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.

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.

Simulation Analysis of Isolation about Spray Boom

2014 ◽  
Vol 900 ◽  
pp. 742-745 ◽  
Author(s):  
Yao Jie He ◽  
Bai Jing Qiu ◽  
Ya Fei Yang
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Modal Analysis ◽  
Simulation Analysis ◽  
Element Model ◽  
The Finite Element Model

In order to attenuate the deformation of spray boom, a finite element model built based on ANSYS, according to the reasults of numerical modal analysis and modal texting, the reliability of the finite element model was affirmed. Then, an isolator was introduced between spray boom and frame, a frame-isolator-spray boom model was built in ADAMS. The effect of the isolators which have different parameters was research, the reasult shows: The isolator has much effect on attenuating spray booms deformation, the stiffness of isolators spring dampers has little effect on spray booms deformation, but the damping of isolators spring dampers has effect on spray booms deformation.

A Comparative Study of the Human Body Finite Element Model Under Blast Loadings

2012 ◽  
Author(s):  
X. G. Tan ◽  
R. Kannan ◽  
Andrzej J. Przekwas
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Human Body ◽  
Material Properties ◽  
Complex Geometry ◽  
Blast Loading ◽  
Element Model ◽  
Stress Wave Propagation ◽  
Brain Response ◽  
Time Step

Until today the modeling of human body biomechanics poses many great challenges because of the complex geometry and the substantial heterogeneity of human body. We developed a detailed human body finite element model in which the human body is represented realistically in both the geometry and the material properties. The model includes the detailed head (face, skull, brain, and spinal cord), the skeleton, and air cavities (including the lung). Hence it can be used to accurately acquire the stress wave propagation in the human body under various loading conditions. The blast loading on the human surface was generated from the simulated C4 blast explosions, via a novel combination of 1-D and 3-D numerical formulations. We used the explicit finite element solver in the multi-physics code CoBi for the human body biomechanics. This is capable of solving the resulting large system containing millions of unknowns in an extremely scalable fashion. The meshes generated for these simulations are of good quality. This enables us to employ relatively large time step sizes, without resorting to the artificial time scaling treatment. In order to study the human body dynamic response under the blast loading, we also developed an interface to apply the blast pressure loading on the external human body surface. These newly developed models were used to conduct parametric simulations to find out the brain biomechanical response when the blasts impact the human body. Under the same blast loading we also show the differences of brain response when having different material properties for the skeleton, the existence of other body parts such as torso.

Comparing Measured Responses of an Offshore Structure with Operational Modal Analysis assisted Classical Model Approach

2020 ◽  
pp. 1-10
Author(s):  
Bruna Nabuco ◽  
Sandro D. Amador ◽  
Evangelos I. Katsanos ◽  
Ulf T. Tygesen ◽  
Erik Damgaard Christensen ◽  
...  
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Modal Analysis ◽  
Element Model ◽  
Operating Conditions ◽  
Operational Modal Analysis ◽  
Mode Shapes ◽  
Wave Forces ◽  
Wave Load ◽  
Offshore Structure

Abstract Aiming to ensure the structural integrity of an offshore structure, wave-induced responses have been measured during normal operating conditions. Operational Modal Analysis is applied to the data obtained from continuously monitoring the structure. Sensors placed only on the topside of an offshore platform are sufficient to provide information to identify the modal properties of the structure, such as natural frequencies, damping ratios, and mode shapes. A finite element model is created and updated in line with the identified dynamic properties for applying a modal expansion technique in the interest of accessing information at any point of the structure. Wave radars are also placed at the platform from which the wave forces are calculated based on basic industrial standard models. In this way, the wave kinematics are estimated according to the linear wave theory associated with Wheeler stretching. Since this study is related to offshore structures composed by slender elements, the wave forces are estimated using Morison formulation. By assigning typical values to the drag and inertia coefficients, wave loads are estimated and applied to the updated finite element model. For the diffraction effect, the wave load has also been evaluated according to MacCamy and Fuchs theory. The responses obtained from this procedure are compared with measured responses. In addition to describing the process, this paper presents a case study to verify the theory using monitoring data from a tripod jacket. Results indicate realistic response estimation that contributes to the knowledge about the state of the structure.

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