Structural Dynamics

This chapter is dedicated to the analysis of framed structures subjected to dynamic loads. Mass matrices are developed for two-dimensional (2D) and three-dimensional (3D) truss and frame elements as well as for the linear triangular element. The above mass matrices along with the stiffness matrices are used to compose the dynamic equation. The next topic presents the numerical procedure for the time-domain discretization of the structure and the finite element method (FEM) solution of the dynamic equation using the central difference method and the Newmark-Beta method. Using the above methodologies, the chapter proceeds with the derivation of the natural frequencies and the associated modes under free vibration. Detailed steps for the solution of the dynamic response of structures under dynamic loading is provided, and the development of a CALFEM/MATLAB computer code is described for the solution of a plane frame subjected to time-varying loading.