Theoretical, numerical and experimental vibration analysis of cracked Reddy - Bickford beam

In this study, the free vibration analysis of a beam with a single crack was investigated in the frames of simplified Reddy-Bickford beam theory theoretically, analytically and experimentally. Firstly, general equations and stiffness matrices of a beam were produced for uncracked beam considering displacement field according to Euler-Bernoulli, Timoshenko and simplified Reddy-Bickford beam theories. The equations about Timoshenko and simplified Reddy-Bickford beam theories were expressed with those obtained for Euler-Bernoulli beam theory and relationship between the beam theories was investigated. Later, stiffness matrix for cracked beam element was obtained by modeling the crack as a massless rotational spring related to the local flexibility. Transposed flexibility matrix of stress intensity factor and strain energy release rate that calculated utilizing fracture mechanics theory was used to obtain spring rigidity. Cracked beam general stiffness matrix was obtained combining the stiffness matrices of cracked and uncracked beam elements. The acquired equations and finite element method were employed to produce 3 different program with Matlab software for each theory that reveal free vibration analysis of cracked beams. Analytic studies were performed by ANSYS finite elements software using models designed with components suitable to Euler-Bernoulli and Timoshenko beam theories. Analytic and theoretic explanations were supported by experimental studies. The effects of changing beam length, crack height and location on the free vibration behavior of the beam were investigated with experiments. Mathematical modeling of the thesis problems are done for plain strain state in the frames of elasticity theory. The results obtained for each methods are compared with earlier studies. The results showed that Euler-Bernoulli, Timoshenko and simplified Reddy-Bickford beam theories generated similar values in small thickness/length ratios. However, deviation between the results expanded as the thickness/length rate increased due to shear deformation and rotary inertia. The analysis was performed utilizing higher order beam theory that suggested in the thesis. The reliability of the results was proven by comparing with the results of Timoshenko beam theory. The results of the study proved that cracked beam vibration analysis can be explained without shear correction factor utilizing simplified Reddy-Bickford beam theory which is one of the higher order beam theories.