Modelling wave propagation in two-dimensional structures using a wave/finite element technique

The purpose of this work is to present a general method for the numerical analysis of wavepropagation in 2-dimensional structures by the use of a finite element method (FEM). Themethod involves typically just one finite element to which periodicity conditions are appliedinstead of modelling the whole structure, thus reducing drastically the cost of calculations. Themass and stiffness matrices are found using conventional FE software. The low order dynamicstiffness matrix so obtained is post-processed and the wavenumbers and the frequencies thenfollow from various resulting eigenproblems.The method is described and numerical examples given. These include isotropic and orthotropicplates, isotropic cylindrical shells and the more complex case of sandwich cylindrical shells forwhich analytical solutions are not available. The last two cases are studied by postprocessingan ANSYS FE model.The main advantage of the technique is its flexibility since standard FE routines can be usedand therefore a wide range of structural configurations can be easily analysed. Moreover thepropagation constants for plane harmonic waves can be easily predicted for different propagationdirections along the structure. The method is seen to give accurate predictions at negligiblecomputational cos