An alternative technique for crack detection in a Timoshenko beam based on the first anti-resonant frequency is presented in this paper. Unlike the natural frequency, the anti-resonant frequency is a local parameter rather than a global parameter of structures, thus the proposed technique can be used to locate the structural defects. An impedance analysis of a cracked beam stimulated by a harmonic force based on the Timoshenko beam formulation is investigated. In order to characterize the local discontinuity due to cracks, a rotational spring model based on fracture mechanics is proposed to model the crack. Subsequently, the proposed method is verified by a numerical example of a simply-supported beam with a crack. The effect of the crack size on the anti-resonant frequency is investigated. The position of the crack of the simply-supported beam is also determined by the anti-resonance technique. The proposed technique is further applied to the ＂contaminated＂ anti-resonant frequency to detect crack damage, which is obtained by adding 1-3% noise to the calculated data. It is found that the proposed technique is effective and free from the environment noise. Finally, an experimental study is performed, which further verifies the validity of the proposed crack identification technique.
As vibration-based structural damage detection methods are easily affected by environmental noise, a new statistie-based noise analysis method is proposed together with the Monte Carlo technique to investigate the influence of experimental noise of modal data on sensitivity-based damage detection methods. Different from the com- monly used random perturbation technique, the proposed technique is deduced directly by Moore-Pen＂ose generalized inverse of the sensitivity matrix, which does not only make the analysis process more efficient but also can analyze the influence of noise on both frequencies and mode shapes for three commonly used sensitivity-based damage detection methods in a similar way. A one-story portal frame is adopted to evaluate the efficiency of the proposed noise analysis technique.
As a boundary-type meshless method, the singular hybrid boundary node method（SHBNM） is based on the modified variational principle and the moving least square（MLS） approximation, so it has the advantages of both boundary element method（BEM） and meshless method. In this paper, the dual reciprocity method（DRM） is combined with SHBNM to solve Poisson equation in which the solution is divided into particular solution and general solution. The general solution is achieved by means of SHBNM, and the particular solution is approximated by using the radial basis function（RBF）. Only randomly distributed nodes on the bounding surface of the domain are required and it doesn＇t need extra equations to compute internal parameters in the domain. The postprocess is very simple. Numerical examples for the solution of Poisson equation show that high convergence rates and high accuracy with a small node number are achievable.
