An Inverse Approach on Load Identification From Optimally Placed Accelerometers

2013 ◽  
Author(s):  
Deepak K. Gupta ◽  
Anoop K. Dhingra
Keyword(s):  
Natural Frequencies ◽  
Mode Shapes ◽  
Load Identification ◽  
Acceleration Response ◽  
Inverse Approach ◽  
Modal Damping ◽  
Modal Model ◽  
Load Transducer ◽  
Modal Coordinates ◽  
Selection Of

This paper presents an inverse approach for estimating dynamic loads acting on a structure from acceleration time response measured experimentally at finite number of optimally placed accelerometers on the structure. The structure acts as its own load transducer. The approach is based on the standard equilibrium equation of motion in modal coordinates. Modal model of a system is defined by its modal parameters — natural frequencies, corresponding mode shapes and modal damping factors. These parameters can be estimated experimentally from measured data, analytically for simple problems, or from finite element method. For measurement of the acceleration response, there can be a large number of combinations of locations on the structure where the accelerometers can be mounted and the results may be quite sensitive to the locations selected for accelerometer placements. In fact, the precision with which the applied loads are estimated from measured acceleration response depends on the number of accelerometers utilized and their location on the component. Implementation of a methodology to determine the optimum set of accelerometer locations, based on the construction of D-optimal design, is presented to guide the selection of number and locations of accelerometers that will provide the most precise load estimates. A technique based on model reduction is proposed to reconstruct the input forces accurately. A numerical validation that helps to understand the main characteristics of the proposed approach is also presented. The numerical results reveal the effectiveness and utility of the technique.

scholarly journals Stochastic Modal Models of Slender Uncertain Curved Beams Preloaded Through Clamping

2012 ◽  
Author(s):  
Javier Avalos ◽  
Lanae A. Richter ◽  
X. Q. Wang ◽  
Raghavendra Murthy ◽  
Marc P. Mignolet
Keyword(s):  
Stochastic Model ◽  
Stiffness Matrix ◽  
Natural Frequencies ◽  
Simulated Data ◽  
Mode Shapes ◽  
Curved Beams ◽  
Shape Information ◽  
Final Shape ◽  
Modal Model ◽  
Clamped Beams

This paper addresses the stochastic modeling of the stiffness matrix of slender uncertain curved beams that are forced fit into a clamped-clamped fixture designed for straight beams. Because of the misfit with the clamps, the final shape of the clamped-clamped beams is not straight and they are subjected to an axial preload. Both of these features are uncertain given the uncertainty on the initial, undeformed shape of the beams and affect significantly the stiffness matrix associated with small motions around the clamped-clamped configuration. A modal model using linear modes of the straight clamped-clamped beam with a randomized stiffness matrix is employed to characterize the linear dynamic behavior of the uncertain beams. This stiffness matrix is modeled using a mixed nonparametric-parametric stochastic model in which the nonparametric (maximum entropy) component is used to model the uncertainty in final shape while the preload is explicitly, parametrically included in the stiffness matrix representation. Finally, a maximum likelihood framework is proposed for the identification of the parameters associated with the uncertainty level and the mean model, or part thereof, using either natural frequencies only or natural frequencies and mode shape information of the beams around their final clamped-clamped state. To validate these concepts, a simulated, computational experiment was conducted within Nastran to produce a population of natural frequencies and mode shapes of uncertain slender curved beams after clamping. The application of the above concepts to this simulated data led to a very good to excellent matching of the probability density functions of the natural frequencies and the modal components, even though this information was not used in the identification process. These results strongly suggest the applicability of the proposed stochastic model.

Vibrational characteristics of an earth dam

1966 ◽  
Vol 56 (6) ◽  
pp. 1207-1226
Author(s):  
W. O. Keightley
Keyword(s):  
Theoretical Analysis ◽  
Natural Frequencies ◽  
Forced Vibrations ◽  
Earth Dam ◽  
Mode Shapes ◽  
Modal Damping ◽  
Vibrational Characteristics ◽  
Good Agreement ◽  
Lower Frequencies

Abstract An earth dam was excited into vibrations, in the upstream-downstream direction, by four rotating eccentric-mass vibration generators which were operated on the crest. Natural frequencies, mode shapes, and equivalent viscous modal damping constants of the dam were revealed by the forced vibrations. A theoretical analysis of the dam, based on consideration of shearing deformations only, shows moderately good agreement with the behavior which was observed at the lower frequencies.

Extending Blind Modal Identification to the Underdetermined Case for Ambient Vibration

2012 ◽  
Author(s):  
Scot McNeill
Keyword(s):  
Natural Frequencies ◽  
Second Order ◽  
Modal Identification ◽  
Ambient Vibration ◽  
Mode Shapes ◽  
Frequency Domain Method ◽  
Blind Identification ◽  
Vibration Data ◽  
Modal Damping ◽  
Six Dof

The modal identification framework known as Blind Modal Identification (BMID) has recently been developed, drawing on techniques from Blind Source Separation (BSS). Therein, a BSS algorithm known as Second Order Blind Identification (SOBI) was adapted to solve the Modal IDentification (MID) problem. One of the drawbacks of the technique is that the number of modes identified must be less than the number of sensors used to measure the vibration of the equipment or structure. In this paper, an extension of the BMID method is presented for the underdetermined case, where the number of sensors is less than the number of modes to be identified. The analytic signal formed from measured vibration data is formed and the Second Order Blind Identification of Underdetermined Mixtures (SOBIUM) algorithm is applied to estimate the complex-valued modes and modal response autocorrelation functions. The natural frequencies and modal damping ratios are then estimated from the corresponding modal auto spectral density functions using a simple Single Degree Of Freedom (SDOF), frequency-domain method. Theoretical limitations on the number of modes identified given the number of sensors are provided. The method is demonstrated using a simulated six DOF mass-spring-dashpot system excited by white noise, where displacement at four of the six DOF is measured. All six modes are successfully identified using data from only four sensors. The method is also applied to a more realistic simulation of ambient building vibration. Seven modes in the bandwidth of interest are successfully identified using acceleration data from only five DOF. In both examples, the identified modal parameters (natural frequencies, mode shapes, modal damping ratios) are compared to the analytical parameters and are demonstrated to be of good quality.

On Frequency-Domain System Identification

1997 ◽  
Author(s):  
Eric L. Blades ◽  
Roy R. Craig
Keyword(s):  
System Identification ◽  
Frequency Domain ◽  
Mode Shapes ◽  
Finite Element Models ◽  
Identification Algorithm ◽  
Parameter System ◽  
Modal Damping ◽  
Stiffness Matrices ◽  
Modal Model ◽  
Vibration Tests

Abstract Over the past three decades vibration tests have frequently been conducted on structures and machines for the purpose of validating (updating) finite element models. Such testing is usually referred to as experimental modal analysis. The results of the vibration test are generally presented as a modal model consisting of natural frequencies, mode shapes, and modal damping factors, and the algorithms most frequently used to reduce the test data to modal-model form are time-domain algorithms. Alternatively, direct-parameter system identification may be performed, in which case the direct-parameter model consists of system mass, damping, and stiffness matrices. This paper discusses several features of a new frequency-domain direct-parameter system identification algorithm. Simulations based on a 52-DOF “payload simulator” are used to illustrate the performance of this algorithm.

Input Force Identification in Time Domain Using Optimally Placed Accelerometers

2012 ◽  
Author(s):  
Deepak K. Gupta ◽  
Anoop K. Dhingra
Keyword(s):  
Finite Number ◽  
Time Domain ◽  
Equilibrium Equation ◽  
Dynamic Loads ◽  
Acceleration Response ◽  
Acceleration Time ◽  
Input Force ◽  
Stiffness Matrices ◽  
Load Transducer ◽  
Selection Of

A technique in time domain is presented that aims at identifying dynamic loads acting on a structure from acceleration time response measured experimentally at finite number of locations on the structure. The structure essentially gets transformed into its own load transducer. The approach is based on the standard equilibrium equation in dynamics in time domain. For measurement of the acceleration response, there can be a large number of combinations of locations on the structure where the accelerometers can be mounted and the recovered loads may be quite sensitive to the locations selected for accelerometer placements. In fact, the precision with which the applied loads are estimated from measured acceleration response depends on the number of accelerometers utilized and their locations on the component. Implementation of a methodology to determine the optimum set of accelerometer locations, based on the sparse nature of the mass, damping and stiffness matrices, is presented to guide the selection of number and locations of accelerometers that will provide the most precise load estimates. A numerical validation that helps understand the main characteristics of the proposed approach is also presented. The numerical results reveal the effectiveness and utility of the proposed technique.

Design guide of bolt locations for bolted-joint plates considering dynamic characteristics

2008 ◽  
Vol 223 (2) ◽  
pp. 363-375 ◽  
Author(s):  
J Yoo ◽  
S-J Hong ◽  
J S Choi ◽  
Y J Kang
Keyword(s):  
Dynamic Characteristics ◽  
Natural Frequencies ◽  
Design Guidelines ◽  
Mode Shapes ◽  
Bolted Joint ◽  
Interface Area ◽  
Fe Modelling ◽  
Modelling Method ◽  
Design Guide ◽  
Selection Of

In this study, a simplified finite-element (FE) modelling method is proposed, which simulates the dynamic characteristics of a bolted-joint structure having a large interface area, by utilizing the concept of the cone-frusta method for the jointed parts and spring elements to represent the contact effects occurring in the interfaced area. A method for providing design guidelines for the selection of additional bolt locations is also proposed based on the natural frequencies and mode shapes of the bolted-joint plates. The natural frequency of a specific mode and its mode shape can be controlled by adjusting bolt locations and the number of bolts, considering the effects of the relative deformations in mode shapes, at the plate interfaces. The proposed modelling method and design guidelines are verified based on the experimental results and the FE analysis.

scholarly journals Research on the dynamics of railway car construction

2019 ◽  
Vol 20 (1-2) ◽  
pp. 142-146
Author(s):  
Jarosław Bednarz
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Structural Model ◽  
Natural Frequencies ◽  
Dynamic Properties ◽  
Structural Models ◽  
Transformation Model ◽  
Mode Shapes ◽  
The Finite Element Method ◽  
Modal Model

Nowadays, one of the basic criteria of the design of mechanical structures are dynamic properties of the object. They have a significant effect on the vibration, emitted noise, fatigue strength, controllability and stability of the structure. The structural models are most often use to describe the dynamics of the structures. These models are built in accordance with the principles of the finite element method . Structural model can be used to determine the modal model which is a collection of natural frequencies and corresponding mode shapes by an appropriate coordinate transformation model. The construction pro-cess is called the modal analysis . The article presented a method of conducting the experimental modal studies of railway car. The aim of the study was to identify the dynamic properties including the frequency and mode shapes of the object..

Design and Optimization of Broadband Vibration Absorbers for Noise Control

2001 ◽  
Author(s):  
Emily S. Heinze ◽  
Michael D. Grissom ◽  
Ashok Belegundu
Keyword(s):  
Natural Frequencies ◽  
Mode Shapes ◽  
Vibration Absorber ◽  
Vibration Absorbers ◽  
Analysis Algorithm ◽  
Design And Optimization ◽  
Forcing Function ◽  
Modal Model ◽  
Practical Design ◽  
Base Structure

Abstract A general and practical approach is presented for optimizing structural additions to a base structure for broadband dynamic objectives when the base structure is excited by an arbitrary forcing function. The mode shapes and natural frequencies of the base structure are first found using a commercial finite element code or an experimental modal analysis. The mode shapes are used as basis shapes to reduce the size of the equations. The structural additions are then added as impedances into the reduced modal model. An efficient analysis algorithm is presented to reduce the computational burden for broadband analysis and optimization loops. The power transferred into a Broadband Vibration Absorber (BBVA) from a base structure is maximized as an example application. The numerical results are experimentally verified demonstrating the practical design capabilities of the method.

The Effect of Close or Repeated Eigenvalues on the Updating of Model Parameters from FRF Data

1992 ◽  
Vol 114 (4) ◽  
pp. 514-520 ◽  
Author(s):  
M. I. Friswell ◽  
J. E. T. Penny
Keyword(s):  
Natural Frequencies ◽  
Analytical Models ◽  
Mode Shapes ◽  
Model Parameters ◽  
Finite Element Models ◽  
Reduced Order ◽  
Vibration Data ◽  
Modal Model ◽  
Equation Error ◽  
Error Method

Methods to update the parameters of finite element models using measured vibration data usually use the experimentally derived modal model, that is, the system natural frequencies, damping coefficients, and mode shapes. Alternatively the frequency response functions have been used directly to update condensed analytical models and so avoid the sometimes difficult step of deriving the modal model. Previously the authors suggested an algorithm using FRF data that is basically a weighted equation error method based on a reduced order model. This paper investigates the performance of the algorithm for systems with closely coupled or repeated natural frequencies or eigenvalues.

Tire Vibrations

1977 ◽  
Vol 5 (4) ◽  
pp. 202-225 ◽  
Author(s):  
G. R. Potts ◽  
C. A. Bell ◽  
L. T. Charek ◽  
T. K. Roy
Keyword(s):  
Natural Frequencies ◽  
Standing Waves ◽  
Resonant Mode ◽  
Mode Shapes ◽  
Resonant Vibrations ◽  
Resonant Frequencies ◽  
Radial Tire ◽  
Analysis Techniques ◽  
Thin Ring ◽  
Good Agreement

Abstract Natural frequencies and vibrating motions are determined in terms of the material and geometric properties of a radial tire modeled as a thin ring on an elastic foundation. Experimental checks of resonant frequencies show good agreement. Forced vibration solutions obtained are shown to consist of a superposition of resonant vibrations, each rotating around the tire at a rate depending on the mode number and the tire rotational speed. Theoretical rolling speeds that are upper bounds at which standing waves occur are determined and checked experimentally. Digital Fourier transform, transfer function, and modal analysis techniques used to determine the resonant mode shapes of a radial tire reveal that antiresonances are the primary transmitters of vibration to the tire axle.

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