Fast Calculation of the Statistics of the Forced Response of Mistuned Bladed Disk Assemblies With Friction Contacts

2002 ◽  
Author(s):  
Walter Sextro ◽  
Lars Panning ◽  
Florian Go¨tting ◽  
Karl Popp
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Frequency Response ◽  
Approximate Method ◽  
Natural Frequencies ◽  
Computation Time ◽  
System Response ◽  
Response Functions ◽  
Frequency Response Functions ◽  
Bladed Disk

In turbomachinery one major problem is still the calculation and the optimization of the spatial vibrations of mistuned bladed disk assemblies with friction contacts. Friction contacts are widely used to reduce dynamic stresses in turbine blades. Due to dry friction and the relative motion of the contact planes energy is dissipated. This effect results in a reduction of blade vibration amplitudes. In the case of a tuned bladed disk cyclic boundary conditions can be used for the calculation of the dynamic response. For a mistuned bladed disk the complete system has to be modeled and simulated. To reduce the computation time the so-called substructure method is applied. This method is based on the modal description of each substructure, especially disk and blades, combined with a reduction of the degrees of freedom, to describe the dynamics of each component. The spatial dynamical behavior of each component is considered and described by the mode shapes, natural frequencies and modal damping ratios. Using the Harmonic Balance Method the nonlinear friction forces can be linearized. From here it is possible to calculate the frequency response functions of a mistuned bladed disk assembly with friction contacts. In many cases Monte-Carlo simulations are used to find regions, where the system response is sensitive to parameter uncertainties like the natural frequencies of the blades. These simulations require a large computation time. Therefore, an approximate method is developed to calculate the envelopes of the frequency response functions for statistically varying natural frequencies of the blades. This method is based on a sensitivity analysis and the Weibull-distribution of the vibration amplitudes. From here, a measure for the strength of localization for mistuned cyclic systems is derived. Regions, where localization can occur with a high probability, can be calculated by this method. The mean value and the standard deviation of the vibration amplitudes are calculated by simulation and by the approximate method. The comparisons between the approximate method and the Monte-Carlo simulations show a good agreement. Therefore, applying this method leads to remarkable reduction of computation time and gives a quick insight into the system behavior. The approximate method can also be applied to systems, that include the elasticity of the disk and/or the coupling by shrouds or other friction devices.

scholarly journals On Solving One-Dimensional Partial Differential Equations With Spatially Dependent Variables Using the Wavelet-Galerkin Method

2013 ◽  
Vol 80 (6) ◽  
Author(s):  
Simon Jones ◽  
Mathias Legrand
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Galerkin Method ◽  
Frequency Response ◽  
Natural Frequencies ◽  
Basis Functions ◽  
Mode Shapes ◽  
Response Functions ◽  
Partial Differential ◽  
Frequency Response Functions

The discrete orthogonal wavelet-Galerkin method is illustrated as an effective method for solving partial differential equations (PDE's) with spatially varying parameters on a bounded interval. Daubechies scaling functions provide a concise but adaptable set of basis functions and allow for implementation of varied loading and boundary conditions. These basis functions can also effectively describe C0 continuous parameter spatial dependence on bounded domains. Doing so allows the PDE to be discretized as a set of linear equations composed of known inner products which can be stored for efficient parametric analyses. Solution schemes for both free and forced PDE's are developed; natural frequencies, mode shapes, and frequency response functions for an Euler–Bernoulli beam with piecewise varying thickness are calculated. The wavelet-Galerkin approach is shown to converge to the first four natural frequencies at a rate greater than that of the linear finite element approach; mode shapes and frequency response functions converge similarly.

scholarly journals Damage detection based on output-only measurements using cepstrum analysis and a baseline-free frequency response function curvature method

2022 ◽  
Vol 105 (1) ◽  
pp. 003685042110644
Author(s):  
Ayisha Nayyar ◽  
Ummul Baneen ◽  
Muhammad Ahsan ◽  
Syed A Zilqurnain Naqvi ◽  
Asif Israr
Keyword(s):  
Damage Detection ◽  
Frequency Response ◽  
Response Function ◽  
Frequency Response Function ◽  
Damage Index ◽  
Real Life ◽  
System Response ◽  
Response Functions ◽  
Frequency Response Functions ◽  
Output Only

Low-severity multiple damage detection relies on sensing minute deviations in the vibrational or dynamical characteristics of the structure. The problem becomes complicated when the reference vibrational profile of the healthy structure and corresponding input excitation, is unavailable as frequently experienced in real-life scenarios. Detection methods that require neither undamaged vibrational profile (baseline-free) nor excitation information (output-only) constitute state-of-art in structural health monitoring. Unfortunately, their efficacy is ultimately limited by non-ideal input excitation masking crucial attributes of system response such as resonant frequency peaks beyond first (few) natural frequency(ies) which can better resolve the issue of multiple damage detection. This study presents an improved frequency response function curvature method which is both baseline-free and output-only. It employs the cepstrum technique to eliminate [Formula: see text] decay of higher resonance peaks caused by the temporal spread of real impulse excitation. Long-pass liftering screens out the bulk of low-frequency sensor noise along with the excitation. With more visible resonant peaks, the cepstrum purified frequency response functions (regenerated frequency response functions) register finer deviation from an estimated baseline frequency response function and yield an accurate damage index profile. The simulation and experimental results on the beam show that the proposed method can successfully locate multiple damages of severity as low as 5%.

Systematic Mistuning of Bladed Disk Assemblies With Friction Contacts

2004 ◽  
Author(s):  
Florian Go¨tting ◽  
Walter Sextro ◽  
Lars Panning ◽  
Karl Popp
Keyword(s):  
Monte Carlo ◽  
Weibull Distribution ◽  
Approximate Method ◽  
Natural Frequencies ◽  
Forced Response ◽  
Mean Values ◽  
Friction Dampers ◽  
System Parameters ◽  
Bladed Disk ◽  
Standard Deviations

In turbomachinery, friction contacts are widely used to reduce dynamic stresses in turbine blades in order to avoid expensive damages. As a result of energy dissipation in the friction contacts the blade vibration amplitudes are reduced. In case of so-called friction dampers, which are pressed on the platforms of the blades by centrifugal forces, the damping effect can be optimized by varying the damper mass. This optimization can be done by means of a simulation model applying the so-called component mode synthesis and the Harmonic Balance Method to reduce computation time. It is based on the modal description of each substructure. In a real turbine or compressor blading great differences in the magnitude of the individual blade amplitudes occur caused by unavoidable mistuning of all system parameters like contact parameters and natural frequencies of the blades. It may happen that most of the blades experience only small stresses whereas a few blades experience critical stresses. Therefore, it is necessary to consider mistuning for all system parameters to simulate the forced response of bladed disk assemblies with friction contacts. For a mistuned bladed disk the complete system has to be modeled to calculate the dynamic response. In practice, usually the standard deviations instead of the distributions of the system parameters are known. Therefore, Monte-Carlo simulations are necessary to calculate the forced response of the blades for given mean values and standard deviations of the system parameters. To reduce the computational time, an approximate method has been developed and extended for small and moderate standard deviations of the system parameters to calculate the distribution and the envelopes of the frequency response functions for statistically varying system parameters, in the following called statistical mistuning. The approximate method is based on a sensitivity analysis and the assumption of a Weibull distribution of the vibration amplitudes of the blades. Both, the approximate method and the assumption of a Weibull distribution of the vibration amplitudes are validated by Monte-Carlo simulations. By these investigations the influence of different arrangements of the system parameters for given mean values and standard deviations of the vibration amplitudes of the blades can be determined, too. For the present investigations only a small influence of the arrangement of blades with respect to their natural frequencies has been observed. On the other hand, an intentional mistuning of the damper masses and the natural frequencies of the blades in a systematic way, in the following called systematic mistuning, can be investigated to reduce the amplitudes of the system. The simulation results of a systematic mistuning has been validated by a test rig with a rotating bladed disk assembly with friction dampers. The investigations show a good agreement between the simulations and the measurements but only a slight decrease of the maximum amplitudes in case of a systematic mistuning.

Alternate Approach of Using Spectral Decomposition for the Identification of Structural Resonant Regions

2009 ◽  
Author(s):  
Steven M. Mankevich ◽  
Stephen Hambric
Keyword(s):  
Frequency Response ◽  
Spectral Decomposition ◽  
Impact Test ◽  
Spectral Characteristics ◽  
System Response ◽  
Acoustic Similarity ◽  
Response Functions ◽  
Frequency Response Functions ◽  
System Frequency ◽  
Similarity Laws

This paper investigates a method called spectral decomposition and is presented as an alternate approach to determine the system frequency response functions of turbomachinery. Spectral decomposition is a method that is based on the principals established by the acoustic similarity laws to determine the spectral characteristics of a source function. The decomposition process was originally implemented to investigate the isolated acoustic source spectra of fans specifically excluding structureborne sources; however, this paper focuses on using the method for the purpose of characterizing the system response functions associated with rotating machinery. During this investigation, static impact test data was acquired on a large industrial motor to characterize the frequency response functions of the motor/compressor system. Spectral decomposition results are then calculated using the motor operational structureborne data and compared to the results of the static impact test. This paper shows that the spectral decomposition is a viable option to use in place of the static impact test results where qualitative frequency response functions are desired.

Estimation of Partial Frequency Response Functions of a Parametrically Excited Flexible Multibody System

2003 ◽  
Author(s):  
Thorsten Prothmann ◽  
Delf Sachau
Keyword(s):  
Frequency Response ◽  
Large Deformations ◽  
Multibody System ◽  
System Response ◽  
Response Functions ◽  
Flexible Multibody System ◽  
Frequency Response Functions ◽  
Partial Frequency ◽  
The Real ◽  
Flexible Multibody

Flexible multibody system simulation allows for fast and adequate investigation of the dynamics of mechanical systems. But in case of a system response with large deformations the time response does not uncover the causes, i. e. the resonances of the system. The identification of the systems eigenfrequencies gives more insight in resonance phenomena, but in case of periodic time-variant systems the often used snap-shot-eigenfrequencies do not reveal the real system dynamics, which has to be described by more than only one frequency response function. Based on the formulation of a flexible multibody system and the theory of ordinary linear periodic differential equations, partial frequency response functions, describing the real characteristics of a periodic system, are calculated and compared to the snapshot-frequency response functions.

scholarly journals Calculation of Characteristics Describing the Properties of Dynamical Systems

2017 ◽  
Vol 17 (1) ◽  
pp. 147-154
Author(s):  
Jozef Melcer ◽  
Daniela Kuchárová ◽  
Mária Kúdelčíková
Keyword(s):  
Dynamical Systems ◽  
Computational Model ◽  
Frequency Response ◽  
Natural Frequencies ◽  
Dynamical Response ◽  
Response Functions ◽  
Frequency Response Functions ◽  
Natural Modes ◽  
Selection Of

Abstract There are characteristics that uniquely define the properties of dynamical systems from the point of its dynamical response. For example, natural frequencies and natural modes or frequency response functions can be assigned to these characteristics. Determination of these characteristics is fixed on the selection of computational model and on the means of structure excitation. This contribution discusses about analysis of such characteristics.

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