scholarly journals Vibrations of an Axial Bar Experiencing Periodic Unilateral Contact Using the Wavelet Balance Method

2014 ◽  
Author(s):  
Simon Jones ◽  
Mathias Legrand
Keyword(s):  
Convergence Rates ◽  
Flexible Structures ◽  
Harmonic Balance Method ◽  
Unilateral Contact ◽  
Balance Method ◽  
Contact Conditions ◽  
Turbine Engine ◽  
Weighted Residuals ◽  
Time Periodic Solutions ◽  
Time Periodic

Efficiently predicting the vibratory responses of flexible structures which experience unilateral contact is becoming of high engineering importance. An example of such a system is a rotor blade within a turbine engine; small operating clearances and varying loading conditions often result in contact between the blade and the casing. The method of weighted residuals is a effective approach to simulating such behaviour as it can efficiently enforce time-periodic solutions of lightly damped, flexible structures experiencing unilateral contact. The Harmonic Balance Method (HBM) based on Fourier expansion of the sought solution is a common formulation, though it is hypothesized wavelet bases that can sparsely define nonsmooth solutions may be superior. This is investigated herein using an axially vibrating rod with unilateral contact conditions. A distributional formulation in time is introduced allowing periodic, square-integrable trial functions to approximate the second-order equations. The mixed wavelet Petrov-Galerkin solutions are found to yield consistent or better results than HBM, with similar convergence rates and seemingly more accurate contact force prediction.

Adaptive harmonic balance method for nonlinear time-periodic flows

2004 ◽  
Vol 193 (2) ◽  
pp. 620-641 ◽  
Author(s):  
Raymond C Maple ◽  
Paul I King ◽  
Paul D Orkwis ◽  
J Mitch Wolff
Keyword(s):  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Balance Method ◽  
Periodic Flows ◽  
Time Periodic

The Development and Application of a Time-Domain Harmonic Balance Flow Solver

2012 ◽  
Author(s):  
Pengcheng Du ◽  
Fangfei Ning
Keyword(s):  
Time Domain ◽  
Harmonic Balance ◽  
Unsteady Flows ◽  
Harmonic Balance Method ◽  
Balance Method ◽  
Computational Time ◽  
Test Cases ◽  
Flow Solver ◽  
The Time Domain ◽  
Time Periodic

Time periodic unsteady flows are often encountered in turbomachinery. Simulating such flows using conventional time marching approach is very time-consuming and hence expensive. To handle this problem, several Fourier-based reduced order models have been developed recently. Among these, the time-domain harmonic balance method solves the governing equations purely in the time domain and there is also no need for the turbulence model to be linearized, making it easy to be implemented in an existing RANS code. Thus, the time-domain harmonic balance method was chosen and incorporated into an in-house Navier-Stokes flow solver. Several test cases were performed for the validations of the developed code. They cover standard unsteady test cases such as the low speed vortex shedding cylinder flow and the Sajben transonic diffuser under periodically oscillating back pressure. Further, two different practical turbomachinery unsteady flows were considered. One is a transonic fan under circumferential inlet distortion and the other is the rotor-stator interactions in a single stage compressor. The results illustrate the capability of the harmonic balance method in capturing the dominant nonlinear effects. The number of harmonics should be retained in the harmonic balance method is depend on the strength of the nonlinear unsteady effects and differs from case to case. With appropriate number of harmonics retained, it can resolve the unsteady flow field satisfactory, meanwhile, reducing the computational time significantly. In a word, the harmonic balance method promise to be an effective way to simulate time periodic unsteady flows.

scholarly journals A Time-Domain Harmonic Balance Method for Rotor/Stator Interactions

2011 ◽  
Vol 134 (1) ◽  
Author(s):  
Frédéric Sicot ◽  
Guillaume Dufour ◽  
Nicolas Gourdain
Keyword(s):  
Time Domain ◽  
Harmonic Balance ◽  
Harmonic Balance Method ◽  
Flow Simulation ◽  
Balance Method ◽  
Test Case ◽  
Phase Lag ◽  
Local Flow ◽  
Periodic Rotation ◽  
Time Periodic

In the absence of instabilities, the large deterministic scales of turbomachinery flows resulting from the periodic rotation of blades can be considered periodic in time. Such flows are not simulated with enough efficiency when using classical unsteady techniques as a transient regime must be bypassed. New techniques, dedicated to time-periodic flows and based on Fourier analysis, have been developed recently. Among these, harmonic balance methods cast a time-periodic flow computation in several coupled steady flow computations. A time-domain harmonic balance method is derived and adapted to phase lag periodic conditions to allow the simulation of only one blade passage per row regardless of row blade counts. Sophisticated space and time interpolations are involved and detailed. The test case is a single stage subsonic compressor. A convergence study of the present harmonic balance is performed and compared with a reference well-resolved classical unsteady flow simulation. The results show, on one hand, the good behavior of the harmonic balance and its ability to correctly predict global quantities as well as local flow pattern; on the other hand, the simulation time is drastically reduced.

q-BREATHERS IN FPU-LATTICES — SCALING AND PROPERTIES FOR LARGE SYSTEMS

2007 ◽  
Vol 21 (23n24) ◽  
pp. 3925-3932 ◽  
Author(s):  
SERGEJ FLACH ◽  
OLEG I. KANAKOV ◽  
KONSTANTIN G. MISHAGIN ◽  
MIKHAIL V. IVANCHENKO
Keyword(s):  
Energy Density ◽  
Normal Modes ◽  
Localization Length ◽  
Nonlinearity Parameter ◽  
First Finding ◽  
Nonlinear Lattices ◽  
Intensive Quantities ◽  
Time Periodic Solutions ◽  
Large Systems ◽  
Time Periodic

Recently q-breathers - time-periodic solutions which localize in the space of normal modes and maximize the energy density for some mode vector q0 - were obtained for finite nonlinear lattices. We scale these solutions to arbitrarily large lattices in various lattice dimensions. We study the scaling consequence for previously obtained analytical estimates of the localization length of q-breathers for β-FPU and α-FPU lattices. The first finding is that the degree of localization depends only on intensive quantities and is size independent. Secondly, a critical wave vector km is identified, which depends on one effective nonlinearity parameter, q-breathers minimize the localization length at k0 = km and completely delocalize in the limit k0 → 0, π.

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