Updating of Non-Conservative Systems Using Inverse Methods

1997 ◽  
Author(s):  
Ladislav Starek ◽  
Milos Musil ◽  
Daniel J. Inman
Keyword(s):  
Analytical Model ◽  
Degrees Of Freedom ◽  
Ad Hoc ◽  
Natural Frequencies ◽  
Eigenvalue Problems ◽  
Model Updating ◽  
Analytical Models ◽  
Mode Shapes ◽  
Element Analysis ◽  
Modal Data

Abstract Several incompatibilities exist between analytical models and experimentally obtained data for many systems. In particular finite element analysis (FEA) modeling often produces analytical modal data that does not agree with measured modal data from experimental modal analysis (EMA). These two methods account for the majority of activity in vibration modeling used in industry. The existence of these discrepancies has spanned the discipline of model updating as summarized in the review articles by Inman (1990), Imregun (1991), and Friswell (1995). In this situation the analytical model is characterized by a large number of degrees of freedom (and hence modes), ad hoc damping mechanisms and real eigenvectors (mode shapes). The FEM model produces a mass, damping and stiffness matrix which is numerically solved for modal data consisting of natural frequencies, mode shapes and damping ratios. Common practice is to compare this analytically generated modal data with natural frequencies, mode shapes and damping ratios obtained from EMA. The EMA data is characterized by a small number of modes, incomplete and complex mode shapes and non proportional damping. It is very common in practice for this experimentally obtained modal data to be in minor disagreement with the analytically derived modal data. The point of view taken is that the analytical model is in error and must be refined or corrected based on experimented data. The approach proposed here is to use the results of inverse eigenvalue problems to develop methods for model updating for damped systems. The inverse problem has been addressed by Lancaster and Maroulas (1987), Starek and Inman (1992,1993,1994,1997) and is summarized for undamped systems in the text by Gladwell (1986). There are many sophisticated model updating methods available. The purpose of this paper is to introduce using inverse eigenvalues calculated as a possible approach to solving the model updating problem. The approach is new and as such many of the practical and important issues of noise, incomplete data, etc. are not yet resolved. Hence, the method introduced here is only useful for low order lumped parameter models of the type used for machines rather than structures. In particular, it will be assumed that the entries and geometry of the lumped components is also known.

Methods of Preserving Symmetry in Model Updating

1995 ◽  
Vol 117 (3A) ◽  
pp. 349-354
Author(s):  
M. J. Lam ◽  
D. J. Inman
Keyword(s):  
Experimental Data ◽  
Analytical Model ◽  
Natural Frequencies ◽  
Model Updating ◽  
Mode Shapes ◽  
Modal Parameter ◽  
Modal Data ◽  
Model Correction ◽  
Damped Systems ◽  
Stiffness And Damping

This work examines the model updating technique for both conservative and nonproportionally damped systems. In model updating, also referred to as model correction, the analytical model is updated until it agrees with the experimental data available. In this paper it is assumed that the measured modal data, i.e., natural frequencies and in some instances mode shapes, disagrees in part with the modal parameter predicted by the analytical model. Many model updating schemes tend to produce nonsymmetric updated stiffness (and damping) matrices. The methods presented here focus on retaining the desired symmetry in the updated model

scholarly journals Model Updating of Friction Stir Welding for Aluminium and Magnesium Plate Structure

2018 ◽  
Vol 150 ◽  
pp. 04004 ◽  
Author(s):  
Nazrotul Afina Nazri ◽  
Mohd Shahrir Mohd Sani ◽  
Muhammad Nasiruddin Mansor ◽  
Siti Norazila Zahari
Keyword(s):  
Friction Stir Welding ◽  
Natural Frequencies ◽  
Model Updating ◽  
Mode Shapes ◽  
Average Error ◽  
Element Analysis ◽  
Structural Dynamic ◽  
Friction Stir ◽  
Dissimilar Friction Stir Welding ◽  
Al 7075

Friction stir welding (FSW) of aluminium and magnesium alloys face high demands in automotive and aerospace application due to its advanced and lightweight properties. FSW is an emerging solid state joining process in which the material that is being welded does not melt and recast. The main objectives of this project are to perform model updating based on finite element analysis (FEA) and experimental modal analysis (EMA) of dissimilar material of aluminium alloy AL 7075 and magnesium alloy AZ 31B. Modal properties such as natural frequencies, mode shapes are obtained and compared between FEA and EMA. The discrepancies of first five modes natural frequencies are below than 10% and the model updating have been conducted to minimize the error between two methods. This model updating are based on sensitivity analysis in order to make sure which parameters are given more influence in this structural dynamic analysis. Young’s modulus and Poisson’s ratio both materials are selected in the model updating process. After perform model updating, total average error of the natural frequencies of dissimilar friction stir welding plate is improved significantly.

Improved Inverse Eigensensitivity Method for Structural Analytical Model Updating

1995 ◽  
Vol 117 (2) ◽  
pp. 192-198 ◽  
Author(s):  
R. M. Lin ◽  
M. K. Lim ◽  
H. Du
Keyword(s):  
Analytical Model ◽  
Model Updating ◽  
Element Model ◽  
Small Error ◽  
Analytical Models ◽  
Engineering Structures ◽  
Modal Data ◽  
Existing Problems ◽  
Practical Engineering ◽  
True Values

In order to update analytical models of practical engineering structures, inverse eigensensitivity method (IEM) has been developed. Though it has nowadays been widely accepted, the classical inverse eigensensitivity method does have some drawbacks such as the assumption of small error magnitudes and slow speed of convergence due to the fact that the sensitivity coefficients are calculated purely based on modal data of analytical model. In the present paper, an improved inverse eigensensitivity method, which avoids the existing problems of classical inverse eigensensitivity method, has been developed. The improved method employs both analytical and experimental modal data to calculate the required eigensensitivity coefficients which are very close to their true values. The method has been further extended to the case where measured coordinates are incomplete. Practical applicability of the method has been assessed by its application to the updating of the finite element model of a plane truss structure.

Analytical model for harmonic response of dissimilar single-lap joints

2017 ◽  
Vol 232 (4) ◽  
pp. 457-472 ◽  
Author(s):  
Mohamed O Gafar ◽  
Khalid H Almitani ◽  
Ramzi Othman
Keyword(s):  
Analytical Model ◽  
Adhesive Bonding ◽  
Natural Frequencies ◽  
Transfer Functions ◽  
Lap Joints ◽  
Analytical Models ◽  
Main Concern ◽  
Element Analysis ◽  
Harmonic Response ◽  
Single Lap Joints

Adhesive bonding is increasingly used in automobile, marine and aeronautical structures. The dynamic response of adhesively bonded joints is therefore a main concern. This paper deals with the harmonic response of single-lap joints. A closed-form analytical solution is derived to account for the case of joints with dissimilar substrates. The transfer functions predicted by the analytical model match well the transfer functions predicted by a two-dimensional finite element analysis, and so do the natural frequencies. The numerical and analytical models show that the natural frequencies are sensitive to the order of substrates. Mainly, fixing the end of the stiffer substrate leads to natural frequencies that are mostly higher than those which are obtained by fixing the end of the softer substrate.

Combining FEA and Field Measurement Techniques for Dynamic Machinery Foundation Design

2019 ◽  
Author(s):  
Seth Cunningham ◽  
Benjamin A. White ◽  
Nathan W. Poerner
Keyword(s):  
Field Measurement ◽  
Degrees Of Freedom ◽  
Natural Frequencies ◽  
Measurement Techniques ◽  
Forced Response ◽  
Modal Testing ◽  
Mode Shapes ◽  
Design Phase ◽  
Foundation Design ◽  
Element Analysis

Abstract Proper foundation design is an essential component in the design process of many types of rotating machinery. Most foundations are designed for static loading, however dynamic foundation design is often overlooked or considered a secondary check. Failing to consider the dynamics of the foundation during the design phase can result in excessive machinery vibrations resulting in failures, forced shutdowns, and expensive in-situ repairs. Foundation dynamics are commonly assessed using finite element analysis (FEA) during the design phase with modal and forced response analyses; however the interactions of machinery, piping, foundation, and soil create a potentially nonlinear system with many degrees-of-freedom. In many applications, it is necessary to design the mechanical natural frequencies of the foundation to avoid excitation mechanisms of the machinery. With modern variable speed machines, accurate prediction of the mechanical natural frequencies is often required to place them in narrow frequency bands between operating orders. These systems are inherently difficult to accurately model, however combining FEA modeling with field measurement techniques allows the possibility of field “tunable” foundation designs. For example, pile foundations can be designed with alternative pile configurations to be connected during commissioning based on the results of modal testing. Modal and vibration data collected on-site can also be used to calibrate the frequencies and mode shapes predicted by the model. This calibrated model is then used to evaluate the effects of proposed changes to the skid and suggest modifications to fix or reduce the problems in existing machinery foundations.

scholarly journals Rapid Evaluation for Position-Dependent Dynamics of a 3-DOF PKM Module

2014 ◽  
Vol 6 ◽  
pp. 238928 ◽  
Author(s):  
Hai-wei Luo ◽  
Hui Wang ◽  
Jun Zhang ◽  
Qi Li
Keyword(s):  
Natural Frequencies ◽  
Mode Shapes ◽  
Parallel Kinematic Machine ◽  
Computationally Efficient ◽  
Element Analysis ◽  
Reduction Techniques ◽  
Modal Reduction ◽  
Governing Differential Equation ◽  
Parallel Kinematic ◽  
Analytical System

Based on the substructure synthesis and modal reduction technique, a computationally efficient elastodynamic model for a fully flexible 3-RPS parallel kinematic machine (PKM) tool is proposed, in which the frequency response function (FRF) at the end of the tool can be obtained at any given position throughout its workspace. In the proposed elastodynamic model, the whole system is divided into a moving platform subsystem and three identical RPS limb subsystems, in which all joint compliances are included. The spherical joint and the revolute joint are treated as lumped virtual springs with equal stiffness; the platform is treated as a rigid body and the RPS limbs are modelled with modal reduction techniques. With the compatibility conditions at interfaces between the limbs and the platform, an analytical system governing differential equation is derived. Based on the derived model, the position-dependent dynamic characteristics such as natural frequencies, mode shapes, and FRFs of the 3-RPS PKM are simulated. The simulation results indicate that the distributions of natural frequencies throughout the workspace are strongly dependant on mechanism's configurations and demonstrate an axial-symmetric tendency. The following finite element analysis and modal tests both validate the analytical results of natural frequencies, mode shapes, and the FRFs.

scholarly journals NASTRAN Analysis of a Turbine Blade and Comparison With Test and Field Data

1975 ◽  
Author(s):  
J. M. Allen ◽  
L. B. Erickson
Keyword(s):  
Turbine Blade ◽  
Natural Frequencies ◽  
Beam Theory ◽  
Mode Shapes ◽  
Stress Distributions ◽  
Free Standing ◽  
Element Analysis ◽  
Metallographic Examination ◽  
Stiffening Effect ◽  
Generalized Beam Theory

A NASTRAN finite element analysis of a free standing gas turbine blade is presented. The analysis entails calculation of the first four natural frequencies, mode shapes, and relative vibratory stresses, as well as deflections and stresses due to centrifugal loading. The stiffening effect of the centrifugal force field was accounted for by using NASTRAN’s differential stiffness option. Natural frequencies measured in a rotating test correlated well with computed results. Areas of maximum vibratory stress (fundamental mode) coincided with the three zones of crack initiation observed in a metallographic examination of a fatigue failure. Airfoil stress distributions were found to be significantly different from that predicted by generalized beam theory, especially near the airfoil-platform junction.

L1 Regularized Model Updating for Structural Damage Detection

2018 ◽  
Vol 18 (12) ◽  
pp. 1850157 ◽  
Author(s):  
Yu-Han Wu ◽  
Xiao-Qing Zhou
Keyword(s):  
Damage Detection ◽  
Structural Damage ◽  
Model Updating ◽  
Regularization Parameter ◽  
Structural Vibration ◽  
Mode Shapes ◽  
Modal Data ◽  
Vibration Data ◽  
Stiffness Reduction ◽  
Regularized Model

Model updating methods based on structural vibration data have been developed and applied to detecting structural damages in civil engineering. Compared with the large number of elements in the entire structure of interest, the number of damaged elements which are represented by the stiffness reduction is usually small. However, the widely used [Formula: see text] regularized model updating is unable to detect the sparse feature of the damage in a structure. In this paper, the [Formula: see text] regularized model updating based on the sparse recovery theory is developed to detect structural damage. Two different criteria are considered, namely, the frequencies and the combination of frequencies and mode shapes. In addition, a one-step model updating approach is used in which the measured modal data before and after the occurrence of damage will be compared directly and an accurate analytical model is not needed. A selection method for the [Formula: see text] regularization parameter is also developed. An experimental cantilever beam is used to demonstrate the effectiveness of the proposed method. The results show that the [Formula: see text] regularization approach can be successfully used to detect the sparse damaged elements using the first six modal data, whereas the [Formula: see text] counterpart cannot. The influence of the measurement quantity on the damage detection results is also studied.

Symmetric Model Correction of Mechanical Systems

1993 ◽  
Author(s):  
Marca Lam ◽  
Daniel J. Inman ◽  
Andreas Kress
Keyword(s):  
Analytical Model ◽  
Model Updating ◽  
Symmetric Model ◽  
Simple Method ◽  
Modal Data ◽  
Model Correction ◽  
Systems Model ◽  
Modal Damping ◽  
Stiffness Matrices ◽  
Damped Systems

Abstract This work examines the model updating problem for simple nonconservative proportionally damped systems. Model correction, also called model updating, refers to the practice of adjusting an analytical model until the model agrees with measured modal data. The specific case examined here assumes that natural frequencies and modal damping ratios are available from vibration tests and that the measured data disagrees in part with the modal data predicted by an analytical model. Most model correction schemes tend to produce updated damping and stiffness matrices which are asymmetric. The simple method presented here focuses on retaining the desired symmetry in the updated model.

Investigation of stiffness of small wind turbine blade based on vibration analysis technique

2019 ◽  
Vol 44 (1) ◽  
pp. 49-59
Author(s):  
Nilesh Chandgude ◽  
Nitin Gadhave ◽  
Ganesh Taware ◽  
Nitin Patil
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Wind Turbine ◽  
Natural Frequency ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Mode Shapes ◽  
Element Analysis ◽  
Finite Element Software ◽  
Small Wind Turbine

In this article, three small wind turbine blades of different materials were manufactured. Finite element analysis was carried out using finite element software ANSYS 14.5 on modeled blades of National Advisory Committee for Aeronautics 4412 airfoil profile. From finite element analysis, first, two flap-wise natural frequencies and mode shapes of three different blades are obtained. Experimental vibration analysis of manufactured blades was carried out using fast Fourier transform analyzer to find the first two flap-wise natural frequencies. Finally, the results obtained from the finite element analysis and experimental test of three blades are compared. Based on vibration analysis, we found that the natural frequency of glass fiber reinforced plastic blade reinforced with aluminum sheet metal (small) strips increases compared with the remaining blades. An increase in the natural frequency indicates an increase in the stiffness of blade.

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