Vibration Analysis Of Cracked Beam Research Articles

Free vibration analysis of cracked beams by using rigid segment method

This paper deals with the analysis of influence of crack parameters to the modal characteristics of beams at various boundary conditions by using rigid segment method. The beam was discretized by a number of rigid segments which were connected by elastic joints with three degrees of freedom, while the crack was described by cracked element based on fracture mechanics. This model allows detection of coupling between the axial and transverse vibrations under the special boundary conditions. The proposed approach covers both the Euler–Bernoulli and Timoshenko beam model. The efficiency of the method was shown through the few numerical examples.

A modeling method for vibration analysis of cracked beam with arbitrary boundary condition

This paper establishes a cracked Timoshenko beams model to investigate the vibration behavior based on the ultraspherical polynomials. Timoshenko beam theory is applied to model the free vibration analysis of the cracked beam and the numerical results are obtained by using ultraspherical orthogonal polynomials. The boundary conditions of both ends of the cracked beam are modeled as the elastic spring and the beam is divided into two parts by the crack section, and continuous conditions at the connecting face are modeled by the inverse of the flexibility coefficients of fracture mechanics theory. Ignoring the influence of boundary conditions, displacements admissible functions of cracked Timoshenko beam can be set up as ultraspherical orthogonal polynomials.The accuracy and robustness of the present method are evidenced through comparison with previous literature and the results achieved by the finite element method (FEM). In addition, the effects of flexibility coefficient on the natural frequencies are also investigated by using the proposed method. Numerical examples are given for free vibration analysis of cracked beams with various boundary conditions, which may be provided as reference data for future study.

Multiple crack identification in Euler beams by means of B-spline wavelet

In this paper, an effective method for identification of multiple cracks is presented based on discrete wavelet transform in a cracked beam. First, a compactly supported semi-orthogonal B-spline wavelet on interval (BSWI) is employed to construct Euler beam-bending element for free vibration analysis of cracked beams. Next, the construction of general order one-dimensional B-spline wavelets is presented and applied for damage identification in a cantilever beam modeled by wavelet-based elements. Also, principles of an appropriate wavelet selection are presented. Natural vibration modes of a cantilever beam with three cracks are analyzed using one-dimensional fourth-order B-spline wavelet. The results illustrate that BSWI elements can be used in determining the un-cracked and cracked beam natural frequencies with a high accuracy and efficiency. Moreover, the applicability of the presented method in crack identification is studied by numerical examples under several situations, such as in the presence of random noises, and the efficiency of B-spline wavelets in damage prognosis is compared with other types of wavelet functions. The obtained results show the effectiveness of B-spline wavelets in modeling of the damaged beam and identifying multiple crack locations in a free baseline scheme.

Semi-analytical approach for free vibration analysis of cracked beams resting on two-parameter elastic foundation with elastically restrained ends

In present study, free vibration of cracked beams resting on two-parameter elastic foundation with elastically restrained ends is considered. Euler-Bernoulli beam hypothesis has been applied and translational and rotational elastic springs in each end considered as support. The crack is modeled as a mass-less rotational spring which divides beam into two segments. After governing the equations of motion, the differential transform method (DTM) has been served to determine dimensionless frequencies and normalized mode shapes. DTM is a semi-analytical approach based on Taylor expansion series that converts differential equations to recursive algebraic equations. The DTM results for the natural frequencies in special cases are in very good agreement with results reported by well-known references. Also, the DTM procedure yields rapid convergence beside high accuracy without any frequency missing. Comprehensive studies to analyze the effects of crack location, crack severity, parameters of elastic foundation and boundary conditions on dimensionless frequencies as well as effects of elastic boundary conditions on cracked beams mode shapes are carried out and some problems handled for first time in this paper. Since this paper deals with general problem, the derived formulation has capability for analyzing free vibration of cracked beam with every boundary condition.

Free vibration analysis of cracked beams by a combination of finite elements and component mode synthesis methods

Previous work on the dynamics of defective structures, by the authors’ colleagues and other studies in the literature, has revealed substantial variability in predicted vibration behaviour depending on the interface conditions. In the current project the authors have set out to develop a strategy which retains the maximum amount of common information concerning the linear regions of the structure, whilst allowing the maximum scope to vary conditions at the (nonlinear) interface. In this paper, the vibrational characteristics of a cracked Timoshenko beam are analysed. The study integrates the finite element method and component mode synthesis. The beam divided into two components related by a flexibility matrix which incorporates the interaction forces. These forces can be derived from fracture mechanics theory as the inverse of the compliance matrix calculated using stress intensity factors and strain energy release rate expressions. Each substructure is modelled by Timoshenko beam finite elements with two nodes and 3 degrees-of-freedom (axial, transverse and rotation) at each node.