Free vibration analysis of euler-bernoulli beam with double cracks

The governing equation for lateral vibration of eulerbernoulli nanobeam is developed based on eringens nonlocal elasticity theory. Moreover, free vibration analyses of the euler bernoulli and timoshenko beams with any number of cracks can be conducted using the unified procedure based on the developed method. In this paper, the influence of two open cracks on the dynamic behavior of a double cracked simply supported beam is investigated both analytically and experimentally. Euler bernoulli beam model is assumed for the theoretical formulation. The eulerbernoulli beam model is proposed to study the frequency factors for bending vibration of cracked beam with ant symmetric boundary conditions as one end is clamped and the.

Pierre department of mechanical engineering and applied mechanics, the university of michigan, ann arbor, michigan 481092125, u. Orhan sadettin 1 has studied the free and forced vibration analysis of a cracked beam was. Research article free transverse vibration analysis of. Pdf in this paper, the influence of two open cracks on the dynamic behavior of a double cracked simply supported beam is investigated both. Eulerbernoulli beam theory also known as engineers beam theory or classical beam theory is a simplification of the linear theory of elasticity which provides a means of calculating the loadcarrying and deflection characteristics of beams. Oct 04, 2014 eulerbernoulli beam theory also known as engineers beam theory or classical beam theory is a simplification of the linear theory of elasticity which provides a means of calculating the load.

Free vibration analysis an overview sciencedirect topics. Simsek, free vibration analysis of beams subjected to axial load under various boundary conditions. Free vibration of the cracked nonuniform beam with cross. First, regions whose stresses are affected by the crack are analyzed, and according to the distance to the. Free vibration analysis for cracked fgm beams by means of. Ozgumus and kaya 9 used a new analytical approximation method namely differential transforms method to analyze flapwise bending vibration analysis of double tapered rotating euler bernoulli beam. Free vibration analysis of nonuniform multicracked euler. In this paper, the influence of two open cracks on the dynamic behavior of a double cracked simply supported beam is investigated both analytically and. Fourbeam model for vibration analysis of a cantilever beam. Airy points, bessel points, minimum gravity sag, and vibration nodal points of uniform beams. Method to solve free vibration of nonuniform euler bernoulli beams with general elastically end conditions. Stiffness estimation of cracked beams based on nonlinear.

Free vibration analysis of microtubules mts is presented based on the eulerbernoulli beam theory. It is very well known that the presence of a crack in a structure produces a change in its frequency response that can be used to determine the crack properties position and size solving what is called an inverse problem. Free vibration analysis of euler bernoulli beam with double cracks hanik yoon a, insoo son, sungjin ahn b a division of mechanical engineering, dongeui university, 995 eomgwangno, busanjin. The aim of the present work is vibration analysis of multi cracked, stepped. Review paper on crack modeling and crack detection methods. Vibrations of a freefree beam vibration and acoustics. Numerical results are presented for free vibration problems and damage detection problems of representative nonuniform and geometrically stepped eulerbernoulli beams with multiple cracks to demonstrate the effectiveness, efficiency, accuracy and reliability of the proposed method. College of mechanical engineering and applied electronics technology, beijing university of technology, beijing 100124, china. Moreover, free vibration analyses of the eulerbernoulli and timoshenko beams with any number of cracks can be conducted using the unified procedure based on the developed method.

Also in the literature 11, different cracked cross section rectangular shape, vshape is mentioned. A method based on the power series solution is proposed to solve the natural frequency of very slender rotating beam at high angular velocity. Free vibration analysis of a cantilever beam with a slant. Free vibration analysis of the cracked composite beam is presented. In this paper, we calculate in detail about vibration frequencies, vibration mode shape of beam structure with cracks. The crack presence causes nonlinear stress distributions along the sections of a beam, which change the neutral axis of the sections and further affect the beam stiffness. Analysis of free and forced vibration of a cracked. It covers the case for small deflections of a beam that are subjected to lateral loads only. The double fourier transform is employed for the free vibration analysis of the semirigid connected reddy bickford beam with variable crosssection on elastic soil and under axial load by yesilce and catal yesilce and catal, 2011. Based on eulerbernoulli beam theory and a continuous stiffness beam model, the free vibration of rectangularsection beams made of functionally graded materials fgms containing open edge cracks. Energy expressions and free vibration analysis of a. Bahrami and teimourian investigated free vibrations of eulerbernoulli and timoshenko nanobeams. This paper presents an approach for free vibration analysis of the cracked nonuniform beam with general boundary conditions, whose mass per unit length and bending moment of inertia varying as polynomial functions.

In this paper, we present a detailed theoretical study of the modal analysis of microbeams partially immersed in a viscous fluid. Vibration analysis of the beam with crack was also considered in few studies lin et al. Received 8 february 1989, and in revised form 14 july 1989 an approximate galerkin solution to the onedimensional cracked beam. Vibration analysis of a cracked beam on an elastic. Sigma journal of engineering and natural sciences, 3, 110, 2005. Analytical approximation of nonlinear vibration of euler. Vibration analysis of eulerbernoulli beams partially. Analysis of crack detection of a cantilever beam using finite. Free vibration analysis of microtubules as cytoskeleton. Vibration analysis of a cracked timoshenko beam request pdf. In this article, monte carlo simulation method is used in conjunction with finite elements fes for probabilistic free vibration and stability analysis of pipes conveying fluid. It is thus a special case of timoshenko beam theory. Direct and inverse problems on free vibration analysis of. Vibration of the eulerbernoulli beam with allowance for dampings.

This paper presents an analytical approach to investigate the free vibration analysis of cracked nonuniform beam carrying springmass systems by finite element method and illustrates a valid and reliable damage identification method which using hybrid neural genetic technique. The purpose of their research was to detect the cracks in stainless steel plates. These elements can be simply extended to spat ial analysis of framed structures. Based on eulerbernoulli beam theory and a continuous stiffness beam model, the free vibration of rectangularsection beams made of functionally graded materials fgms containing open edge cracks is studied. A transfer matrix method for free vibration analysis of. Free vibration analysis of eulerbernoulli beam with double. A transfer matrix method for free vibration analysis of euler bernoulli beams with variable cross section mihail boiangiu, valentin ceausu, and costin d untaroiu journal of vibration and control 2014 22. An effective crack identification procedure has been developed based on the dynamic behavior of a eulerbernoulli cracked beam.

Maiti and sinha 11 used higher order shear deformation theory for the analysis of composite beams. Vibrations analysis of cracked nanobeams using quadrature. International journal of structural stability and dynamics. An analytical solution for free vibration of elastically. Research article free vibration analysis for cracked fgm beams by means of a continuous beam model echuanyang, 1,2 xiangzhao, 1 andyinghuili 1 school of mechanics and engineering, southwest jiaotong university, chengdu, china school of mechanical of engineering, chongqing university of technology, chongqing, china. The aim of the present work is vibration analysis of multi cracked, stepped nanobeams by using wave approach. Free vibration analysis of cracked stepped beams of rectangular crosssection. In a plane stress analysis, the effects of various crack positions and depths, different boundary conditions and other geometric parameters on the displacement and the stress contours are detected. The governing equations of motion are derived using a variational approach and the free frequencies of vibrations are obtained employing two different. In this paper, free lateral vibration of eulerbernoulli nanobeam with multiple. Euler bernoulli beam theory also known as engineers beam theory or classical beam theory is a simplification of the linear theory of elasticity which provides a means of calculating the loadcarrying and deflection characteristics of beams.

Free vibration analysis of uniform beams with arbitrary. Erol, effect of mass attachment on the free vibration of cracked beam, the 8th int. In this article, a spectral finite element sfe model is presented for vibration analysis of a cracked viscoelastic beam subjected to moving loads. Free vibration analysis of eulerbernoulli beam with double cracks hanik yoon a, insoo son, sungjin ahn b a division of mechanical engineering, dongeui university, 995 eomgwangno, busanjin. Nine node isoparametric elements are used in the analysis. A research on modal analysis of beam structures was done by kumar p.

Dynamic analysis of cantilever beam with transverse crack. Vibration analysis of a multispan continuous beam with cracks. A reaches a certain lever and the effect of shear deformation could be ignored. Assuming the material gradients follow exponential distribution along beam thickness direction, the conversion relation between the vibration governing equations of a fgm beam and that of. Abstractthe eulerbernoulli uniform elastically supported beam model with incorporated dissipation mechanisms is dealt with. This work concerns with free vibration analysis of cracked nanobeam problems. In simsek 2010a the vibration response is examined of a simply supported fg beam to a moving mass by using euler bernoulli, timoshenko and the thirdorder shear deformation beam theories.

It is considered with either constant velocity or acceleration. To show the benefits of this method, the effect of different physical parameters on the amplitude is discussed for a cantilever beam with a cyclically varying axial load. This paper deals with dynamic analysis of a multispan continuous beam with an arbitrary number of cracks. However, it is well understood that the e ects of the shear deformation. Seyedpoor developed a twostage method to identify the locations and extent of multiple damage in beam.

Vibration of a cracked cantilever beam under moving mass. Positive sign convention for nodal degrees of freedom and forces. Vibration analysis of cracked composite bendingtorsion. Free vibration analysis of a cantilever beam with a slant edge crack. The simply supported beam is modeled by the eulerbemoulli beam theory. The modal analysis of free vibration on central crack plate was done. The beam is modeled as two segments connected by a rotational spring located at the cracked section.

Nonlinear vibration and stability analysis of thermally postbuckled double layered graphene sheet under 1. Flexural free vibrations of multistep nonuniform beams. Free vibration analysis of dwcnts using cdm and rayleigh. Solution of free vibration equations of eulerbernoulli. The main features of the gfem are discussed and the partition of unity functions and the local approximation spaces are presented. Vibration of the eulerbernoulli beam with allowance for dampings leopold herrmann. An analytical method for free vibration of multi cracked and. Both single and double edged crack are considered for the formulation. Vibration analysis of beams wi th and without cracks using the composite element model 27 represents the cracked section rizos et al. In this study, free and forced vibration analysis of a cracked beam were performed in order to identify the crack in a cantilever beam. For fluidstructure interaction, eulerbernoulli beam model is used for analyzing pipe structure and plug flow model for representing internal fluid flow in the pipe. Euler bernoulli beam theory is a simplification of the linear theory of elasticity which provides a means of calculating the loadcarrying and deflection characteristics of beams. Vibrations of a freefree beam by mauro caresta 4 chladni 2 patterns it is possible in a laboratory experiment to visualize the nodes of a vibrating beam nodal lines in this case since the beam has a real width by sprinkling sand on it.

Vibration analysis of beams with open and breathing cracks. Conditions are given to ensure oscillatory character of solutions. Vibration analysis of a cracked cantilever beam under moving mass loads has been investigated in the present paper. And racks are the main cause of structural failure. Hamid reza mirdamadi phd iran professional profile. The generalized finite element method applied to free. A new method to study free transverse vibration of the. The study results suggest that free vibration analysis provides suitable information for the detection of single and two cracks, whereas forced vibration can detect only the single crack condition. Free vibration analysis of cracked beam semantic scholar. The dynamic shape functions are derived from the exact solution of the governing wave equations and are utilized for frequencydomain representation of a moving load. The aim of this study is to propose a method for studying the free transverse vibration of the human lumbar spine using timoshenko and eulerbernoulli beam theories. It is assumed that strain at a certain point is a function of the strains at all points within the influence domain. Their analysis can be used for the prediction of the dynamic response of a simply supported beam with open surface cracks.

Free vibration analysis of rotating euler beams at high. Study on modified differential transform method for free vibration analysis of uniform euler bernoulli beam. A numerical method for free vibration analysis of beams. Dec 31, 2016 deriving the equation of motion and for an euler bernoulli beam and solving for the response. Naguleswaran, transverse vibration of an euler bernoulli uniform beam on up to five resilient supports including ends, journal of sound and vibration, 261, 372384, 2003.

Oct 09, 2009 vibration analysis of beams with open and breathing cracks subjected to moving masses vibration analysis of beams with open and breathing cracks subjected to moving masses ariaei, a ziaeirad, s ghayour, m. He studied the crack detection of cantilever beam by vibration analysis method. Study on modified differential transform method for free. Free vibration analysis of nonuniform multicracked eulerbernoulli beam k. The free vibration response of double walled carbon nanotubes dwcnts is investigated. Keywords nonlinear vibration, euler bernoulli beam, homotopy analysis. The crack is assumed to be distributed along the width of the beam as a straight line and a parabola. Vibration simulation for a cantilever beam including a. Moreover, in a free vibration analysis, changes of natural frequencies and mode shapes due to the aforementioned effects are determined. Transverse vibration analysis of eulerbernoulli beams using. Referring to the dynamic behavior of a beam with a crack, the.

Free vibration and stability of axially functionally graded. A new continuous model for flexural vibration analysis of a cracked. Free vibration analysis for cracked fgm beams by means of a. Research article free vibration analysis for cracked fgm. Saltation is observed in some mode shapes at the crack location, especially for larger crack depths. It was first enunciated circa 1750, but was not applied on a large scale until the development of the eiffel tower and the ferris wheel in the late 19th century. This continuous cracked beam vibration theory lead to a good approximation for the dynamic response to lateral excitation, as it can be easily extended to other vibration modes. Numerical examples demonstrate that the surface energy increases the natural frequency of the beam. The vibrational characteristics of a microbeam are well known to strongly depend on the fluid in which the beam is immersed. Ostachowicz and krawczuk 2 presented a method of analysis of the effect of two open cracks upon the. As a result, free and forced vibration characteristics of bendingtorsion coupled beams have been an interesting area for many researchers. Free vibration and stability of axially functionally graded tapered euler bernoulli beams fig. The finite element analysis was performed in ansys 18. Free vibration of microscaled timoshenko beams abstract in this paper, a comprehensive model is presented to investigate the influence of surface elasticity and residual surface tension on the natural frequency of flexural vibrations of microbeams in the presence of rotary inertia and shear deformation effects.

They also used a rotational spring model to describe the effects of the cracks. On the fundamental transverse vibration frequency of a 1 free. Transverse vibration analysis of an eulerbernoulli beam. Vibration analysis of multicracked beam traversed by. Free vibration analysis of multiple cracked functionally. In this study, the differential equations for free bending vibrations of straight beams with variable cross section are solved using bessel s functions. Free vibration analysis of beams and frames with multiple. Adaptive finite element analysis for damage detection of. A transfer matrix method for free vibration analysis of euler.

These advantages of the proposed procedure would be more remarkable as the increase of the number of cracks. Centripetal and coriolis forces which become important in the case of long beams and mass load with high velocity have been inserted into the theory. Transverse vibration analysis of an euler bernoulli beam continuous system. Free lateral vibration of doublewalled nanobeam is investigated by zhang et al. Zhifeng liu, yunyao yin, feng wang, yongsheng zhao and ligang cai.

With regard to beam like structural free vibration, it can be treated as plane stress problem, so a 2dfem analysis is more accurate than a 1dfem analysis in theory. The transfer matrix method is an analytical method for investigating the vibrations in many structures such as beams, sheets, and shells. Timoshenko beam model for the vibration analysis of a cracked. Beam deflection using double integration method duration.

A study on modal analysis of central crack stainless steel plate using ansys was done by maliky f. The beam is modeled by two different beam theories, which are eulerbernoulli beam theory and timoshenko beam theory. An analytical method for free vibration analysis of. Journal of mechanical science and technology 21 2007 476485. The theoretical results are also validated by a comparison with experimental measurements. A fixed free microbeam vibrating in a viscous fluid is modeled using the euler bernoulli equation for the beams. The cracked nanobeam is simplified to a system of two segments joined by a rotational spring located at the cracked section. The free bending vibration of a beam of a constant. Christides and barr 1984 developed the onedimensional vibration theory for the lateral vibration of a cracked eulerbernoulli beam with one or more pairs of symmetric cracks. The crack is an open type edge crack placed in the medium of the beam and it is uniform along the width of the beam. Firstly, based on the finite element method, the dynamic characteristics of nonuniform cracked beam carrying spring. Results obtained for a cantilever beam with two cracks analysis show an efficient state of. Action of cyclic loads leads to formation of double sided cracks on the beam. Free vibration study of vshape and rectangular shape double.

Houbolt and brooks 1 derived the equations of motion of a cantilever eulerbernoulli beam in coupled bending bendingtorsion vibration. Crack detection in composite cantilever beam by vibration. Study of free undamped and damped vibrations of a cracked. Transverse vibration analysis of an eulerbernoulli beam continuous system. To the best knowledge of the author, study on the multicracked beam under moving mass has not been yet recorded in the literature. Free vibration analysis of microtubules as cytoskeleton components.

The cracked beam is modeled as multisegments connected by a rotational. He compared the frequency results with and without cracked. Based on eringens nonlocal elasticity theory, the governing equation of eulerbernoulli and timoshenko nanobeams, are derived. The eulerbernoulli beam model is proposed to study the frequency factors for bending vibration of cracked beam with ant symmetric boundary conditions as one end is clamped and the other is simply supported. Free vibration analysis of eulerbernoulli beam with double cracks. In this paper, free vibration differential equations of cracked beam are solved by using differential transform method dtm that is one of the numerical methods for ordinary and partial differential equations.

The crack in this particular case is assumed to be an open surface crack and the damping is not being considered in this theory. An efficient method for crack identification in simply. Free vibration analysis of eulerbernoulli beam with. To perform vibration analysis, many structures could be modeled entirely or partially as beams with variable or constant cross section. A dsc regularized diracdelta method for flexural vibration of elastically supported fg beams subjected to a moving load. Beam like structures are widely used in various aeronautical, civil and mechanical engineering fields. Theoretical analysis of free vibration of microbeams under different. Eulerbernoulli microbeam based on the nonlocal strain gradient theory. The natural frequency of the flapwise bending vibration, and coupled lagwise bending and axial vibration is investigated for the rotating beam. Sfem is an efficient tool for the treatment of vibration problems in free vibration of bernoulli euler beam using the spectral element method hamioud, s khalfallah, s. For easy of calculation, the beam like structure can be treated as eulerbernoulli beam when lh. Thus, this paper presents a method for the stiffness estimation of cracked beams based on the stress distributions.

Free vibration of a cracked nanobeam with consideration of surface energy and transverse shear deformation is studied. Deriving the equation of motion and for an eulerbernoulli beam and solving for the response. Therefore, the free vibration analysis of cracked beams have been investigated by. Huang, shih, and kim 2009 attempted to use an inverse vibration method to solve the forced vibration problem raised in cutting tools that were modeled as euler bernoulli beams.

Free vibration analysis of cracked uniform cantilever beam 24 5. This problem is solved by a hybrid analytical numerical method that is the basis for applying to a method of damage detection in the multispan continuous beam later. Krawczuk 12 for the cantilever beam which has two open double sided v shape cracks. Spectral finite element for vibration analysis of cracked. Effect of damage parameters on vibration signatures of a. An analytical method for free vibration of multi cracked and stepped. Minimum gravity sag, and vibration nodal points of uniform beams airy points bessel points eulerbernoulli beam free free beam nodal points optimal support location vibration. Jul 20, 2019 hanik yoon, insoo son, sungjin ahn, free vibration of euler bernoulli beam with double cracks. The theory was validated experimentally for simply supported beams with singleedge and double edge cracks. Authors also studied free and forced vibration of inhomogeneous eulerbernoulli beams under an axial force and a transverse moving load. Rahimi2 1department of mechanical engineering, isfahan university, isfahan, iran 2department of mechanical engineering, kashan university, kashan, iran abstract this paper provides an exact approach for free.

Free vibrational analysis of cracked and uncracked. Detection of cracks in beam structures using measurements of natural frequencies. Free vibration analysis of multicracked micro beams based on. Vibration analysis of beams with and without cracks using. Free vibration analysis of beams considering different. It is possible to predict the location and the depth of a crack based on the changes in vibration parameters.

The size e ect is taken into consideration using the eringens nonlocal elasticity theory. The rotating beam is subdivided into several equal segments. Static and free vibration analysis of carbon nano wires based on timoshenko beam theory using differential quadrature method. The equation of motion is derived by using the hamiltons principle and analyzed by numerical method.