Theoretical and Experimental Vibration Study of Continuous Beam Wiht Crack Depth and Location Effect

In this research the natural frequency of a cracked beam with different simply supported beam, is investigated analytically and experimental with different crack depth and location effect and the results are compared. The analytical results of the effect of a crack in a continuous beam are calculated the stiffness, EI, for a rectangular beam to involve an exponential function. A comparison made between analytical results from theoretical solution of general equation of motion of beam with crack effect with experimental results, where the biggest error percentage is about (9.4 %). Also it is found that the frequency of beam when the crack is in the middle position is less than the frequency with crack near the end position and the natural frequency of beam decreasing with increasing of crack depth due to decreasing of beam stiffness at any location of crack in beam. INTRODUCTION Many engineering components used in the aeronautical, aerospace and naval construction industries are considered by designers as vibrating structures, operating under a large number of random cyclic stresses. Consequently, it is natural to expect that fatigue crack initiation and propagation in critically stressed zones of such structures, in particular when local or general resonance occurs, [3]. The importance of the beam and its engineering applications is obvious, and it undergoes many different of loading. Many types of loading may cause cracks in the beam. These cracks and their locations effect on the shapes and values of the beam frequency. Recently these topics are so prevailing in the industry of spacecraft, airplanes, wind turbines, turbines, robot arm and many other applications. Many studies were performed to examine the vibration and dynamic of cracked beams, as, M. I. Friswell and J. E. T. Penny [1], presented a compares the different approaches to crack modeling, and demonstrates that for structural health monitoring using low frequency vibration, simple models of crack flexibility based on beam elements are adequate. This paper also addresses the effect of the excitation for breathing cracks, where the beam stiffness is bilinear, depending on whether the crack is open or closed. Most structural health monitoring methods assume that the structure is behaving linearly, whereas in practice the response will be nonlinear to an extent that varies with the form of the excitation. This paper will demonstrate these effects for a simple beam structure. K. El Bikri et. al. [3], presented a theoretical investigation of the geometrically non-linear free vibrations of a clamped– clamped beam containing an open crack. The approach uses a semi-analytical model based on an extension of the Rayleigh–Ritz method to non-linear vibrations, which is mainly influenced by the choice of the admissible functions. The general formulation is established using new admissible functions, called ‘‘cracked beam functions’’, and denoted as ‘‘CBF’’, which satisfy the natural and geometrical end conditions, as well as the inner boundary conditions at the crack location. The work is restricted to the fundamental mode in order to concentrate on the study of the influence of the crack on the non-linear dynamic response near to the fundamental resonance. H. R. Oz and M. T. Das [4], presented the in plane vibrations of cracked circular curved beams is investigated. The beam is an Euler-Bernoulli beam. Only bending and extension effects are included. The curvature is in a single plane. In plane vibrations is analyzed using FEM. In the analysis, elongation, bending and rotary inertia effects are included. Four degrees of freedom for in-plane vibrations is assumed. Natural frequencies of the beam with a crack in different locations and depths are calculated using FEM. Comparisons are made for different angles. Liao-Liang Ke et. al. [5], presented the post-buckling response of beams made of functionally graded materials (FGMs) containing an open edge crack is studied based on Timoshenko beam theory and von Karman nonlinear kinematics. Ritz method is employed to derive the nonlinear governing equations, which are then solved by using Newton–Raphson method to obtain the post-buckling load-end shortening curves and post-buckling deflection-end shortening curves. Unlike isotropic homogeneous beams, bifurcation buckling does not occur for both intact and cracked FGM beams due to the presence of bending–extension coupling effect. The objective of this paper is to study the effect of crack depth and position on the natural frequency of the beam by using of analytical solution of general equation of motion of beam with crack effect and compared with experimental results evaluated by test of beam samples with crack effect of beam. To achieve the above objectives, analytical solution is developed for dynamic analysis of beam with and without crack effect to evaluate the fundamental natural frequency of beam by using the analytical solution of general equation of motion of beam with crack effect, by building a computer program for analytical solution using Fortran power station 4.0 program. In addition to, evaluated the natural frequency of beam with crack effect by experimental work with different crack location and depth with different supported of beam. EXPERIMENTAL WORK The experimental work include vibration test to calculate the fundamental natural frequency of beam with and without crack effect for different beam material, and boundary conditions of beam with dimensions (-length of beam, -width of the beam, -depth of the beam, -depth of crack in beam, and -location of the crack in the beam) and with different crack size and location effect. The beam sample using in experimental study with crack effect shown in the Fig. 1. And The (TM16 universal vibration apparatus) from TQ company is employed at this study