An Approach to Approximate the Full Strain Field of Turbofan Blades During Operation

2018 ◽  
Author(s):  
Gen Fu ◽  
Alexandrina Untaroiu ◽  
Walter O’Brien
Keyword(s):  
Numerical Model ◽  
Cantilever Beam ◽  
Strain Field ◽  
Measured Data ◽  
Mode Shapes ◽  
Beam Model ◽  
Reference Solution ◽  
Full Field ◽  
Field Response ◽  
Critical Locations

The measurement of the aeromechanical response of the fan blades is important to quantifying their integrity. The accurate knowledge of the response at critical locations of the structure is crucial when assessing the structural condition. A reliable and low cost measuring technique is necessary. Currently, sensors can only provide the measured data at several discrete points. A significant number of sensors may be required to fully characterize the aeromechanical response of the blades. However, the amount of instrumentation that can be placed on the structure is limited due to data acquisition system limitations, instrumentation accessibility, and the effect of the instrumentation on the measured response. From a practical stand point, it is not possible to place sensors at all the critical locations for different excitations. Therefore, development of an approach that derives the full strain field response based on a limited set of measured data is required. In this study, the traditional model reduction method is used to expand the full strain field response of the structure by using a set of discrete measured data. Two computational models are developed and used to verify the expansion approach. The solution of the numerical model is chosen as the reference solution. In addition, the numerical model also provides the mode shapes of the structure. In the expansion approach, this information is used to develop the algorithm. First, a cantilever beam model is created. The influences of the sensor location, number of sensors and the number of modes included are analyzed using this cantilever beam model. The expanded full field response data is compared with the reference solution to evaluate the expansion procedure. The rotor 67 blade model is then used to test the expansion method. The results show that the expanded full field data is in good agreement with the calculated data. The expansion algorithm can be used for the full field strain by using the limited sets of strain data.

Horizontal and Torsional Modes of an Ultra Large Container Ship (ULCS)

2020 ◽  
Author(s):  
P. P. Vijith ◽  
Suresh Rajendran
Keyword(s):  
Numerical Model ◽  
Numerical Method ◽  
Natural Frequency ◽  
Flexible Structures ◽  
Complex Problem ◽  
Mode Shapes ◽  
Beam Model ◽  
Torsional Vibrations ◽  
Hydrodynamic Loads ◽  
Structural Responses

Abstract The hydro elastic responses of flexible structures under fluid loading is an important concern during the design of large ocean structures. The two-way coupling between the structural responses and the hydrodynamic loads is a complex problem in large flexible floating structures since the structures can vibrate in longitudinal, vertical, horizontal, or torsional modes. The antisymmetric distortion modes may be coupled depending on the location of the centroid and the shear centre. In the case of thin walled open structures, horizontal and torsional vibrations are usually coupled due to the asymmetry of cross section as well as eccentricity between centroid of the section and shear deformation centres. The acurate estimation of dry natural frequency and modes shapes of structure is indispensable since it helps to validate the accuracy of the structural modelling. A numerical method available from one of the existing literatures is used for the estimation of dry and wet natural frequencies, and mode shapes of horizontal and torsional vibrations of an ULCS. The natural frequency and modes are essential parameters for the analysis of interaction between structural responses and hydrodynamic loads. The numerical method is based on a 1D FEM beam model. Distortion due to warping is included in the numerical model since it is well known that containerships with large hatch opening are susceptible to warping. The numerical model is subdivided into 50 stations and the mass distribution and the sectional properties are calculated in order to match the bending, shear, torsion and warping moduli of the experimental model. The dry and wet natural frequency and mode shapes for the horizontal and torsional vibrations of the ULCS is numerically calculated and compared with the experimental results.

Full Field Response Prediction Technique in Dynamic Design

2010 ◽  
Vol 34-35 ◽  
pp. 1635-1639
Author(s):  
Qian Jin Wang ◽  
Wen Zhong Qu ◽  
Li Xiao
Keyword(s):  
Response Prediction ◽  
Mode Shapes ◽  
Vibration Test ◽  
Limited Data ◽  
Dynamic Design ◽  
Full Field ◽  
Field Response ◽  
Prediction Technique ◽  
Sufficient Set ◽  
Equivalent Reduction

Structure vibration test plays an important role in dynamic design, but in most cases the experimental data we get is always limited and insufficient for succeeding upgrade and optimization. The response prediction technique presented in this paper is the corresponding technique to deduce the full field response from the limited data obtained by simple vibration test instead of conducting the full-size test. SEREP (System Equivalent Reduction-Expansion Process) method was used to conduct the prediction research and the procedure was elaborated in detail theoretically first, then several simulations were carried on to demonstrate the prediction procedure, inspect the accuracy under various loads and investigate the factors which may influence the accuracy including the number of modes used in the prediction, the noise, and the measured points. Results show that this method has excellent accuracy and good adaptability to various loads as long as a sufficient set of orthogonal mode shapes participate in the prediction procedure.

scholarly journals Underwater Dynamic Response at Limited Points Expanded to Full-Field Strain Response

2018 ◽  
Vol 140 (5) ◽  
Author(s):  
Yuanchang Chen ◽  
Dagny Joffre ◽  
Peter Avitabile
Keyword(s):  
Real Time ◽  
Measured Data ◽  
Great Success ◽  
Strain Response ◽  
Full Field ◽  
Field Displacement ◽  
Health Assessments ◽  
Field Response ◽  
Applied Forces ◽  
Measured Response

Expansion of real-time operating data from limited measurements to obtain full-field displacement data has been performed for structures in air. This approach has shown great success, and its main advantage is that the applied forces do not need to be identified. However, there are applications where structures may be immersed in water and the full-field real-time response may be needed for design and structural health assessments. This paper presents the results of a structure submersed in water to identify full-field response using only a handful of measured data. The same approach is used to extract the full-field displacements, and the results are compared to the actual full-field measured response. The advantage of this approach is that the force does not need to be identified and, most importantly, the damping and fluid–structure interaction does not need to be identified in order to perform the expansion. The results show excellent agreement with the measured data.

Free vibration analysis of a cantilever beam with a slant edge crack

2016 ◽  
Vol 231 (5) ◽  
pp. 823-843 ◽  
Author(s):  
J Liu ◽  
YM Shao ◽  
WD Zhu
Keyword(s):  
Cantilever Beam ◽  
Edge Crack ◽  
Crack Detection ◽  
Failure Modes ◽  
Free Vibration Analysis ◽  
Mode Shapes ◽  
Beam Model ◽  
Equivalent Stiffness ◽  
Proposed Model ◽  
Detection And Diagnosis

As one of major failure modes of mechanical structures subjected to periodic loads, edge cracks due to fatigue can cause catastrophic failures in such structures. Understanding vibration characteristics of a structure with an edge crack is useful for early crack detection and diagnosis. In this work, a new cracked cantilever beam model is presented to study the vibration of a cantilever beam with a slant edge crack, which cannot be modeled by previous methods considering a uniform edge crack along the width of the beam in the literature. An equivalent stiffness model is proposed by dividing the beam into numerous uniform independent thin pieces along its width. The beam is assumed to be an Euler–Bernoulli beam. The crack is assumed to be distributed along the width of the beam as a straight line and a parabola. The methodology proposed in this work can also be extended to model a crack with an arbitrary curve. Effects of crack depths on the nondimensional equivalent stiffness at the crack section of the cracked cantilever beam are studied. The first three nature frequencies and mode shapes of the cracked cantilever beam are obtained using compatibility conditions at crack tips and the transfer matrix method. Effects of depths and the location of the crack on the first three natural frequencies and mode shapes of the cracked cantilever beam are studied using the proposed cracked cantilever beam model. Numerical results from the proposed model are compared with those from the finite element method and an experimental investigation in the literature, which can validate the proposed model.

Flexural Vibration of Prestressed Concrete Bridges with Corrugated Steel Webs

2017 ◽  
Vol 17 (02) ◽  
pp. 1750023 ◽  
Author(s):  
Xia-Chun Chen ◽  
Zhen-Hu Li ◽  
Francis T. K. Au ◽  
Rui-Juan Jiang
Keyword(s):  
Finite Element ◽  
Shear Deformation ◽  
Prestressed Concrete ◽  
Natural Frequencies ◽  
Sandwich Beam ◽  
Flexural Vibration ◽  
Concrete Bridges ◽  
Mode Shapes ◽  
Beam Model ◽  
Prestressed Concrete Bridges

Prestressed concrete bridges with corrugated steel webs have emerged as a new form of steel-concrete composite bridges with remarkable advantages compared with the traditional ones. However, the assumption that plane sections remain plane may no longer be valid for such bridges due to the different behavior of the constituents. The sandwich beam theory is extended to predict the flexural vibration behavior of this type of bridges considering the presence of diaphragms, external prestressing tendons and interaction between the web shear deformation and flange local bending. To this end, a [Formula: see text] beam finite element is formulated. The proposed theory and finite element model are verified both numerically and experimentally. A comparison between the analyses based on the sandwich beam model and on the classical Euler–Bernoulli and Timoshenko models reveals the following findings. First of all, the extended sandwich beam model is applicable to the flexural vibration analysis of the bridges considered. By letting [Formula: see text] denote the square root of the ratio of equivalent shear rigidity to the flange local flexural rigidity, and L the span length, the combined parameter [Formula: see text] appears to be more suitable for considering the diaphragm effect and the interaction between the shear deformation and flange local bending. The diaphragms have significant effect on the flexural natural frequencies and mode shapes only when the [Formula: see text] value of the bridge falls below a certain limit. For a bridge with an [Formula: see text] value over a certain limit, the flexural natural frequencies and mode shapes obtained from the sandwich beam model and the classical Euler–Bernoulli and Timoshenko models tend to be the same. In such cases, either of the classical beam theories may be used.

Aeroelastic Analysis of NREL Wind Turbine

2017 ◽  
Author(s):  
Yaozhi Lu ◽  
Fanzhou Zhao ◽  
Loic Salles ◽  
Mehdi Vahdati
Keyword(s):  
Numerical Model ◽  
Wind Turbine ◽  
Wind Turbines ◽  
Gas Turbines ◽  
High Cycle Fatigue ◽  
Turbine Blades ◽  
Measured Data ◽  
Forced Response ◽  
Cycle Fatigue ◽  
Aeroelastic Analysis

The current development of wind turbines is moving toward larger and more flexible units, which can make them prone to fatigue damage induced by aeroelastic vibrations. The estimation of the total life of the composite components in a wind turbine requires the knowledge of both low and high cycle fatigue (LCF and HCF) data. The first aim of this study is to produce a validated numerical model, which can be used for aeroelastic analysis of wind turbines and is capable of estimating the LCF and HCF loads on the blade. The second aim of this work is to use the validated numerical model to assess the effects of extreme environmental conditions (such as high wind speeds) and rotor over-speed on low and high cycle fatigue. Numerical modelling of this project is carried out using the Computational Fluid Dynamics (CFD) & aeroelasticity code AU3D, which is written at Imperial College and developed over many years with the support from Rolls-Royce. This code has been validated extensively for unsteady aerodynamic and aeroelastic analysis of high-speed flows in gas turbines, yet, has not been used for low-speed flows around wind turbine blades. Therefore, in the first place the capability of this code for predicting steady and unsteady flows over wind turbines is studied. The test case used for this purpose is the Phase VI wind turbine from the National Renewable Energy Laboratory (NREL), which has extensive steady, unsteady and mechanical measured data. From the aerodynamic viewpoint of this study, AU3D results correlated well with the measured data for both steady and unsteady flow variables, which indicated that the code is capable of calculating the correct flow at low speeds for wind turbines. The aeroelastic results showed that increase in crosswind and shaft speed would result in an increase of unsteady loading on the blade which could decrease the lifespan of a wind turbine due to HCF. Shaft overspeed leads to significant increase in steady loading which affects the LCF behaviour. Moreover, the introduction of crosswind could result in significant dynamic vibration due to forced response at resonance.

scholarly journals Confinement of Vibrations in Variable-Geometry Nonlinear Flexible Beam

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
W. Gafsi ◽  
F. Najar ◽  
S. Choura ◽  
S. El-Borgi
Keyword(s):  
Passive Control ◽  
Inverse Eigenvalue Problem ◽  
Beam Dynamics ◽  
Mode Shapes ◽  
Physical Parameters ◽  
Geometrical Parameters ◽  
Flexible Beam ◽  
Beam Model ◽  
Nonlinear Frequency ◽  
Nonlinear Beam

In this paper, we propose a novel strategy for controlling a flexible nonlinear beam with the confinement of vibrations. We focus principally on design issues related to the passive control of the beam by proper selection of its geometrical and physical parameters. Due to large deflections within the regions where the vibrations are to be confined, we admit a nonlinear model that describes with precision the beam dynamics. In order to design a set of physical and geometrical parameters of the beam, we first formulate an inverse eigenvalue problem. To this end, we linearize the beam model and determine the linearly assumed modes that guarantee vibration confinement in selected spatial zones and satisfy the boundary conditions of the beam to be controlled. The approximation of the physical and geometrical parameters is based on the orthogonality of the assumed linear mode shapes. To validate the strategy, we input the resulting parameters into the nonlinear integral-partial differential equation that describes the beam dynamics. The nonlinear frequency response curves of the beam are approximated using the differential quadrature method and the finite difference method. We confirm that using the linear model, the strategy of vibration confinement remains valid for the nonlinear beam.

Study on Displacement Measurement for Induced Strain Field Based on Digital Speckle Pattern Interferometry Method

2013 ◽  
Vol 273 ◽  
pp. 510-514
Author(s):  
Jing Liu ◽  
Hui Zhang ◽  
Jun Li ◽  
Da Chuan Chen ◽  
Yan Kun Tang
Keyword(s):  
Strain Field ◽  
High Speed ◽  
Speckle Pattern ◽  
Measuring Method ◽  
Full Field ◽  
Digital Speckle Pattern Interferometry ◽  
Level Measurement ◽  
On Line ◽  
Interferometry Method ◽  
Digital Speckle

Digital Speckle Pattern Interferometry ( DSPI for short ) method has become one of the most practical worthy techniques for speckle measuring methods with the high-speed development of optic-electronical technique, image processing technology and electronic computer technology. There is a lot of advantages about it, such as uncomplicated operation, non-contacting, advanced automatic level, measurement on-line and extensive using. In this thesis, the displacement variation of the induced strain field for driving by piezoelectric ceramics can be measured by using this method. Thus we can come to a conclusion that digital speckle pattern interferometry is a new measuring method for extracting small-signal. It also provides a powerfully theoretical and experimental platform for study of automated, full-field, high-precision and nondestructive measurement.

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