NONLINEAR MODELING AND IDENTIFICATION OF CRACKS IN BEAMS BY USING EULER-BERNOULLI BEAM THEORY AND EXPERIMENTS

Date

2023-8-04

Author

Batıhan, Ali Çağrı

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In this thesis nonlinear transverse vibration of a beam with a breathing edge crack is studied. The beam is modeled by utilizing Euler-Bernoulli beam theory. The breathing crack remains open in some period of the cycle and it remains closed in the rest of the cycle. Therefore, in case the crack is closed the beam behaves as an intact beam, whereas it behaves as a beam with an open edge crack when the crack is open. In this study the state of crack is determined by checking the slope difference at the crack location. Eigenfunctions of the linear system, namely intact and open cracked beams are used as trial functions and by utilizing Galerkin's method partial differential equation of motion is transformed into nonlinear set of ordinary differential equations. Harmonic balance method (HBM) with multi harmonics is applied and a nonlinear set of algebraic equations that represents the nonlinear transverse vibration of a beam with a breathing edge crack is obtained. An experimental test set up is constructed in which intact and two cracked specimens each with a different crack location are used. Using a cantilever boundary condition each specimen is excited from a point near to the free end. Response controlled stepped-sine tests are conducted where the specimens are excited such that the transverse displacement response of the excitation point is kept constant in the vicinity of first two natural frequencies and the required force is acquired. Repeating the displacement response controlled tests with different amplitudes reveals the nonlinear properties due to existence of the breathing crack. The natural frequencies and the amplitudes of the frequency response functions at the corresponding natural frequencies are observed to depend on the displacement amplitude. It is also observed in the experimental tests that the damping of the cracked beam depends on the displacement amplitude. Utilizing the excitation response data of two different natural frequencies gives more information about the crack location than the case in which excitation about single natural frequency is considered. Based on the results obtained from the experimental tests, the mathematical model is improved by adding displacement amplitude dependent damping and nonlinear force multipliers. Utilizing the improved mathematical model, simulations with constant force excitation are carried out and effect of crack parameters on nonlinear vibration response are analyzed. The enhanced mathematical model can also be utilized for the reverse problem where a measured vibration response data from a cracked beam can be used as a reference and the crack parameters can be estimated.

Subject Keywords

Nonlinear Vibration, Breathing Edge Crack, Galerkin's Method, Harmonic Balance Method, Response Controlled Test,

URI

https://hdl.handle.net/11511/105091

Collections

Graduate School of Natural and Applied Sciences, Thesis