unsteady simulations of turbomachinery flows have gained importance over the last years since increasing computing power allows the user to consider 3D unsteady flows for industrially relevant configurations. Furthermore, for turbomachinery flows, the last two decades have seen considerable efforts in developing adequate CFD methods which exploit the rotational symmetries of blade rows and are therefore up to several orders of magnitude more efficient than the standard unsteady approach for full wheel configurations. This paper focusses on the harmonic balance method which has been developed recently by the authors. The system of equations as well as the iterative solver are formulated in the frequency domain. The aim of this paper is to compare the harmonic balance method with the time-linearized as well as the non-linear unsteady approach. For the latter the unsteady flow fields in a fan stage are compared to reference results obtained with a highly resolved unsteady simulation. Moreover the amplitudes of the acoustic modes which are due to the rotor stator interaction are compared to measurement data available for this fan stage. The harmonic balance results for different sets of harmonics in the blade rows are used to explain the minor discrepancies between the time-linearized and unsteady results published by the authors in previous publications. The results show that the differences are primarily due to the neglection of the two-way coupling in the time-linearized simulations.

Dynamic Analysis of Structures With Nonlinear Bolted Joints by Using an Adaptive Harmonic Balance Method

2009 ◽  
Author(s):  
Vincent Jaumouille´ ◽  
Jean-Jacques Sinou
Keyword(s):  
Harmonic Balance ◽  
Strain Energy ◽  
Harmonic Balance Method ◽  
Bolted Joints ◽  
Balance Method ◽  
Continuation Methods ◽  
Computational Time ◽  
Bolted Joint ◽  
Non Linear ◽  
Linear Effects

Aeronautical structures are commonly assembled with bolted joints in which friction phenomena provide damping on the dynamic behaviour. Some models, mostly non linear, have consequently been developed and the harmonic balance method (HBM) is adapted to compute non linear response functions in the frequency domain. The basic idea is to develop the response as a Fourier series and to solve equations linking Fourier coefficients. One specific HBM feature is that response accuracy improves as the number of harmonics increases, at the expense of larger computational time. Thus the aim of this study is to develop an adaptive HBM which appreciates numerically the contribution of each harmonic on the dynamic response. For a given precision, the number of retained harmonics is adapted by an algorithm which integrates a numerical criterion based on an approximate strain energy. The application case is an asymmetrical two cantilever beam system linked by a bolted joint represented by a nonlinear LuGre model. Condensation and continuation methods are used to accelerate calculation. Adaptive HBM shows that, for a given value of the criterion, the number of harmonics may increase on resonances indicating that non linear effects are predominant.

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