scholarly journals Identification of the Essential Features of the Transient Amplification of Mistuned Systems

2020 ◽  
Author(s):  
Luigi Carassale ◽  
Vincent Denoël ◽  
Carlos Martel ◽  
Lars Panning-von Scheidt
Keyword(s):  
Linear System ◽  
Numerical Simulations ◽  
Mechanical System ◽  
Asymptotic Expansions ◽  
Damping Ratio ◽  
Multiple Scale ◽  
Analytic Solutions ◽  
Sweep Rate ◽  
Scale Method ◽  
Complex Manner

Abstract The dynamic behavior of bladed disks in resonance crossing has been intensively investigated in the community of turbomachinery, addressing the attention to (1) the transienttype response that appear when the resonance is crossed with a finite sweep rate and (2) the localization of the vibration in the disk due to the blade mistuning. In real conditions, the two mentioned effects coexist and can interact in a complex manner. This paper investigates the problem by means of analytic solutions obtained through asymptotic expansions, as well as numerical simulations. The mechanical system is assumed as simple as possible: a 2-dof linear system defined through the three parameters: damping ratio ξ, frequency mistuning Δ, rotor acceleration Ω˙. The analytic solutions are calculated through the multiple-scale method.

scholarly journals Key Features of the Transient Amplification of Mistuned Systems

2021 ◽  
Author(s):  
Luigi Carassale ◽  
Vincent Denoel ◽  
Carlos Martel ◽  
Lars Panning-von Scheidt
Keyword(s):  
Linear System ◽  
Asymptotic Expansions ◽  
Damping Ratio ◽  
Multiple Scale ◽  
Analytic Solutions ◽  
Sweep Rate ◽  
Scale Method ◽  
Key Features ◽  
Type Response ◽  
Complex Manner

Abstract The dynamic behavior of bladed disks in resonance crossing has been intensively investigated in the community of turbomachinery, addressing the attention to (1) the transient-type response that appear when the resonance is crossed with a finite sweep rate and (2) the localization of the vibration in the disk due to the blade mistuning. In real conditions, the two mentioned effects coexist and can interact in a complex manner. This paper investigates the problem by means of analytic solutions obtained through asymptotic expansions, as well as numerical simulations. The mechanical system is assumed as simple as possible: a 2-dof linear system defined through the three parameters: damping ratio ?, frequency mistuning ?, rotor acceleration . The analytic solutions are calculated through the multiple-scale method.

A Survey in Mathematics for Industry: Two-timing and matched asymptotic expansions for singular perturbation problems

2011 ◽  
Vol 22 (6) ◽  
pp. 613-629 ◽  
Author(s):  
R. E. O'MALLEY ◽  
E. KIRKINIS
Keyword(s):  
Asymptotic Expansions ◽  
Multiple Scale ◽  
Singularly Perturbed ◽  
Matched Asymptotic Expansions ◽  
Amplitude Equations ◽  
Singularly Perturbed Problems ◽  
Multi Scale ◽  
Scale Method ◽  
Perturbation Problems ◽  
Appl Math

Following the derivation of amplitude equations through a new two-time-scale method [O'Malley, R. E., Jr. & Kirkinis, E (2010) A combined renormalization group-multiple scale method for singularly perturbed problems.Stud. Appl. Math.124, 383–410], we show that a multi-scale method may often be preferable for solving singularly perturbed problems than the method of matched asymptotic expansions. We illustrate this approach with 10 singularly perturbed ordinary and partial differential equations.

Turing Patterns of a Lotka–Volterra Competitive System with Nonlocal Delay

2018 ◽  
Vol 28 (07) ◽  
pp. 1830021 ◽  
Author(s):  
Bang-Sheng Han ◽  
Zhi-Cheng Wang
Keyword(s):  
Theoretical Analysis ◽  
Numerical Simulations ◽  
Dynamical Behavior ◽  
Multiple Scale ◽  
Multiple Scale Method ◽  
Turing Patterns ◽  
Amplitude Equations ◽  
Competitive System ◽  
Scale Method ◽  
Nonlocal Delay

This paper focuses on the dynamical behavior of a Lotka–Volterra competitive system with nonlocal delay. We first establish the conditions of Turing bifurcation occurring in the system. According to it and by using multiple scale method, the amplitude equations of the different Turing patterns are obtained. Then, we observe when these patterns (spots pattern and stripes pattern) arise in the Lotka–Volterra competitive system. Finally, some numerical simulations are given to verify our theoretical analysis.

Vortex-Induced Vibrations of a Cylinder at Subcritical Reynolds Number

2011 ◽  
Author(s):  
Yoann Jus ◽  
Elisabeth Longatte ◽  
Jean-Camille Chassaing ◽  
Pierre Sagaut
Keyword(s):  
Reynolds Number ◽  
Numerical Simulations ◽  
Numerical Study ◽  
Damping Ratio ◽  
Experimental Studies ◽  
Cross Flow ◽  
Physical Analysis ◽  
Arbitrary Lagrangian Eulerian ◽  
Vortex Induced Vibrations ◽  
Low Mass

The present work focusses on the numerical study of Vortex-Induced Vibrations (VIV) of an elastically mounted cylinder in a cross flow at moderate Reynolds numbers. Low mass-damping experimental studies show that the dynamic behavior of the cylinder exhibits a three-branch response model, depending on the range of the reduced velocity. However, few numerical simulations deal with accurate computations of the VIV amplitudes at the lock-in upper branch of the bifurcation diagram. In this work, the dynamic response of the cylinder is investigated by means of three-dimensional Large Eddy Simulation (LES). An Arbitrary Lagrangian Eulerian framework is employed to account for fluid solid interface boundary motion and grid deformation. Numerous numerical simulations are performed at a Reynolds number of 3900 for both no damping and low-mass damping ratio and various reduced velocities. A detailed physical analysis is conducted to show how the present methodology is able to capture the different VIV responses.

Numerical simulation of squeezing Cu–Water nanofluid flow by a kernel-based method

2021 ◽  
pp. 2250005
Author(s):  
Mojtaba Fardi ◽  
Yasir Khan
Keyword(s):  
Numerical Simulation ◽  
Hilbert Space ◽  
Linear System ◽  
Numerical Simulations ◽  
Numerical Results ◽  
Kernel Matrix ◽  
Nanofluid Flow ◽  
Parallel Disks ◽  
Engineering Problems ◽  
Well Conditioning

The main aim of this paper is to propose a kernel-based method for solving the problem of squeezing Cu–Water nanofluid flow between parallel disks. Our method is based on Gaussian Hilbert–Schmidt SVD (HS-SVD), which gives an alternate basis for the data-dependent subspace of “native” Hilbert space without ever forming kernel matrix. The well-conditioning linear system is one of the critical advantages of using the alternate basis obtained from HS-SVD. Numerical simulations are performed to illustrate the efficiency and applicability of the proposed method in the sense of accuracy. Numerical results obtained by the proposed method are assessed by comparing available results in references. The results demonstrate that the proposed method can be recommended as a good option to study the squeezing nanofluid flow in engineering problems.

Analysis of Motion of the Impact-Dry-Friction Pair of Bodies and its Application to the Investigation of the Impact Dampers Dynamics

1999 ◽  
Author(s):  
František Peterka
Keyword(s):  
Analytical Solution ◽  
Numerical Simulations ◽  
Mechanical System ◽  
Relative Motion ◽  
Dry Friction ◽  
Friction Pair ◽  
Strong Nonlinearity ◽  
Friction Forces ◽  
The Impact ◽  
Analysis Of Motion

Abstract The motion with impacts and dry friction forces appears in some mechanical systems as mechanisms with clearances, (e.g., in gearings, pins, slots, guides, valve gears etc.), impact dampers, relays, forming and mailing machines, power pics etc. Such mechanisms include one or more pairs of impacting bodies, which introduce the strong nonlinearity into the system motion. The motion of the general pair of bodies with the both-sides impacts and dry friction forces is assumed (Fig.1). It can be the part of a more complex chain of masses in the mechanical system. Dead zones in the relative motion of bodies can be caused by assumed nonlinearities. The mathematical conditions controlling the numerical simulations or analytical solution of the motion are introduced. The application of this method is explained by the study of the influence of dry friction force on amplitude-frequency characteristics of four types of dynamical and impact dampers with optimised parameters.

Shaft Instabilities in Two-Stage Gear Systems

2013 ◽  
Vol 275-277 ◽  
pp. 930-935
Author(s):  
Zhe Rao ◽  
Chun Yan Zhou
Keyword(s):  
Multiple Scale ◽  
Gear System ◽  
Dynamic Equations ◽  
Time Varying ◽  
Kutta Method ◽  
Two Stage ◽  
Scale Method ◽  
System A ◽  
Runge Kutta Method ◽  
Intermediate Shaft

The present paper is focused on the torsional instabilities of the intermediate shaft in a two stage gear system. A theoretical model is established taking account in the torsional flexibility of the intermediate shaft and the meshing time-varying stiffness of the gears. Multiple scale method is applied to analysis the instability areas of the gear system for which the generalized modal coordinate is adopted. The result is certificated by numerical integrals of the dynamic equations by Runge-Kutta Method.

Natural Frequencies and Damping of a Full-Scale Pipe Loop in Air and Water

2017 ◽  
Author(s):  
Hugh Goyder
Keyword(s):  
Oil And Gas ◽  
Natural Frequencies ◽  
Damping Ratio ◽  
Full Scale ◽  
Surrounding Water ◽  
Sea Floor ◽  
Dry Conditions ◽  
Vibration Tests ◽  
Complex Manner ◽  
Submerged Conditions

A full scale pipework system, typical of oil and gas installations located on the sea floor, was subjected to vibration tests in both dry and submerged conditions. The frequency range examined covered 10 Hz to 500 Hz. The objective of the tests was to provide experimental data so that computer simulations could be developed and validated. The method used to determine the vibration properties was that of an experimental modal analysis using an impact hammer. The hammer was modified for underwater use. In dry conditions the damping was found to be very small (damping ratio less than 0.0002) despite the construction being typical. When submerged the effect of the surrounding water was significant. The changes in the natural frequencies from the dry case to the wet case occurred in such a complex manner that it was not possible to identify a simple shift between wet and dry vibration modes. It was necessary to include appropriate added mass coefficients in the computer simulation for both the pipe and the support system. The effect of the surrounding water on the damping was measured but found to be insignificant. It was concluded that immersion in water does not add significant damping to oil and gas pipework.

Sign in / Sign up

Export Citation Format

Share Document