scholarly journals An Updating Method for Finite Element Models of Flexible-Link Mechanisms Based on an Equivalent Rigid-Link System

2018 ◽  
Vol 2018 ◽  
pp. 1-14 ◽  
Author(s):  
R. Belotti ◽  
R. Caracciolo ◽  
I. Palomba ◽  
D. Richiedei ◽  
A. Trevisani
Keyword(s):  
Dynamic Models ◽  
Model Updating ◽  
Body Motion ◽  
Transformation Model ◽  
Mode Shapes ◽  
Deformation Model ◽  
Flexible Link ◽  
Static Tests ◽  
State Observers ◽  
Stiffness And Damping

This paper proposes a comprehensive methodology to update dynamic models of flexible-link mechanisms (FLMs) modeled through ordinary differential equations. The aim is to correct mass, stiffness, and damping matrices of dynamic models, usually based on nominal and uncertain parameters, to accurately represent the main vibrational modes within the bandwidth of interest. Indeed, the availability of accurate models is a fundamental step for the synthesis of effective controllers, state observers, and optimized motion profiles, as those employed in modern control schemes. The method takes advantage of the system dynamic model formulated through finite elements and through the representation of the total motion as the sum of a large rigid-body motion and the elastic deformation. Model updating is not straightforward since the resulting model is nonlinear and its coordinates cannot be directly measured. Hence, the nonlinear model is linearized about an equilibrium point to compute the eigenstructure and to compare it with the results of experimental modal analysis. Once consistency between the model coordinates and the experimental data is obtained through a suitable transformation, model updating has been performed solving a constrained convex optimization problem. Constraints also include results from static tests. Some tools to improve the problem conditioning are also proposed in the formulation adopted, to handle large dimensional models and achieve reliable results. The method has been experimentally applied to a challenging system: a planar six-bar linkage manipulator. The results prove their capability to improve the model accuracy in terms of eigenfrequencies and mode shapes.

Truncation errors of assumed shape modeling for flexible-link manipulators

2012 ◽  
Vol 226 (11) ◽  
pp. 2627-2644 ◽  
Author(s):  
Fatemeh Heidari ◽  
Mohammad Vakil ◽  
Reza Fotouhi ◽  
Peter N Nikiforuk
Keyword(s):  
Mode Shape ◽  
Dynamic Models ◽  
Transfer Functions ◽  
Degree Of Freedom ◽  
Flexible Manipulator ◽  
Mode Shapes ◽  
Physical Parameters ◽  
Flexible Link ◽  
Dimensional Parameters ◽  
Assumed Mode

The assumed mode shape method has been widely used to derive finite degree-of-freedom dynamic models for flexible-link manipulators, which theoretically have infinite degree-of-freedom dynamics. For a single flexible manipulator, this approximation changes locations of the zeros of transfer functions between base torque and end-effector displacement. The change in locations of zeros considerably affects accuracy of the model and therefore the performance of model-based controllers. This article presents a comprehensive study on the change in locations of zeros due to the truncation associated with assumed mode shape method. It is shown that the locations of approximate zeros depend on four non-dimensional parameters, whereas the locations of analytical zeros depend on only two non-dimensional parameters. Approximate zeros are obtained from assumed mode shape method models, whereas analytical zeros are derived from infinite order models. A thorough study of the differences between approximate zeros and analytical zeros versus the number of mode shapes as well as all the physical parameters is performed. Moreover, guidelines are provided to select the numbers of mode shapes such that the approximate zeros become close to the analytical zeros. These guidelines can easily be used by control and modeling engineers, making them valuable for modeling and control of flexible robot manipulators.

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

Rotor-Dynamics of Different Shaft Configurations for a 6 kW Micro Gas Turbine for Concentrated Solar Power

2016 ◽  
Author(s):  
A. Arroyo ◽  
M. McLorn ◽  
M. Fabian ◽  
M. White ◽  
A. I. Sayma
Keyword(s):  
Gas Turbines ◽  
High Speed ◽  
Dynamic Models ◽  
Solar Power ◽  
Critical Issue ◽  
Rotor Dynamics ◽  
Mode Shapes ◽  
Concentrated Solar Power ◽  
Element Analysis ◽  
Rotor Dynamic

Rotor-dynamics of Micro Gas Turbines (MGTs) under 30 kW have been a critical issue for the successful development of reliable engines during the last decades. Especially, no consensus has been reached on a reliable MGT arrangement under 10 kW with rotational speeds above 100,000 rpm, making the understanding of the rotor-dynamics of these high speed systems an important research area. This paper presents a linear rotor-dynamic analysis and comparison of three mechanical arrangements of a 6 kW MGT intended for utilising Concentrated Solar Power (CSP) using a parabolic dish concentrator. This application differs from the usual fuel burning MGT in that it is required to operate at a wider operating speed range. The objective is to find an arrangement that allows reliable mechanical operation through better understanding of the rotor dynamics for a number of alternative shaft-bearings arrangements. Finite Element Analysis (FEA) was used to produce Campbell diagrams and to determine the critical speeds and mode shapes. Experimental hammer tests using a new approach based on optical sensing technology were used to validate the rotor-dynamic models. The FEA simulation results for the natural frequencies of a shaft arrangement were within 5% of the measurements, while the deviation for the shaft-bearings arrangement increased up to 16%.

Influence of Geometric Imperfections on Vibrational Frequencies of Thin Rings

1975 ◽  
Vol 97 (4) ◽  
pp. 1199-1203
Author(s):  
Joseph R. Gartner ◽  
Shrikant T. Bhat
Keyword(s):  
Cross Section ◽  
Natural Frequencies ◽  
Rectangular Cross Section ◽  
Circular Ring ◽  
Body Motion ◽  
Mode Shapes ◽  
Geometric Imperfections ◽  
Modal Coupling ◽  
Truncated Fourier Series ◽  
Energy Formulation

A relatively thin—thickness to radius ratio—circular ring with rectangular cross section has been investigated to numerically evaluate the effect of eccentricity on the in plane bending natural frequencies and mode shapes. The assumed boundary conditions correspond to a ring freely supported in space such that it is free to translate and rotate with rigid body motion. A truncated Fourier series solution is assumed in an energy formulation to obtain numerical approximations of the eigenvalues and the corresponding eigenvectors for different eccentricities. Extensional and inextensional models for both Flu¨gge and Love-Timoshenko ring models were considered with two thickness to radius ratios. Results show different rates of decrease in the magnitudes of the natural frequencies for different mode configurations. Existence of closely spaced frequencies along with modal coupling are noticeable at 50 percent eccentricity.

Identification of stiffness and damping of the weld in stiffened plates using model updating

2022 ◽  
Vol 82 ◽  
pp. 103140
Author(s):  
Kshitij Shrivastava ◽  
Kiran Vijayan ◽  
Vikas Arora
Keyword(s):  
Model Updating ◽  
Stiffened Plates ◽  
Stiffness And Damping

scholarly journals Damage Diagnosis in 3D Structures Using a Novel Hybrid Multiobjective Optimization and FE Model Updating Framework

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-13 ◽  
Author(s):  
Nizar Faisal Alkayem ◽  
Maosen Cao ◽  
Minvydas Ragulskis
Keyword(s):  
Structural Damage ◽  
Model Updating ◽  
Complex Problem ◽  
Dynamic Responses ◽  
Mode Shapes ◽  
Fe Model ◽  
Modal Strain Energy ◽  
3D Structures ◽  
Multiobjective Particle Swarm Optimization ◽  
Damage Tracking

Structural damage detection is a well-known engineering inverse problem in which the extracting of damage information from the dynamic responses of the structure is considered a complex problem. Within that area, the damage tracking in 3D structures is evaluated as a more complex and difficult task. Swarm intelligence and evolutionary algorithms (EAs) can be well adapted for solving the problem. For this purpose, a hybrid elitist-guided search combining a multiobjective particle swarm optimization (MOPSO), Lévy flights (LFs), and the technique for the order of preference by similarity to ideal solution (TOPSIS) is evolved in this work. Modal characteristics are employed to develop the objective function by considering two subobjectives, namely, modal strain energy (MSTE) and mode shape (MS) subobjectives. The proposed framework is tested using a well-known benchmark model. The overall strong performance of the suggested method is maintained even under noisy conditions and in the case of incomplete mode shapes.

Dynamical Model Updating Based on Gradient Regularization Method

2013 ◽  
Vol 351-352 ◽  
pp. 118-121
Author(s):  
He Long Xu ◽  
Jun Xiao ◽  
Yu Xin Zhang
Keyword(s):  
Regularization Method ◽  
Solution Method ◽  
Model Updating ◽  
Input Parameter ◽  
Mode Shapes ◽  
Problem Solution ◽  
Finite Element Program ◽  
Element Program ◽  
Important Input ◽  
The Mathematical Model

Modulus of elasticity is an important input parameter in all kinds of structural analyses. The mathematical model used to identify the structural elastic modulus with measured Frequencies and mode shapes at several points is thusly built up in this paper, and then Gradient-Regularization method, an inverse problem solution method, is employed to solve the problem. General finite element program is compiled, and numerical examples have proved that the method of this thesis is efficient. The issues such as the choice of model error and the choice of measuring points are discussed as well.

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.

Analysis of Instabilities in Railway Vehicles Employing Operational Modal Analysis

2015 ◽  
Author(s):  
Lara Erviti Calvo ◽  
Gorka Agirre Castellanos ◽  
Germán Gimenez
Keyword(s):  
Numerical Model ◽  
Modal Analysis ◽  
Mode Shape ◽  
Operational Modal Analysis ◽  
Mode Shapes ◽  
Correct Identification ◽  
Unstable Condition ◽  
Static Tests ◽  
Railway Vehicles ◽  
Damping Rate

The application of Operational Modal Analysis (OMA) in the railway sector opens a broad field of opportunities. The validation of the numerical model employed in the design phase is usually performed employing data obtained in static tests. The drawback is that some suspension parameters, such as dampers, only have an influence in the dynamic behavior and not in the static behavior. Because of that, the use of the mode shapes identified from track measurements in combination with the static tests leads to a more accurate validation of the numerical model. Apart from that, most passenger comfort and dynamic problems are associated to slightly damped modes. A correct identification of the modal parameters can be used as a continuous design improvement tool to improve the comfort and dynamic characteristics of future designs. Another valuable application of OMA techniques is the identification of the mode shapes corresponding to instabilities, due to the safety impact that they have. In railway vehicles, instabilities are associated to mode shapes that present a damping rate which decreases with the increase of the running speed. Above a certain speed value, the excitation coming from track cannot be damped by the vehicle and it reaches an unstable condition. This unstable condition leads to high acceleration levels experienced by the passengers and high interaction forces between the wheel and the rail that may lead to safety hazards. The speed above which the vehicle is unstable is known as critical speed, and has to be greater than the maximum speed of the vehicle with a reasonable safety margin. The use of OMA techniques allows identifying the mode shape that causes the instability. This paper presents the application of OMA techniques to measurements performed on a passenger vehicle, in which the speed was increased until the vehicle was unstable. The mode shape that caused the instability was identified as well as its corresponding natural frequency and damping rate.

Sign in / Sign up

Export Citation Format

Share Document