Investigation Of Elastic Guided Waves Using The Wave Finite Element Method

As a new technology of nondestructive testing,guided wave testing has been more and more commonplace with the advantages of large coverage area,long propagation distance,low cost as well as high precision compared to the traditional methods.Besides,in terms of the influence of different factors including environment,load,geometry,boundary and physical field,much interest in guided wave analysis is focused on the investigation of dispersion and multi-mode.Moreover,one proper mode is needed to excite for interrogating a structure component and developing a sensor.The wave finite element method is suitable for wave propagation in periodic structures.The main contents of the thesis are given asFirstly,the group velocity of the wave finite element method is derived from its definition and differential rules.The dispersive equation of a helically curved rod is established combining with Cartesian coordinate helical system with this method and guided wave propagation in helically curved rod is analyzed.Besides,the results are verified by that of the software Disperse and commercial finite element software Abaqus and the dispersive spectra about the output guided wave signals are obtained with the coordinate transformation and twodimensional Fast Fourier Transform(2D-FFM).Moreover,it is proved that the wave finite element method is credible for wave propagation in a helically curved rod.Combing with 2D high spectral element and Gauss integration,the modified formulation of the wave finite element method is obtained based on the Fourier series expansion of displacements,which provides the diagonal mass matrix and the stiffness matrix for lower sparsity.Meanwhile,the wave equation about thermoelastic waves is built considering generalized thermoelastic theory(GN model)and it is used for wave propagation in circular hollow cylinder.There appear new thermoelastic modes,which are recognized by the wave structures and displacement vectors.Then,based on the updating Lagrangian formula the wave finite element method with prestress is given for analyzing wave propagation in prestressed structures.The simplified model of strands is considered and the stress fields are derived from the plane strain assumption and the Hertzian contact theory.Besides,the phenomena of the notch frequency,the cutoff frequency and modal transition are discussed in detail and the effect of prestress on wave propagation is studied.Moreover,the wave structures and displacement vectors are utilized to recognize each mode.The results indicate that the seven cylindrical rods can't describe the steel strands simply.Finally,combining the wave finite element method with Isogeometric Analysis,a new proposal wave isogeometric analysis is established.Meanwhile,the convergence and the precision are discussed.Then,the updating Lagrangian formulation is utilized to linearize the virtual power equation of rotating media,and the energy velocity is derived from the Poynting theorem.In addition,wave propagation in rotating functionally graded annular plate and rod are considered and the influences of material gradient index,rotating speed and damping are shown in detail.