Application of Discretization of Continuous System for Vibration Analysis of Structures

Modelling structures with discrete coordinates provides a practical approach for the structural vibration problems. The closed-form solution approaches for beams with arbitrary boundary conditions have been developed in the useful form of finite element suitable for inclusion in a computer program. Both the frequency domain analysis and the modal analysis are considered to evaluate the dynamic responses. The frequency-dependent shape functions of a beam element are obtained from the deflection function derived by solving the governing differential equation. Integration of the shape functions gives the element stiffness, mass and damping matrices that can be used to assemble the global matrices for the whole structure by the direct method as usual. Dynamic force may be separated into its harmonic components by means of a Fourier series expansion. Response spectra to general type of loading are presented.