Procedures for the forced,damped vibration analysis of structural frames using distributed parameter models

The paper summarises an approach to the forced vibration analysis of skeletal elastic structures, making use of “exact” matrix technique. The analysis is based on the modal superposition method, which has been developed in the context of models that retain characteristics of both distributed mass and stiffness. The free vibration analysis is performed using generalised dynamic stiffness functions appropriate to a Rayleigh-Timoshenko-Euler beam-column element. The contributions to dynamic displacements and dynamic internal forces by inertia effects during forced vibration are properly accounted for, and all results are obtained from explicit solutions to the relevant equations at all stages. Numerical integration or other approximate procedures are not required. It is the objective of the present paper to summarise procedures, numerical examples being available elsewhere (e.g. [1–3]). However, the paper is concluded with a practical example illustrating results obtainable by the techniques described below.