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This research presents a comparison of the natural frequency between solid and hollow simple supported cracked beam for different crack depths and positions. Three methods utilized in this research experimental and two numerical method (Rayleigh Method and Finite Element Method (using ANSYS)). The beam is made of iron with dimensions of L*W*H=(0.84*0.02* 0.02m ), and density = 7680kg/m3, E=200Gpa. A comparison made between ANSYS results with experimental results, the biggest error percentage is about (17%) in crack position (42 cm) and depth (10 mm) for the hollow beam. While the biggest error percentage between Rayleigh method with experimental results is about (29 %) for the same crack position and depth and for the hollow beam. The effect of the depth of the crack on the natural frequency of hollow beam is nearly the same effect as in the solid beam as a ratio. INTRODUCTION Cracks present a serious threat to the performance of structures since most of the structural failures are due to material fatigue. For this reason, many methods allowing early detection and localization of cracks have been the subject of intensive investigation the last two decades. As a result, a variety of analytical, numerical and experimental investigations now exist. Cracks found in structural elements have various causes. They may be fatigue cracks that take place under service conditions as a result of the limited fatigue strength. They may be also due to mechanical defects, as in the turbine blades of jet engines. In these engines the cracks are caused by sand and small stones sucked from the surface of runway. Another group involves cracks which are inside the material. They are created as a result of manufacturing processes. The presence of vibrations on structures and machine components leads to cyclic stresses resulting in material fatigue and failure. Most of the failures of the equipment are due to material fatigue. It is very essential to detect the cracks in structures and machine members from very early stage. For crack identification change in natural frequency and modal value has been studied. In some cases crack properties are used to obtain the dynamic behavior as in [1-4] and sometimes inverse methods are used [5-8]. The first two natural frequencies were used by Narkis [9] to identify the crack and later Morassi [10] used it on simply supported beam and rods. Although it can be solved by using 2D or 3D finite element method (FEM), analysis of this approximate model results in algebraic equations which relate the natural frequencies of beam and crack characteristics. These expressions are then applied to study of the inverse problem identification of crack location from frequency measurements. It is found that the only information required for accurate crack identification is the variation of the first two natural frequencies due to the crack, with no other information needed concerning the beam geometry or material and the crack depth or shape. The proposed method is confirmed by comparing it with results of numerical finite element calculations the researchers still try to detect it with the help of physical parameters of the crack i.e. crack depth, position and support condition to the beam. Freud and Herrmann [17] modeled the problem using a torsional spring in the place of crack whose stiffness is related. The first model is used to Euler-Bernoulli cracked beam with different end conditions [4, 11, 19-23, 18] and recently on Timoshenko beams [24, 25]. Chondros et. al [26] used a continuous cracked beam vibration theory for predication of changes in transverse vibration of simply supported beam with a breathing crack. They found that the changes in vibration frequencies for fatigue breathing crack are smaller than the ones caused by open cracks. Utilizing aluminum beams with fatigue cracks for experimental setup they compared the results with the analytical. Chondros [27] used a continuous cracked beam vibration theory for predication of changes in dynamic characteristic due to loading conditions and vibration amplitude. He used the numerical results to correlate the analytical results for lumped crack beam vibration analysis for aluminum and steel beams with open cracks. He supported the theoretical result by experimental results for the same cases. Cam et. al. [28] studied ,experimentally and theoretically, the effect of the crack on vibration of cracked beam. They used echo method for predication the size and location of the crack in cracked beam. They found that the theoretical results (ANSYS) were agreed with experimental results. In this paper three approaches are employed, an analytical approach compared with experimental result and with that gained numerically by ANSYS program to verify the results. The objective of this paper is the study of the effect crack depth and position on the natural frequency of the simple supported hollow and solid beam and comparing between them and finding the best method that give good results comparing with experimental results. EXPERIMENTAL WORK The (TM16 universal vibration apparatus) from TQ company is employed at this study shown in Fig.(1). The dimensions of the solid beam specimen used are (L*W*H=0.84*0.02 *0.02 m) shown in Fig.(2). While the dimensions of the cross section area of hollow beam specimen used are shown in Fig.(3). The material of the specimen was stainless steel (Code No.: 314, Robert L. Norton [16]) with density of (7680 kg/m3), Young modulus (200 GPa) and Poisson’s Ratio (0.3). The crack was created in the specimen with the certain dimensions of crack (see Table (1)).

Experimental and Numerical Comparison Between the Natural Frequency of Cracked Simply Supported Hollow and Solid Beams