Papers by Keyword: Cracked Beam

Abstract: The design of structures and machineries in present days are based on optimizing of multi-objectives such as maximum strength, maximum life, minimum weight and minimum cost. Due to this flexiblity they allow having a very high level of stresses. This leads to development of cracks in their elements. Due to long-term service many engineering structures may have structural defects such as cracks. So it is very much essential to know the property of structures and response of such structures in various cases. In this article the natural frequencies and mode shapes of an uncracked and cracked cantilever Timoshenko beam is studied by using finite element method (FEM) and MATLAB programme. The effect of crack on the natural frequencies of the uncracked and cracked Timoshenko beam is studied.

Abstract: This paper deals with dynamic analysis of a multi-span continuous beam with an arbitrary number of cracks. This problem is solved by a hybrid analytical/ numerical method that is the basis for applying to a method of damage detection in the multi-span continuous beam later. In this paper, we calculate in detail about vibration frequencies, vibration mode shape of beam structure with cracks. The proposed method is the method that improved the transfer matrix method combined with the mode-superposition method. Only need to use two unknowns, this method can solve the problem of multi-span continuous beam with an arbitrary number of cracks. Calculation cases of beam with cracks and beam without cracks are compared with previous studies.

Abstract: A new analytical method for vibration fatigue life of cracked beams was proposed with the structural response changes as crack growth. In analysis, the damping loss factor was introduced by the complex elastic modulus, and the crack growth was simulated by employing a Paris equation, and the coupling effect of vibration and crack growth was considered through vibration analysis and estimation of fatigue crack propagation cycles by cycles. Results indicate that impacts of exciting frequency and damping on the crack growth are obvious. The resonance fatigue crack growth rate decreases rapidly when big damping is involved, and the first mode is more important to the crack growth than that of other mode.

Abstract: 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 Euler–Bernoulli 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). The beam is modeled as two segments connected by a rotational spring located at the cracked section. This model promotes discontinuities in both vertical displacement and rotational due to bending. The differential equations for the free bending vibrations are established and then solved individually for each segment with the corresponding boundary conditions and the appropriated compatibility conditions at the cracked section by using DTM and analytical solution. The results show that DTM provides simple method for solving equations and the results obtained by DTM converge to the analytical solution with much more accurate for both shallow and deep cracks. This study demonstrates that the differential transform is a feasible tool for obtaining the analytical form solution of free vibration differential equation of cracked beam with simple expression.

Abstract: Simple mathematical model that describes the lateral vibration of elastically coupled cracked cantilever beams carrying rigid disk at their tips is derived. The derived model is used to study the effect of elastic coupling, crack depth and location on the dynamic characteristics of the system. The cracked beam is presented as two beams connected with torsional spring at the crack location. Model verification is carried out using three dimensional finite element analysis using ANSYS program, the verification results showed good agreement with that obtained from the proposed model. The study reveals that the first system natural frequency is affected by the crack and the elastic coupling.

Abstract: The composite element method is utilized to discretise a stepped Euler-Bernoulli beam with a crack. The local stiffness reduction due to the crack is introduced by using a simplified crack model. The finite element equation for the forced vibration analysis is obtained using the composite element method (CEM). The forced vibration response of the cracked stepped beam is numerically calculated using Newmark integration method. Numerical results indicate that the position and depth of a crack affects the low and high natural frequencies and modes of a cantilever beam, respectively. And the position of the crack has significant effects on the dynamic responses of the beam.

Abstract: The aim of the work is to develop a procedure allowing the test engineer to determine the probability of finding a crack in a beam structure. The procedure is based on the use of wavelet analysis and the simulation is performed by taking advantage of spectral elements to represent accurately the dynamic behaviour of beam structures in the high frequency range. In this context, numerical analyses are performed with the final scope of simulating a real testing environment: measurement error is considered and spectral elements are used so as to avoid influencing the capacity of the procedure with regard to solving the inverse problem. In this article the relation between the excitation frequency and the probability of locating the fault is shown. In particular, it is demonstrated by simulation that the probability of correctly determining the fault location increases with the excitation frequency.

Abstract: This paper presents a method for the vibration of a beam with a breathing crack under harmonic excitation. The infinitely thin crack is characterised by a parameter that takes into account the shape and the depth of the crack. The closed- and open-crack states are both modelled by a modal approach: two sets of equations of motion cast in the modal coordinates of their individual mode shapes. The state change (from closed to open or vice versa) involves the calculation of the modal coordinates associated with the new state from the modal coordinates of the previous state. By imposing the continuity of displacement and velocity the beam at the instant of the state change, the matrix that transforms the modal coordinates from one state to the other is determined and proved to be the Modal Scale Factor matrix. This analytical approach takes advantage of exact nature and mathematical convenience of beam modes and is time-efficient. Forced vibration at various values of crack parameter is determined. It is found that as decreases (crack length increases) the vibration becomes increasingly erratic and finally chaotic.

Abstract: The goal of this paper is to generate the stability maps for an elastic cracked beam resting on elastic soils and loaded by a constant distribution of sub-tangential forces. The soil behavior is simulated by a two-parameter Pasternak model. Firstly, the extend version of the Hamilton principle is used to formulate the weak form of the governing equation for the undamaged beam problem. Secondly, a finite element procedure, in which the effect of an open surface crack is computed via the Line-spring model, leads to the discrete governing equation for the cracked beam. Finally, the effect of several parameters on divergence or flutter instability, such as the crack depth and location, the non-conservativeness of the applied load as well as the stiffness of the two soil parameters, is highlighted.