• Smart Structures and Systems
• /
• v.29 no.3
• /
• pp.387-393
• /
• 2022

This paper presents the vibration analysis of cracked ceramic-reinforced aluminum composite beams by using a method based on changes in modal strain energy. The crack is considered to be straight. The effective properties of composite materials of the beams are estimated through Mori-Tanaka micromechanical model. Comparison study and numerical simulations with various parameters; ceramic volume fraction, reinforcement aspect ratio, ratio of the reinforcement Young's modulus to the matrix Young's modulus and ratio of the reinforcement density to the matrix density are taken into investigation. Results demonstrate the pronounced effects of these parameters on intact and cracked ceramic aluminum beams.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 2002.11b
• /
• pp.725-730
• /
• 2002

This paper presents an efficient modeling method for open cracked beam structures. An equivalent bending spring model is introduced to represent the structural weakening effect in the presence of open cracks. The proposed method adopts the exact dynamic element method (EDEM) to avoid the difficulty and numerical errors in association with re-meshing the structure. The proposed method is rigorously compared with a commercial finite element code. Experiments are also performed to validate the proposed modeling method. Finally, a diagnostic scheme for open cracked beam structures is proposed and demonstrated through a numerical example.

• Journal of the Korean Society for Precision Engineering
• /
• v.20 no.6
• /
• pp.197-204
• /
• 2003

This paper presents an efficient modeling and dynamic analysis method for open cracked beam structures. An equivalent bending spring model is introduced to represent the structural weakening effect in the presence of cracks. The proposed method adopts the exact dynamic element method (EDEM) to avoid the inconvenience and numerical errors in association with re-meshing the structural model with the crack position changed. The proposed modeling method is validated through a series of simulation and experiments. First, the proposed method is rigorously compared with a commercial finite element code. Then, two kinds of experiments are performed to validate the proposed modeling method. Finally, a diagnostic scheme fur open cracked beam structures is proposed and demonstrated through a numerical example.

• Transactions of the Korean Society for Noise and Vibration Engineering
• /
• v.18 no.12
• /
• pp.1327-1334
• /
• 2008

In this paper, the purpose is to investigate the stability of cracked Timoshenko cantilever beams subjected to subtangential follower force. In addition, an analysis of the instability(critical follower force of flutter and divergence) of a cracked beam as slenderness ratio and subtangential coefficient is investigated. The governing differential equations of a Timoshenko beam subjected to an end tangential follower force is derived via Hamilton's principle. The crack is assumed to be in the first mode of fracture and to be always opened during the vibrations. The results of this study will contribute to the safety test and stability estimation of structures of a cracked beam subjected to subtangential follower force.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 2004.11a
• /
• pp.713-716
• /
• 2004

In this paper a dynamic behavior of a double-cracked cnatilver beam with a tip mass and the moving mass is presented. Based on the Euler-Bernoulli beam theory, the equation of motion is derived by using Lagrange's equation. The influences of the moving mass, a tip mass and double cracks have been studied on the dynamic behavior of a cantilever beam system by numerical method. The cracks section are represented by the local flexibility matrix connecting two undamaged beam segments. ,Therefore, the cracks are modelled as a rotational spring. Totally, as a tip mass is increased, the natural frequency of cantilever beam is decreased. The position of the crack is located in front of the cantilever beam, the frequencies of a double-cracked cantilever beam presents minimum frequency.

• Structural Engineering and Mechanics
• /
• v.63 no.4
• /
• pp.551-565
• /
• 2017

In this paper, an analytical approach is proposed for determining vibration characteristics of cracked non-uniform continuous Timoshenko beam carrying an arbitrary number of spring-mass systems. This method is based on the Timoshenko beam theory, transfer matrix method and numerical assembly method to obtain natural frequencies and mode shapes. Firstly, the beam is considered to be divided into several segments by spring-mass systems and support points, and four undetermined coefficients of vibration modal function are contained in each sub-segment. The undetermined coefficient matrices at spring-mass systems and pinned supports are obtained by using equilibrium and continuity conditions. Then, the overall matrix of undetermined coefficients for the whole vibration system is obtained by the numerical assembly technique. The natural frequencies and mode shapes of a cracked non-uniform continuous Timoshenko beam carrying an arbitrary number of spring-mass systems are obtained from the overall matrix combined with half-interval method and Runge-Kutta method. Finally, two numerical examples are used to verify the validity and reliability of this method, and the effects of cracks on the transverse vibration mode shapes and the rotational mode shapes are compared. The influences of the crack location, depth, position of spring-mass system and other parameters on natural frequencies of non-uniform continuous Timoshenko beam are discussed.

• Proceedings of the Korea Committee for Ocean Resources and Engineering Conference
• /
• 2004.11a
• /
• pp.271-276
• /
• 2004

In this paper. dynamic behavior of the cracked beam under a moving mass is presented using the finite element method (FEM). Model accuracy is improved with the following consideration: (1) FE model with Timoshenko beam element (2) Additional flexibility matrix due to crack presence (3) Interaction forces between the moving mass and supported beam. The Timoshenko bean model with a two-node finite element is constructed based on Guyan condensation that leads to the results of classical formulations. but in a simple and systematic manner. The cracked section is represented by local flexibility matrix connecting two unchanged beam segments and the crack as modeled a massless rotational spring. The inertia force due to the moving mass is also involved with gravity force equivalent to a moving load. The numerical tests for various mass levels. crack sizes. locations and boundary conditions were performed.

• Steel and Composite Structures
• /
• v.39 no.5
• /
• pp.543-564
• /
• 2021

In this study free vibration analysis of a cracked Goland composite wing is investigated. The wing is modelled as a cantilevered beam based on Euler- Bernoulli equations. Also, composite material is modelled based on lamina fiber-reinforced. Edge crack is modelled by additional boundary conditions and local flexibility matrix in crack location, Castigliano's theorem and energy release rate formulation. Governing differential equations are extracted by Hamilton's principle. Using the separation of variables method, general solution in the normalized form for bending and torsion deflection is achieved then expressions for the cross-sectional rotation, the bending moment, the shear force and the torsional moment for the cantilevered beam are obtained. The cracked beam is modelled by separation of beam into two interconnected intact beams. Free vibration analysis of the beam is performed by applying boundary conditions at the fixed end, the free end, continuity conditions in the crack location of the beam and dynamic stiffness matrix determinant. Also, the effects of various parameters such as length and location of crack and fiber angle on natural frequencies and mode shapes are studied. Modal analysis results illustrate that natural frequencies and mode shapes are affected by depth and location of edge crack and coupling parameter.

• Structural Engineering and Mechanics
• /
• v.74 no.1
• /
• pp.33-54
• /
• 2020

The aim of this study is to calculate natural frequencies and harmonic responses of cracked frames with general boundary conditions by using transfer matrix method (TMM). The TMM is a straightforward technique to obtain harmonic responses and natural frequencies of frame structures as the method is based on constructing a relationship between state vectors of two ends of structure by a chain multiplication procedure. A single variable shear deformation theory (SVSDT) is applied, as well as, Timoshenko beam theory (TBT) and Euler-Bernoulli beam theory (EBT) for comparison purposes. Firstly, free vibration analysis of intact and cracked frames are performed for different crack ratios using TMM. The crack is modelled by means of a linear rotational spring that divides frame members into segments. The results are verified by experimental data and finite element method (FEM) solutions. The harmonic response curves that represent resonant and anti-resonant frequencies directly are plotted for various crack lengths. It is seen that the TMM can be used effectively for harmonic response analysis of cracked frames as well as natural frequencies calculation. The results imply that the SVSDT is an efficient alternative for investigation of cracked frame vibrations especially with thick frame members. Moreover, EBT results can easily be obtained by ignoring shear deformation related terms from governing equation of motion of SVSDT.

• Structural Engineering and Mechanics
• /
• v.56 no.5
• /
• pp.797-811
• /
• 2015

An analytical-computational method along with finite element analysis (FEA) has been employed to analyse the dynamic behaviour of deteriorated structures excited by time- varying mass. The present analysis is focused on the comparative study of a double cracked beam with inclined edge cracks and transverse open cracks subjected to traversing mass. The assumed computational method applied is the fourth order Runge-Kutta method. The analysis of the structure has been carried out at constant transit mass and speed. The response of the structure is determined at different crack depth and crack inclination angles. The influence of the parameters like crack depth and crack inclination angles are investigated on the dynamic behaviour of the structure. The results obtained from the assumed computational method are compared with those of the FEA for validation and found good agreements with FEA.