An Efficient Response Analysis Method for a Non-Linear/Parameter Changing System Using Sub-Structure Modes

1993 ◽  
Vol 207 (1) ◽  
pp. 41-52
Author(s):  
H K Kim ◽  
Y-S Park
Keyword(s):  
Equations Of Motion ◽  
Forced Response ◽  
Suggested Method ◽  
Response Analysis ◽  
Synthesis Methods ◽  
Lumped Mass ◽  
State Equations ◽  
Mass Model ◽  
Non Linear ◽  
Forced Responses

An efficient state-space method is presented to determine time domain forced responses of a structure using the Lagrange multiplier based sub-structure technique. Compared with the conventional mode synthesis methods, the suggested method can be particularly effective for the forced response analysis of a structure subjected to parameter changes with time, such as a missile launch system, and/or having localized non-linearities, because this method does not need to construct the governing equations of the combined whole structure. Both the loaded interface free-free modes and free interface modes can be employed as the modal bases of each sub-structure. The sub-structure equations of motion are derived using Lagrange multipliers and recurrence discrete-time state equations based upon the concept of the state transition matrix are formulated for transient response analysis. The suggested method is tested with two example structures, a simple lumped mass model with a non-linear joint and an abruptly parameter changing structure. The test results show that the suggested method is very accurate and efficient in calculating forced responses and in comparing it with the direct numerical integration method.

Modal and Aeroelastic Analysis of a Compressor Blisk Considering Mistuning

2011 ◽  
Author(s):  
Jens Nipkau ◽  
Arnold Ku¨hhorn ◽  
Bernd Beirow
Keyword(s):  
Equations Of Motion ◽  
Computing Time ◽  
Element Model ◽  
Forced Response ◽  
Lumped Mass ◽  
Aerodynamic Forces ◽  
Mass Model ◽  
Influence Coefficients ◽  
Aeroelastic Analysis ◽  
Lumped Mass Model

Focussing on three basic blade modes the effect of the flow’s influence on the forced response of a mistuned HPC-blisk is studied using a surrogate lumped mass model called equivalent blisk model (EBM). Both measured and intentionally allowed mistuning is considered to find out in principle if the flow contributes to a slowdown of blade displacements with increasing mistuning. In a first step the mechanical properties of the EBM are adjusted to a finite element model and known mistuning distributions given in terms of blade frequencies and damping. Taking into account the flow structure interaction CFD-computations are carried out in order to derive aerodynamic influence coefficients (AIC) which are used to describe the aerodynamic forces coming along with the motion of each blade in the flow. These aerodynamic forces can be included directly in the EBM equations of motion or alternatively be used to calculate aeroelastic eigenvalues from which additional equivalent aerodynamic elements representing the co-vibrating air mass as well as aerodynamic stiffening and damping effects are derived. Both kinds of EBM are applied to study the forced response at least in a qualitative manner aiming to demonstrate some basic effects at low computing time.

Comparative Studies of Surrogate Models for Response Analysis of Mistuned Bladed Disks

2020 ◽  
Vol 17 (10) ◽  
pp. 2050012 ◽  
Author(s):  
Shiyuan Deng ◽  
Jianyao Yao ◽  
Linlin Wang ◽  
Jianqiang Xin ◽  
Ning Hu
Keyword(s):  
Degrees Of Freedom ◽  
Surrogate Models ◽  
Forced Response ◽  
Statistical Characteristics ◽  
Kriging Interpolation ◽  
Response Analysis ◽  
Bladed Disks ◽  
Single Output ◽  
Random Mistuning ◽  
Forced Responses

The forced responses of bladed disks are highly sensitive to inevitable random mistuning. Considerable computational efforts are required for the sampling process to assess the statistical vibration properties of mistuned bladed disks. Therefore, efficient surrogate models are preferred to accelerate the process for probabilistic analysis. In this paper, four surrogate models are utilized to construct the relation between random mistuning and forced response amplitudes, which are polynomial chaos expansion (PCE), response surface method (RSM), artificial neural networks (ANN) and Kriging interpolation, respectively. A bladed disk with 2-degrees-of-freedom (2-DOF) each sector is used to validate the effectiveness of the surrogate models. The effects of number of training samples on the surrogate model accuracy are discussed. The responses results of one blade (single output) and maximum response of all blades (multi-output) indicate that PCE and Kriging interpolation could yield accurate and stable predictions of the statistical characteristics of the forced responses. PCE is recommended for the mistuned response predictions due to its accuracy and efficiency.

Investigation of Damping Potential of Strip Damper on a Real Turbine Blade

2016 ◽  
Author(s):  
M. Afzal ◽  
I. Lopez Arteaga ◽  
L. Kari ◽  
V. Kharyton
Keyword(s):  
Boundary Conditions ◽  
Dynamic Properties ◽  
Equations Of Motion ◽  
Iterative Solution ◽  
Element Model ◽  
Forced Response ◽  
Contact Forces ◽  
Response Analysis ◽  
Bladed Disk ◽  
Different Types

This paper investigates the damping potential of strip dampers on a real turbine bladed disk. A 3D numerical friction contact model is used to compute the contact forces by means of the Alternate Frequency Time domain method. The Jacobian matrix required during the iterative solution is computed in parallel with the contact forces, by a quasi-analytical method. A finite element model of the strip dampers, that allows for an accurate description of their dynamic properties, is included in the steady-state forced response analysis of the bladed disk. Cyclic symmetry boundary conditions and the multiharmonic balance method are applied in the formulation of the equations of motion in the frequency domain. The nonlinear forced response analysis is performed with two different types of boundary conditions on the strip: (a) free-free and (b) elastic, and their influence is analyzed. The effect of the strip mass, thickness and the excitation levels on the forced response curve is investigated in detail.

Detection of Cracks in Mistuned Bladed Disks Using Reduced-Order Models and Vibration Data

2012 ◽  
Vol 134 (6) ◽  
Author(s):  
Chulwoo Jung ◽  
Akira Saito ◽  
Bogdan I. Epureanu
Keyword(s):  
Degrees Of Freedom ◽  
Dimensional Space ◽  
Equations Of Motion ◽  
Computational Cost ◽  
Three Dimensional ◽  
Cost Savings ◽  
Forced Response ◽  
Response Analysis ◽  
Reduced Order Models ◽  
Reduced Order

A novel methodology to detect the presence of a crack and to predict the nonlinear forced response of mistuned turbine engine rotors with a cracked blade and mistuning is developed. The combined effects of the crack and mistuning are modeled. First, a hybrid-interface method based on component mode synthesis is employed to develop reduced-order models (ROMs) of the tuned system with a cracked blade. Constraint modes are added to model the displacements due to the intermittent contact between the crack surfaces. The degrees of freedom (DOFs) on the crack surfaces are retained as active DOFs so that the physical forces due to the contact/interaction (in the three-dimensional space) can be accurately modeled. Next, the presence of mistuning in the tuned system with a cracked blade is modeled. Component mode mistuning is used to account for mistuning present in the uncracked blades while the cracked blade is considered as a reference (with no mistuning). Next, the resulting (reduced-order) nonlinear equations of motion are solved by applying an alternating frequency/time-domain method. Using these efficient ROMs in a forced response analysis, it is found that the new modeling approach provides significant computational cost savings, while ensuring good accuracy relative to full-order finite element analyses. Furthermore, the effects of the cracked blade on the mistuned system are investigated and used to detect statistically the presence of a crack and to identify which blade of a full bladed disk is cracked. In particular, it is shown that cracks can be distinguished from mistuning.

Modal and Forced Response Analysis of Vehicle Systems With Latent Vibration Modes Due to Hydraulic Mounts

2020 ◽  
Vol 142 (4) ◽  
Author(s):  
Hyeon Gyu Sakong ◽  
Gyunchul Hur ◽  
Kwang-Joon Kim ◽  
Wonju Jeon
Keyword(s):  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Time Domain Analysis ◽  
Hydraulic Modeling ◽  
Internal Variable ◽  
Forced Response ◽  
Response Analysis ◽  
Car Body ◽  
Modeling Approaches ◽  
Mechanical Mass

Abstract Hydraulic mounts used in vehicles for better isolation of vibrations were often approximated by lumped or mechanical mass-damper-spring (m-c-k) models, although deficiency in such modeling was pointed out and “hydraulic” modeling was proposed as an alternative. In this paper, a brief review on the mechanical m-c-k modeling and “hydraulic” modeling of the hydraulic mounts is presented. A simplest system consisting of a single mass and a hydraulic mount is used to illustrate both equivalence and difference in a closed form between the two modeling approaches. Then, modal analyses are done on an apparently three degrees-of-freedom (DOF) quarter car with a hydraulic mount, where the key idea is to use an internal variable for the movement of fluid mass which is responsible for a “latent” vibration mode. Equations of motion for the apparently 3DOF system, 4DOF system in fact, by the two modeling are formulated. Modal parameters by the proposed “hydraulic” modeling of the hydraulic mount are compared with those by the m-c-k modeling. Forced responses to transient base excitations are also compared between the two modeling approaches to illustrate how much errors can arise in the frequency and time domain analysis. To be more realistic, the modal and forced response analysis on a full car of an apparently 10DOF (3DOF for powertrain, 3DOF for car body, and 4DOF for knuckles and tires) with two more DOF internally for two hydraulic mounts between the powertrain and car body is presented.

Construction of Generalized Neural Network System for Recognizing Several Non-Linear Behaviors

2003 ◽  
Author(s):  
Taiji Mazda ◽  
Hisanori Otsuka ◽  
Wataru Yabuki ◽  
Kensuke Iwamoto
Keyword(s):  
Neural Network ◽  
Mathematical Model ◽  
Hysteretic Behavior ◽  
Response Analysis ◽  
Network System ◽  
Mass Model ◽  
Recognition Ability ◽  
Non Linear ◽  
Neural Network System ◽  
Linear Spring

Generally, in formulating a spring-mass model for hysteric behavior of materials and members with inelastic characteristic, a mathematical model based on load-deformation experimental results is considered. The model must approximate the inelastic hysteresis of the material. However, assumption of material’s behavior using mathematical models is crucial, since it may cause serious errors if inappropriate model is applied for a particular situation. This paper describes multiple layered neural network to simulate the non-linear hysteretic behavior like Ramberg-Osgood model, modified bilinear model and Takeda model. In this study, based on the pattern recognition ability of neural network, non-linear hysteretic behavior was modeled by the network directly without replacing it with a mathematical model. The effectiveness and applicability of the network in numerical analysis were evaluated. Generalized multiple layered neural network to evaluate non-linear hysteretic curve was constructed. The network can recognize well the three types of hysteretic curve. The network is available as a subroutine of non-linear spring in dynamic response analysis.

A High-Accuracy Model Reduction for Analysis of Nonlinear Vibrations in Structures With Contact Interfaces

2011 ◽  
Vol 133 (10) ◽  
Author(s):  
E. P. Petrov
Keyword(s):  
Nonlinear Vibrations ◽  
Frequency Domain Analysis ◽  
Forced Response ◽  
Response Analysis ◽  
Synthesis Methods ◽  
Test Cases ◽  
Response Matrix ◽  
Computationally Efficient ◽  
Matrix Methods ◽  
Reduced Modeling

A highly accurate and computationally efficient method is proposed for reduced modeling of jointed structures in the frequency domain analysis of nonlinear steady-state forced response. The method has significant advantages comparing with the popular variety of mode synthesis methods or forced response matrix methods and can be easily implemented in the nonlinear forced response analysis using standard finite element codes. The superior qualities of the new method are demonstrated on a set of major problems of nonlinear forced response analysis of bladed disks with contact interfaces: (i) at blade roots, (ii) between interlock shrouds, and (iii) at underplatform dampers. The numerical properties of the method are thoroughly studied on a number of special test cases.

Application of Annular Damper Reaction Wall in Seismic Isolated LNG Tank

2010 ◽  
Author(s):  
Rui-Fu Zhang ◽  
Da-Gen Weng ◽  
Wei-Bo Ni
Keyword(s):  
Equations Of Motion ◽  
Time Base ◽  
Base Shear ◽  
Lumped Mass ◽  
Mass Model ◽  
Isolation System ◽  
Lead Rubber Bearings ◽  
Lumped Mass Model ◽  
Lng Tank ◽  
Rubber Bearings

Most of the large LNG tanks have a fundamental frequency between 2 and 10 Hz which involves range of resonance of most earthquake ground motions. It is a fact that tanks could be damaged easily in the earthquake, which had been proved in many cases in the past few decades. It is an effective way to reduce the response for an isolation system being used for large LNG storage tanks in the strong earthquake. However, the displacement of the isolation story for actual project is very large in soft site so that the design of connection components is relatively difficult. In order to solve this problem, isolation system which is composed of annular damper reaction wall, viscous dampers, and lead rubber bearings mounted on the top of the piles is presented in this paper. The annular damper reaction wall which is not connected with the piles is embedded into the ground independently. The multi-degree-of-freedom lumped mass model is used to solve the governing equations of motion in which convective, impulsive and rigid masses are included. Simplified model of an actual LNG tank which can contain 160000m3 gases is analyzed by using isolators and annular damper reaction wall. The efficiency of the isolation system is investigated by analyzing various parameters such as displacement of the isolation story, base shear and so on. The results show that isolation system is very effective to control the displacement of isolation story, and at the same time base shear and other parameters are also effectively controlled.

Conceptual Analysis of the Non-Linear Forced Response of Aerodynamically Unstable Bladed-Discs

2013 ◽  
Author(s):  
Roque Corral ◽  
Juan Manuel Gallardo ◽  
Rahul Ivaturi
Keyword(s):  
Time Domain ◽  
Linear Response ◽  
Harmonic Excitation ◽  
Friction Model ◽  
Forced Response ◽  
Response Analysis ◽  
Non Linear ◽  
Aerodynamic Instability ◽  
Time Domain Response ◽  
The Time Domain

The response of aerodynamically unstable tuned bladed-discs with non-linear friction dissipation at blade-root attachments due to harmonic external excitation is studied. The bladed-disc is modeled using a simple mass-spring system and the effect of friction is modeled using a micro-slip friction model. The response is computed in time domain using a Runge-Kutta scheme. The time domain response is decomposed to obtain the evolution of traveling waves in the bladed-disc. Parametric studies have been conducted to study the non-linear response at different vibration amplitudes at high and low engine orders of excitation. It is seen that the non-linearity due to friction gives rise to a complicated interaction between the synchronous response of the system due to harmonic excitation and the non-synchronous response of the system due to aerodynamic instability. For low excitation levels the system behaves as in the pure flutter regime where a single, or at most a few, aerodynamically unstable modes may be found in the final state when a limit cycle is reached. When the forcing is large enough the aerodynamic instability is suppressed and only the non-linear response of the excited mode may be seen. It is concluded that the superimposition of the flutter and forced response analysis in terms of vibration amplitude is not valid and leads to prediction of vibration amplitudes significantly larger than that obtained when both phenomena are simulated together.

Detection of Cracks in Mistuned Bladed Disks Using Reduced Order Models and Vibration Data

2011 ◽  
Author(s):  
Chulwoo Jung ◽  
Akira Saito ◽  
Bogdan I. Epureanu
Keyword(s):  
Degrees Of Freedom ◽  
Dimensional Space ◽  
Equations Of Motion ◽  
Computational Cost ◽  
Three Dimensional ◽  
Cost Savings ◽  
Forced Response ◽  
Response Analysis ◽  
Reduced Order Models ◽  
Reduced Order

A novel methodology to detect the presence of a crack and to predict the nonlinear forced response of mistuned turbine engine rotors with a cracked blade and mistuning is developed. The combined effects of the crack and mistuning are modeled. First, a hybrid-interface method based on component mode synthesis is employed to develop reduced order models (ROMs) of the tuned system with a cracked blade. Constraint modes are added to model the displacements due to the intermittent contact between the crack surfaces. The degrees of freedom (DOFs) on the crack surfaces are retained as active DOFs so that the physical forces due to the contact/interaction (in the three-dimensional space) can be accurately modeled. Next, the presence of mistuning in the tuned system with a cracked blade is modeled. Component mode mistuning is used to account for mistuning present in the un-cracked blades while the cracked blade is considered as a reference (with no mistuning). Next, the resulting (reducedorder) nonlinear equations of motion are solved by applying an alternating frequency/time-domain method. Using these efficient ROMs in a forced response analysis, it is found that the new modeling approach provides significant computational cost savings, while ensuring good accuracy relative to full-order finite element analyses. Furthermore, the effects of the cracked blade on the mistuned system are investigated, and used to detect statistically the presence of a crack and to identify which blade of a full bladed disk is cracked. In particular, it is shown that cracks can be distinguished from mistuning.

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