Analytical and finite element solutions of free and forced vibration of unrestrained and braced thin-walled beams

2019 ◽  
Vol 26 (5-6) ◽  
pp. 255-276
Author(s):  
Wassim Jrad ◽  
Foudil Mohri ◽  
Guillaume Robin ◽  
El Mostafa Daya ◽  
Jihad Al-Hajjar
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Forced Vibration ◽  
Degrees Of Freedom ◽  
Element Model ◽  
Vibration Modes ◽  
Coupled Modes ◽  
Steady State Method ◽  
Thin Walled ◽  
Benchmark Solutions

In this article, vibration of thin-walled beams with arbitrary open cross-section shape is investigated. Based on the beam element model accounting for warping and flexural–torsional coupling, analytical solutions for different boundary conditions are derived for higher free vibration modes in bending, torsion and flexural–torsional coupled modes. In the model, the effects of rotational inertial kinematic terms are considered. The finite element approach of the model is also investigated. Three-dimensional beams with seven degrees of freedom per node are adopted in the mesh process. Free vibration and forced vibration analyses are possible. In forced vibration, the behaviour of the beams is studied in the frequency domain using the steady-state method (modal analysis). Damping is considered using the Rayleigh model. The model is validated by comparing the results to benchmark solutions found in the literature and to other recent numerical and experimental results. Additional finite element simulations are performed by means of commercial softwares (Abaqus and Adina). In slender unrestrained beams, the vibration behaviour is predominated by torsion and lateral bending modes. In design, recourse to braces is a good compromise. This solution is discussed, and improvement of the vibration behaviour in the presence of intermediate braces is confirmed. Application of higher vibration modes in building and bridge design is outlined. The effects of the number and distribution of the intermediate braces to improve structural stability against vibration behaviour is outlined.

Vibration Response of a Thin-Walled Cylindrical Pipe with Liquid

2012 ◽  
Vol 189 ◽  
pp. 345-349
Author(s):  
Yu Lan Wei ◽  
Bing Li ◽  
Li Gao ◽  
Ying Jun Dai
Keyword(s):  
Finite Element ◽  
Natural Frequencies ◽  
Element Model ◽  
Beam Model ◽  
Vibration Modes ◽  
Timoshenko Beam Model ◽  
Cylindrical Pipe ◽  
Bending Vibration ◽  
Beam Bending ◽  
Thin Walled

Vibration characteristics of the thin-walled cylindrical pipe are affected by the liquid within the pipe. The natural frequencies and vibration modes of the pipe without liquid are analyzed by the theory of beam bending vibration and finite element model, which is based on the Timoshenko beam model. The first three natural frequencies and vibration modes of the pipe with or without liquid are acquired by experiments. As shown in the experiment results, the natural frequencies of the containing liquid pipe are lower than the natural frequencies of the pipe without liquid.

Free-Free Vibration Extraction From Available Vibration Data

2000 ◽  
Author(s):  
Thomas T. Yi
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Boundary Conditions ◽  
Finite Element Model ◽  
Degrees Of Freedom ◽  
Element Model ◽  
Fe Model ◽  
Modal Data ◽  
Vibration Data ◽  
Dynamic Formulation

Abstract This paper presents a procedure for identifying the free-free vibration data of a structure from the available vibration data of the same structure with boundary conditions. For a structure in a mechanical system, depending upon the dynamic formulation used, we may need a set of free-free modal data or a set of constrained modal data. If a finite element model of the structure is available, its vibration data can be obtained analytically under any desired boundary conditions. However, if a finite element model is not available, the vibration data may be determined experimentally. Since experimentally measured vibration data are obtained for a structure supported by some form of boundary conditions, we may need to determine its free-free vibration data. The aim of this study is to extract, based on experimentally obtained vibration data, the necessary free-free frequencies and the associated modes for structures to be used in dynamic formulations. The available vibration data may be obtained for a structure supported either by springs or by fixed boundary conditions. Furthermore, the available modes may be either a complete set; i.e., as many modes as the number of degrees of freedom of the associated FE model is available, or it can be an incomplete set.

Dynamic Characteristics of a Long-Span Cable-Stayed Bridge

2011 ◽  
Vol 480-481 ◽  
pp. 1496-1501
Author(s):  
Liu Hui
Keyword(s):  
Finite Element ◽  
Dynamic Characteristics ◽  
Iteration Method ◽  
Natural Frequencies ◽  
Element Model ◽  
Vibration Modes ◽  
Cable Stayed Bridge ◽  
Long Span ◽  
Subspace Iteration ◽  
Floating System

In order to study the dynamic characteristics of a super-long-span cable-stayed bridge which is semi-floating system, the spatial finite element model of this cable-stayed bridge was established in ANSYS based on the finite element theory.Modal solution was conducted using subspace iteration method, and natural frequencies and vibration modes were obtained.The dynamic characteristics of this super-long-span cable-stayed bridge were then analyzed.Results showed that the super-long-span cable-stayed bridge of semi-floating system has long basic cycle, low natural frequencies, dense modes and intercoupling vibration modes.

scholarly journals On the Finite Element Model of Rotating Functionally Graded Graphene Beams Resting on Elastic Foundation

2021 ◽  
Vol 2021 ◽  
pp. 1-18
Author(s):  
Nguyen Van Dung ◽  
Nguyen Chi Tho ◽  
Nguyen Manh Ha ◽  
Vu Trong Hieu
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Elastic Foundation ◽  
Mechanical Response ◽  
Shear Deformation Theory ◽  
Free Vibration Analysis ◽  
Element Model ◽  
Functionally Graded ◽  
Mode Shapes ◽  
Engineering Practice

Rotating structures can be easily encountered in engineering practice such as turbines, helicopter propellers, railroad tracks in turning positions, and so on. In such cases, it can be seen as a moving beam that rotates around a fixed axis. These structures commonly operate in hot weather; as a result, the arising temperature significantly changes their mechanical response, so studying the mechanical behavior of these structures in a temperature environment has great implications for design and use in practice. This work is the first exploration using the new shear deformation theory-type hyperbolic sine functions to carry out the free vibration analysis of the rotating functionally graded graphene beam resting on the elastic foundation taking into account the effects of both temperature and the initial geometrical imperfection. Equations for determining the fundamental frequencies as well as the vibration mode shapes of the beam are established, as mentioned, by the finite element method. The beam material is reinforced with graphene platelets (GPLs) with three types of GPL distribution ratios. The numerical results show numerous new points that have not been published before, especially the influence of the rotational speed, temperature, and material distribution on the free vibration response of the structure.

Self-Vibration Characteristics of Plane Gate in Inverted Siphon Project

2012 ◽  
Vol 160 ◽  
pp. 64-68
Author(s):  
Hui Fang Xue ◽  
You Wang
Keyword(s):  
Finite Element ◽  
Large Scale ◽  
Element Model ◽  
Vibration Characteristics ◽  
The Self ◽  
Vibration Modes ◽  
Vibration Frequencies ◽  
Small Opening ◽  
First Order ◽  
Inverted Siphon

Based on the vibration problem of the plane gate in the inverted siphon exit of a large-scale hydraulic project in northern Xinjiang, the software ANSYS is used to build the entity model and finite element model. Considering the influence of fluid-solid coupling, the self-vibration characteristics of the gate in the water and without water are analyzed. The first six self-vibration frequencies and vibration modes of the gate are calculated. The results show that the height of water has a significant impact on the self-vibration frequencies of the plane gate. The first order natural frequency on the condition of small opening is decreased by 28.5%. It shows that the structure of the plane gate must be improved.

A Parallel Solution Strategy for Finite Element Models

1996 ◽  
Author(s):  
Jordan J. Cox ◽  
Jeffrey A. Talbert ◽  
Eric Mulkay
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Element Model ◽  
Decomposition Methods ◽  
Finite Element Models ◽  
Unique Contribution ◽  
Matrix Equations ◽  
Parallel Solution ◽  
The Finite Element Model ◽  
Parallel Fashion

Abstract This paper presents a method for naturally decomposing finite element models into sub-models which can be solved in a parallel fashion. The unique contribution of this paper is that the decomposition strategy comes from the geometric features used to construct the solid model that the finite element model represents. Domain composition and domain decomposition methods are used to insure global compatibility. These techniques reduce the N2 behavior of traditional matrix solving techniques, where N is the number of degrees of freedom in the global set of matrix equations, to a sum of m matrices with n2 behavior, where n represents the number of degrees of freedom in the smaller sub-model matrix equations.

Finite Element Model of the Human Knee Joint to Study Tibio-Femoral Contact Mechanics

2000 ◽  
Author(s):  
Tammy Haut Donahue ◽  
Maury L. Hull ◽  
Mark M. Rashid ◽  
Christopher R. Jacobs
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Degrees Of Freedom ◽  
Soft Tissues ◽  
Element Model ◽  
Human Knee ◽  
Human Knee Joint ◽  
Solid Models ◽  
Flexion Extension ◽  
A New Technique

Abstract A finite element model of the tibio-femoral joint in the human knee was created using a new technique for developing accurate solid models of soft tissues (i.e. cartilage and menisci). The model was used to demonstrate that constraining rotational degrees of freedom other than flexion/extension when the joint is loaded in compression markedly affects the load distribution between the medial and lateral sides of the joint. The model also was used to validate the assumption that the bones can be treated as rigid.

scholarly journals Dynamic Analysis of Tapered Thin-Walled Beams Using Spectral Finite Element Method

2019 ◽  
Vol 2019 ◽  
pp. 1-13 ◽  
Author(s):  
Yiping Shen ◽  
Zhijun Zhu ◽  
Songlai Wang ◽  
Gang Wang
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Wind Turbine ◽  
Element Model ◽  
Rotor Blades ◽  
Mode Shapes ◽  
Modal Frequency ◽  
Thin Walled Structures ◽  
Thin Walled ◽  
Spectral Finite Element

Tapered thin-walled structures have been widely used in wind turbine and rotor blade. In this paper, a spectral finite element model is developed to investigate tapered thin-walled beam structures, in which torsion related warping effect is included. First, a set of fully coupled governing equations are derived using Hamilton’s principle to account for axial, bending, and torsion motion. Then, the differential transform method (DTM) is applied to obtain the semianalytical solutions in order to formulate the spectral finite element. Finally, numerical simulations are conducted for tapered thin-walled wind turbine rotor blades and validated by the ANSYS. Modal frequency results agree well with the ANSYS predictions, in which approximate 30,000 shell elements were used. In the SFEM, one single spectral finite element is needed to perform such calculations because the interpolation functions are deduced from the exact semianalytical solutions. Coupled axial-bending-torsion mode shapes are obtained as well. In summary, the proposed spectral finite element model is able to accurately and efficiently to perform the modal analysis for tapered thin-walled rotor blades. These modal frequency and mode shape results are important to carry out design and performance evaluation of the tapered thin-walled structures.

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.

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