scholarly journals An Analytical Method for Crack Detection of Beams with Uncertain Boundary Conditions by a Concentrated Test Mass

2018 ◽  
Vol 4 (7) ◽  
pp. 1629
Author(s):  
Seyed Milad Mohtasebi ◽  
Naser Khaji
Keyword(s):  
Boundary Conditions ◽  
Crack Detection ◽  
Beam Theory ◽  
Element Model ◽  
Test Mass ◽  
Cracked Beam ◽  
Stationary Mass ◽  
Numerical Finite Element ◽  
Torsion Springs ◽  
Uncertain Boundary

The aim of this study is to introduce a method for crack detection and simultaneously assessing boundary conditions in beams. This study suggests a method based on the effect of a concentrated test mass on the natural frequency that is defined as a stationary mass, which can be located in different positions of the beam and cannot be separated from the beam. Timoshenko beam theory is used to calculate the frequencies. In this method, a beam with the desired number of cracks is modeled. The beam is divided into separated parts at crack section which are joined together by elastic weightless torsion springs, to avoid non-linearity effects, it is assumed that the crack is always open. At the first step, equations for a cracked beam are extracted by considering the spring boundary conditions. Then, to verify the equations, numerical finite element model is used. In this way, a new method is also applied to model the torsion springs in supports and it is shown that suggested model is acceptable. Eventually, the obtained responses are evaluated and the sources of errors are identified. To correct the existing errors, a modifying function is suggested. Finally, the inverse problem is solved.

Radial stiffness analysis of circular ring with uncertain boundary conditions: Mechanical elastic wheel as an example

2021 ◽  
pp. 095440622110505
Author(s):  
Chenxi Zhang ◽  
Youqun Zhao ◽  
Shilin Feng ◽  
Han Xu ◽  
Qiuwei Wang ◽  
...  
Keyword(s):  
Finite Element ◽  
Boundary Conditions ◽  
Finite Element Model ◽  
Element Model ◽  
Circular Ring ◽  
Chain Model ◽  
Elastic Wheel ◽  
Radial Stiffness ◽  
Mechanical Elastic Wheel ◽  
Uncertain Boundary

The paper studies the radial stiffness of mechanical elastic wheel (MEW), which is regarded as a circular ring with uncertain boundary conditions for the first time, and proposes a ring-chain model to solve the radial stiffness of the ring. Different from assuming the boundary conditions by experience or building finite element model with complex processes from previous researches, the ring-chain model coupling circular ring model and dynamics of multi-rigid body is accurate and simple to find the loaded positions of ring and make the boundary conditions clear. The results show that the ring-chain model can be solved to get the deformations and loaded positions of ring, the radial stiffness of MEW is large, and the radial displacement of MEW increases non-linearly. The results are consistent with that from finite element model under the same settings, but the time cost of ring-chain model is less. In addition, the influence factors of ring radial stiffness are also found and analyzed. The method presented in this paper can provide data for the response analyses of vehicle and references for the analysis of circular ring with uncertain boundary conditions.

scholarly journals Free Vibration of Axially Loaded Multi-Cracked Beams Using the Transfer Matrix Method

2019 ◽  
Vol 24 (No 1) ◽  
pp. 119-138
Author(s):  
Yousef S. Al Rjoub ◽  
Azhar G. Hamad
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Beam Theory ◽  
Mode Shapes ◽  
Physical Parameters ◽  
Cracked Beam ◽  
Axially Loaded

In this paper, an analytical method is developed to study the free vibration of multi-cracked, axially loaded beams with differing boundary conditions, namely, hinged-hinged, clamped-clamped, clamped-hinged, and clamped-free. The cracked beam system is modelled as a number of beam segments connected by massless rotational springs with sectional flexibility. Each segment is assumed to obey the Euler-Bernoulli beam theory. The characteristic equation of the cracked beam with differing boundary conditions, which is a function of the natural frequency, sizes and location of the cracks, and the physical parameters of the beam, as well as the corresponding mode shapes, is derived using a simple transfer matrix method. In this paper, a detailed parametric study is conducted to show the effects of cracks and axial load on vibrational properties of the cracked beam. The results obtained in this study agree well with analytical results available in the literature.

scholarly journals Stiffness Estimation and Equivalence of Boundary Conditions in FEM Models

2021 ◽  
Vol 11 (4) ◽  
pp. 1482
Author(s):  
Róbert Huňady ◽  
Pavol Lengvarský ◽  
Peter Pavelka ◽  
Adam Kaľavský ◽  
Jakub Mlotek
Keyword(s):  
Boundary Condition ◽  
Finite Element ◽  
Boundary Conditions ◽  
Model Updating ◽  
Element Model ◽  
Computational Time ◽  
Stiffness Coefficients ◽  
First Case ◽  
Numerical Approaches

The paper deals with methods of equivalence of boundary conditions in finite element models that are based on finite element model updating technique. The proposed methods are based on the determination of the stiffness parameters in the section plate or region, where the boundary condition or the removed part of the model is replaced by the bushing connector. Two methods for determining its elastic properties are described. In the first case, the stiffness coefficients are determined by a series of static finite element analyses that are used to obtain the response of the removed part to the six basic types of loads. The second method is a combination of experimental and numerical approaches. The natural frequencies obtained by the measurement are used in finite element (FE) optimization, in which the response of the model is tuned by changing the stiffness coefficients of the bushing. Both methods provide a good estimate of the stiffness at the region where the model is replaced by an equivalent boundary condition. This increases the accuracy of the numerical model and also saves computational time and capacity due to element reduction.

Modeling of a One-Sided Bonded and Rigid Constraint Using Beam Theory

2008 ◽  
Vol 75 (3) ◽  
Author(s):  
Peter J. Ryan ◽  
George G. Adams ◽  
Nicol E. McGruer
Keyword(s):  
Boundary Conditions ◽  
Microelectromechanical Systems ◽  
Three Dimensional ◽  
Beam Theory ◽  
Rotational Stiffness ◽  
Element Analysis ◽  
Transverse Loads ◽  
Rigid Constraint ◽  
Dimensional Finite Element ◽  
Three Dimensional Finite Element

In beam theory, constraints can be classified as fixed/pinned depending on whether the rotational stiffness of the support is much greater/less than the rotational stiffness of the freestanding portion. For intermediate values of the rotational stiffness of the support, the boundary conditions must account for the finite rotational stiffness of the constraint. In many applications, particularly in microelectromechanical systems and nanomechanics, the constraints exist only on one side of the beam. In such cases, it may appear at first that the same conditions on the constraint stiffness hold. However, it is the purpose of this paper to demonstrate that even if the beam is perfectly bonded on one side only to a completely rigid constraining surface, the proper model for the boundary conditions for the beam still needs to account for beam deformation in the bonded region. The use of a modified beam theory, which accounts for bending, shear, and extensional deformation in the bonded region, is required in order to model this behavior. Examples are given for cantilever, bridge, and guided structures subjected to either transverse loads or residual stresses. The results show significant differences from the ideal bond case. Comparisons made to a three-dimensional finite element analysis show a good agreement.

scholarly journals Exact receptance function and receptance curvature of a clamped-clamped continuous cracked beam

2019 ◽  
Vol 41 (4) ◽  
pp. 349-361
Author(s):  
Nguyen Viet Khoa ◽  
Cao Van Mai ◽  
Dao Thi Bich Thao
Keyword(s):  
Numerical Simulations ◽  
Frequency Domain ◽  
Crack Detection ◽  
Harmonic Excitation ◽  
Second Derivative ◽  
Cracked Beam ◽  
Cracked Beams

The receptance function has been studied and applied widely since it interrelates the harmonic excitation and the response of a structure in the frequency domain. This paper presents the derivation of the exact receptance function of continuous cracked beams and its application for crack detection. The receptance curvature is defined as the second derivative of the receptance. The influence of the crack on the receptance and receptance curvature is investigated. It is concluded that when there are cracks the receptance curvature has sharp changes at the crack positions. This can be applied for the crack detection purpose. In this paper, the numerical simulations are provided.

scholarly journals Influence of the Parameterization in the Interval Solution of Elastic Beams

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Stefano Gabriele ◽  
Valerio Varano
Keyword(s):  
Boundary Conditions ◽  
Closed Form ◽  
Interval Analysis ◽  
Elastic Beam ◽  
Elastic Beams ◽  
Analysis Theory ◽  
Set Intersection ◽  
Interval Solution ◽  
Uncertain Boundary

We are going to analyze the interval solution of an elastic beam under uncertain boundary conditions. Boundary conditions are defined as rotational springs presenting interval stiffness. Developments occur according to the interval analysis theory, which is affected, at the same time, by the overestimation of interval limits (also known as overbounding, because of the propagation of the uncertainty in the model). We suggest a method which aims to reduce such an overestimation in the uncertain solution. This method consists in a reparameterization of the closed form Euler-Bernoulli solution and set intersection.

scholarly journals Effect of spatial distribution of fibers on elastic properties of unidirectional carbon/carbon composites

2021 ◽  
Vol 309 ◽  
pp. 01214
Author(s):  
M.V.N Mohan ◽  
Ramesh Bhagat Atul ◽  
Vijay Kumar Dwivedi
Keyword(s):  
Finite Element ◽  
Spatial Distribution ◽  
Elastic Properties ◽  
Element Model ◽  
Experimental Methods ◽  
Design Stage ◽  
Carbon Composites ◽  
Numerical Predictions ◽  
Numerical Finite Element ◽  
Very High

Carbon/Carbon composites finds its applications in several high temperature applications in the field of Space, Aviation etc. Designing of components or sub systems with carbon/carbon composites is a challenging task. It requires prediction of elastic properties with a very high accuracy. The prediction can be normally done by analytical, numerical or experimental methods. At the design stage the designers resort to numerical predictions as the experimental methods are not feasible during design stage. Analytical methods are complex and difficult to implement. The designers use numerical methods for prediction of elastic properties using Finite Element Modeling (FEM). The spatial distribution of fibers in matrix has an effect on results of prediction of elastic constants. The generation of random spatial distribution of fibers in representative volume element (RVE) challenging. The present work is aimed at study of effect of spatial distribution of fiber in numerical prediction of elastic properties of unidirectional carbon/carbon composites. MATLAB algorithm is used to generate the spatial distribution of fibers in unidirectional carbon/carbon composites. The RVE elements with various random fiber distributions are modeled using numerical Finite element Model using ABAQUS with EasyPBC plugin. The predicted elastic properties have shown significant variation to uniformly distributed fibers.

scholarly journals Monitoring a sudden crack of beam-like bridge during earthquake excitation

2013 ◽  
Vol 35 (3) ◽  
Author(s):  
Nguyen Viet Khoa
Keyword(s):  
Fourier Transform ◽  
Crack Detection ◽  
Crack Depth ◽  
Sudden Change ◽  
Wavelet Spectrum ◽  
Cracked Beam ◽  
Earthquake Excitation ◽  
Time Frequency ◽  
Short Time ◽  
Time Information

This paper presents a wavelet spectrum technique for monitoring a sudden crack of a beam-like bridge structure during earthquake excitation. When there is a sudden crack caused by earthquake excitation the stiffness of the structure is changed leading to a sudden change in natural frequencies during vibration. It is difficult to monitor this sudden change in the frequency using conventional approaches such as Fourier transform because in Fourier transform the time information is lost so that it is impossible to analyse short time events. To overcome this disadvantage, wavelet spectrum, a time-frequency analysis, is used for monitoring a sudden change in frequency duringearthquake excitation for crack detection. In this study, a model of 3D crack is applied. The derivation of the stiffness matrix of a 3D cracked beam element with rectangular section adopted from fracture mechanics is presented. Numerical results showed that the sudden occurrence of the crack during earthquake excitation can be detected by the sudden change in frequency using wavelet power spectrum. When the crack depth increases, the instantaneous frequency (IF) of the structure is decreased.

scholarly journals Non linear analysis of vibrations generated by a contact with friction

2010 ◽  
pp. 305-316
Author(s):  
Anissa Meziane ◽  
Laurent Baillet
Keyword(s):  
Physical Phenomenon ◽  
Element Model ◽  
Interface State ◽  
Linear Analysis ◽  
Bimaterial Interface ◽  
Dynamic Rupture ◽  
Elastic Solids ◽  
Nonlinear Analyses ◽  
Beam System ◽  
Numerical Finite Element

The aim of this paper is to study vibrations generated at contact with friction for two different applications. The first one is an investigation of friction-induced vibrations of a beam-on-beam system in contact with friction. For this study the complementary use of linear and nonlinear analyses drives to the understanding of physical phenomenon induced in these vibrations. The second parts consists in investigating numerically dynamic rupture of a bimaterial interface. The numerical Finite Element model is composed of two homogeneous and isotropic elastic solids which are brought in contact with friction by remote normal compression and shear traction. The rupture is nucleated by decreasing instantaneously the friction coefficient to zero at nucleation area. The properties of the obtained ruptures (velocity, generated waves, interface state…) are analyzed.

Generalised Beam Theory for composite beams with longitudinal and transverse partial interaction

2016 ◽  
Vol 22 (10) ◽  
pp. 2011-2039 ◽  
Author(s):  
Gerard Taig ◽  
Gianluca Ranzi
Keyword(s):  
Structural Response ◽  
Beam Theory ◽  
Element Model ◽  
Composite Beams ◽  
Cross Sectional ◽  
Shear Connections ◽  
Dynamic Analyses ◽  
Partial Interaction ◽  
Deformation Modes ◽  
Generalised Beam Theory

This paper presents a Generalised Beam Theory formulation to study the partial interaction behaviour of two-layered prismatic steel–concrete composite beams. The novelty of the proposed approach is in its capacity to handle the deformability of the shear connections at the interface between the slab and steel beam in both the longitudinal and transverse directions in the evaluation of the deformation modes. This method falls within a category of cross-sectional analyses available in the literature for which a suitable set of deformation modes, including conventional, extension and shear, is determined from dynamic analyses of discrete planar frame models representing the cross-section. In this context, the shear connections are modelled using shear deformable spring elements. As a result, the in-plane partial shear interaction behaviour is accounted for in the planar dynamic analysis during the evaluation of the conventional and extension modes, while the longitudinal partial interaction behaviour associated with the shear modes is included in the out-of-plane dynamic analyses. In the case of the conventional modes, the longitudinal slip is accounted for in the post-processing stage where the warping displacements are determined. A numerical example of a composite box girder beam is presented and its structural response investigated for different levels of shear connection stiffness in both the longitudinal and transverse directions. The accuracy of the numerical results is validated against those obtained with a shell finite element model implemented in ABAQUS/Standard software.

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