In this study, a time-marching method for solving wave equation in structures having one-dimensional members, as well as problems with infinite boundaries and on irregular domains will be developed. The idea of time-marching method is using pre-integration equations accompanied by equilibrium equation. In this method, the initial conditions are exactly satisfied in a time marching manner and the equilibrium equation is satisfied using a time-weighted residual method. Boundary conditions are also satisfied by employing a collection approach and a set of boundary points at the end of each time step. The main advantage of this method is saving of the time step information on the coefficients of some exponential basis functions (EBFs), so that the solution advances in time without the need of domain points for discretization. In the other words, just a recursive relation has been used for updating the EBF’s coefficients. The present study consists of three main parts. In the first part, wave propagation in structures having a few members is studied by taking axial stiffness and deformation into consideration. Afterwards, wave propagation in finite and infinite domains is investigated by proposing semi-infinite elements consistent with the aforementioned time weighted residual method. Furthermore, the capability of the proposed formulation in being used in the finite element formulation is demonstrated. In the second part, the formulation of the time weighted residual method for solving the lateral vibration of flexural members, considering Bernoulli-Euler beam and Timoshenko beam theory, is developed. Finally, in the third part of this study, 2D scalar wave propagation problems, on irregular domains, with two different approaches, using time weighted residual method, are solved. At the end of each chapter, while validating the results, stability and accuracy of the proposed methods for solving wave propagation is investigated by solving different problems. Key words : Time-marchingc method, Wave propagation, Exponential basis functions, Semi-infinite domains, Irregular domains.
