Parametric Identification of a Vibratory System With a Clearance

1991 ◽  
Author(s):  
Richard M. Alexander ◽  
Sherif T. Noah ◽  
Charles G. Franck
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Closed Form ◽  
Piecewise Linear ◽  
Closed Form Solution ◽  
Parametric Identification ◽  
Element Model ◽  
Form Solution ◽  
Vibratory System ◽  
Experimental Structure

Abstract An analytical and experimental investigation of a vibratory system with a clearance was conducted. A finite element model and an equivalent single degree of freedom closed-form solution were used to determine the dynamic parameters and response of an experimental structure interacting with a gap. The closed-form solution is obtained by taking advantage of the piecewise linearity of the system. Results from these solution methods are in agreement with experimental data. The results also suggest that the closed-form solution approximates the response of the experimental structure with accuracy greater than that of the finite element model. The closed-form solution was also used to determine the gap size of the structure. The parameter identification procedure utilized in this study appears to be simple to use and can be readily extended to other types of piecewise-linear multidegree of freedom systems.

Parametric Identification of a Vibratory System With a Clearance

1993 ◽  
Vol 115 (1) ◽  
pp. 25-32 ◽  
Author(s):  
R. M. Alexander ◽  
S. T. Noah ◽  
C. G. Franck
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Closed Form ◽  
Piecewise Linear ◽  
Closed Form Solution ◽  
Element Model ◽  
Form Solution ◽  
Degree Of Freedom ◽  
Vibratory System ◽  
Experimental Structure

An analytical and experimental investigation of a vibratory system with a clearance was conducted. A finite element model and an equivalent single-degree-of-freedom closed-form solution were used to determine the dynamic parameters and response of an experimental structure interacting with a gap. The closed-form solution is obtained by taking advantage of the piecewise linearity of the system. Results from these solution methods are in agreement with experimental data. The results also suggest that the closed-form solution approximates the response of the experimental structure with accuracy greater than that of the finite element model. The closed-form solution was also used to determine the gap size of the structure. The parameter identification procedure utilized in this study appears to be simple to use and can be readily extended to other types of piecewise-linear multi-degree-of-freedom systems.

Identification of cracks in an Euler–Bernoulli beam using Bayesian inference and closed-form solution of vibration modes

2020 ◽  
pp. 146442072096971
Author(s):  
Tianyu Wang ◽  
Mohammad Noori ◽  
Wael A. Altabey
Keyword(s):  
Finite Element ◽  
Bayesian Inference ◽  
Finite Element Model ◽  
Crack Detection ◽  
Closed Form Solution ◽  
Element Model ◽  
Form Solution ◽  
Vibration Modes ◽  
Vibration Data ◽  
The Finite Element Model

Over the past two decades, extensive research has been carried out in the field of structural health monitoring for damage detection in structural systems. Some crack detection methods are based on the finite element model of a beam and use vibration data are developed. These methods identify the crack by updating of the finite element model according to the vibration data of structure. This paper proposes a novel method for crack detection in Euler–Bernoulli beams based on the closed-form solution of mode shapes using Bayesian inference. The expression of vibration modes is derived analytically with the crack parameters as unknown variables. Subsequently, the Bayesian inference is used to obtain the probability density function of crack parameters and to evaluate the uncertainty of the modes. Finally, the method is applied to a series of numerical examples, including a beam with a single-crack and multi-cracks, to verify the effectiveness of this method.

A Finite Element Model of Skin Subjected to a Flash Fire

1994 ◽  
Vol 116 (3) ◽  
pp. 250-255 ◽  
Author(s):  
D. A. Torvi ◽  
J. D. Dale
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Closed Form Solution ◽  
Blood Perfusion ◽  
Element Model ◽  
Form Solution ◽  
Bioheat Transfer ◽  
Multiple Layer ◽  
Degree Burn ◽  
Flash Fire

A variable property, multiple layer finite element model was developed to predict skin temperatures and times to second and third degree burns under simulated flash fire conditions. A sensitivity study of burn predictions to variations in thermal physical properties of skin was undertaken using this model. It was found that variations in these properties over the ranges used in multiple layer skin models had minimal effects on second degree burn predictions, but large effects on third degree burn predictions. It was also found that the blood perfusion source term in Pennes’ bioheat transfer equation could be neglected in predicting second and third degree burns due to flash fires. The predictions from this model were also compared with those from the closed form solution of this equation, which has been used in the literature for making burn predictions from accidents similar to flash fires.

Validation of Nitinol SMA Characteristics Using Finite Element Analysis and Closed Form Solutions

2013 ◽  
Vol 856 ◽  
pp. 147-152
Author(s):  
S.H. Adarsh ◽  
U.S. Mallikarjun
Keyword(s):  
Experimental Data ◽  
Finite Element Analysis ◽  
Finite Element ◽  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
Fe Analysis ◽  
Element Analysis ◽  
Complex Behaviour ◽  
Closed Form Solutions

Shape Memory Alloys (SMA) are promising materials for actuation in space applications, because of the relatively large deformations and forces that they offer. However, their complex behaviour and interaction of several physical domains (electrical, thermal and mechanical), the study of SMA behaviour is a challenging field. Present work aims at correlating the Finite Element (FE) analysis of SMA with closed form solutions and experimental data. Though sufficient literature is available on closed form solution of SMA, not much detail is available on the Finite element Analysis. In the present work an attempt is made for characterization of SMA through solving the governing equations by established closed form solution, and finally correlating FE results with these data. Extensive experiments were conducted on 0.3mm diameter NiTinol SMA wire at various temperatures and stress conditions and these results were compared with FE analysis conducted using MSC.Marc. A comparison of results from finite element analysis with the experimental data exhibits fairly good agreement.

scholarly journals On the Convergence of Nonlinear Modes of a Finite Element Model

2008 ◽  
Vol 15 (6) ◽  
pp. 655-664
Author(s):  
Ramesh Balagangadhar ◽  
Joseph C. Slater
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Modal Analysis ◽  
Complex Geometry ◽  
Linear Part ◽  
Mesh Refinement ◽  
Closed Form Solution ◽  
Element Model ◽  
Mesh Independence ◽  
Nonlinear Modal Analysis

Convergence of finite element models is generally realized via observation of mesh independence. In linear systems invariance of linear modes to further mesh refinement is often used to assess mesh independence. These linear models are, however, often coupled with nonlinear elements such as CFD models, nonlinear control systems, or joint dynamics. The introduction of a single nonlinear element can significantly alter the degree of mesh refinement necessary for sufficient model accuracy. Application of nonlinear modal analysis [1,2] illustrates that using linear modal convergence as a measure of mesh quality in the presence of nonlinearities is inadequate. The convergence of the nonlinear normal modes of a simply supported beam modeled using finite elements is examined. A comparison is made to the solution of Boivin, Pierre, and Shaw [3]. Both methods suffer from the need for convergence in power series approximations. However, the finite element modeling method introduces the additional concern of mesh independence, even when the meshing the linear part of the model unless p-type elements are used [4]. The importance of moving to a finite element approach for nonlinear modal analysis is the ability to solve problems of a more complex geometry for which no closed form solution exists. This case study demonstrates that a finite element model solution converges nearly as well as a continuous solution, and presents rough guidelines for the number of expansion terms and elements needed for various levels of solution accuracy. It also demonstrates that modal convergence occurs significantly more slowly in the nonlinear model than in the corresponding linear model. This illustrates that convergence of linear modes may be an inadequate measure of mesh independence when even a small part of a model is nonlinear.

Generalized and Simplified Linear Closed-Form Solution of an Active Tensegrity Unit in the Form of Octahedral Cell

2014 ◽  
Vol 969 ◽  
pp. 192-198
Author(s):  
Stanislav Kmeť ◽  
Peter Platko
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Analysis ◽  
Closed Form ◽  
Closed Form Solution ◽  
Point Load ◽  
Form Solution ◽  
Cable System ◽  
Form Analysis ◽  
Tensile Forces

Results of the generalized and simplified linear closed form solution of an active or adaptive tensegrity unit, as well as its numerical analysis using finite element method are presented in the paper. The shape of the unit is an octahedral cell with a square base and it is formed by thirteen members (four bottom and four top cables, four edge struts and one central strut). The central strut is designed as an actuator that allows for an adjustment of the shape of the unit which leads to changes of tensile forces in the cables. Due to the diagonal symmetry of the 3D tensegrity unit the closed-form analysis is based on the 2D solution of the equivalent planar biconvex cable system with one central strut under a vertical point load.

Finite Element Model Updating for Damage Localisation and Quantification Using Experimental Modal Data

2005 ◽  
Vol 293-294 ◽  
pp. 297-304
Author(s):  
A.S. Kompalka ◽  
S. Reese
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Model Updating ◽  
Element Model ◽  
Mode Shapes ◽  
Identification Algorithm ◽  
Modal Data ◽  
Additional Equipment ◽  
Structure Vibration ◽  
Experimental Structure

In this contribution we present a validation of an identification procedure and a modeling method with regard to detection, localisation and quantification of damage in a structure. Vibration measurements of an excited experimental structure are used as input for a stochastic subspace system identification algorithm. The identified experimental modal data (eigenvalues and mode shapes) serve to update the underlying finite element model. The experimental setup consists of a cantilever beam and an additional equipment to damage the structure locally and progressively. In contrast to earlier contributions the evolution of damage is quantified in order to estimate the lifetime of the structure.

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