Analysis Of Lamb Waves Propagation In Structures By The Spectral Finite Element Method

It is important to predict the characteristic, distribution, extend and progress of damages in structures by applying the structural health monitoring system (SHMS), thus the damages can be repaired in time to increase the stability and reliability of the aircraft structures and deduce the maintenance cost. Due to the complication of the SHMS's working condition, however, the monitoring signals acquired by sensors contain a larger quantity of redundant information. Therefore, it is critical to get the useful information related to the structural status. To provide a guidance for extracting the structure damage characteristic parameters, it is necessary to build an effective mechanical model of the structural system with integrated devices for analyzing and simulating its response numerically. In this thesis, the spectral finite element method is utilized to investigate the characteristics of Lamb wave propagating in aircraft structures. Firstly, the formulas for the spectral finite element are deduced. The modeling procedures of bar element, beam element, plane spectral element and three-dimensional spectral element are given. Secondly, three new spectral elements: the anti-symmetrical spectral element, symmetrical spectral element and 6 DOFs spectral element are proposed. After that, several programs are developed. The characteristics of Lamb wave propagating in bars, beams, aluminum plates and composite laminate plates are investigated. Together with the elliptical position technology, a single damage in an aluminum plate is identified. Comparisons to existing data in literatures verify the correctness of deduced formulas, solution procedures and developed programs. Numerical results reveal that the three new spectral elements are more efficient computationally than the 3D spectral element to achieve the same solution accuracy. In addition, the problem of a rigid ball impacting a flexiable bar is studied by using the spectral finite element method and the discrete singular convolution (DSC). At the same time, an improved spectral finite element modeling method is proposed to raise the accuracy of the simulations. The study extends the application range of the DSC.