Random vibration of the point-driven portal and multi-bay planar frames.

In this study, an analytical model is presented to determine the random response of point-driven portal and multi-bay planar frame structures. Coupling effects between bending and longitudinal deformations are taken into account, with the Timoshenko-Ehrenfest beam theory being applied to model the bending deformations. With the excitation taken as band-limited white noise, expressions are derived for the mean square displacements and velocities in terms of the autocorrelation and cross-correlation components. The influence of modal cross-correlations on the overall response is shown to be dependent on the number of bays. For a lightly damped single-bay frame, the natural frequencies are generally well separated and the modal cross-correlations are small. In this situation, the velocity response displays a near symmetric distribution about the center point of the frame. Moreover, narrow zones of intensified response begin emerging as the number of responding modes increases. For frames having two or more bays, the contribution of modal cross-correlations is larger due to the increased occurrence of clusters of natural frequencies. In such cases, modal cross-correlations introduce asymmetry into the overall response distribution of the frame. Additionally, the drive-point velocity of the multi-bay frame can be severely underestimated if modal cross-correlations are ignored. The study also investigates the influence of increased damping on the response characteristics. • An analytical model is developed to analyse the random vibrations of a Timoshenko-Ehrenfest multi-bay planar frame structure. • Expressions for the mean square velocities are derived in terms of the modal autocorrelation and cross correlation components. • The significance of modal cross-correlations increases as the number of bays increases causing dramatic changes in the spatial distribution of the response. • Localized zones of highly intensified response levels are located at symmetric positions on the frame. • Finite element simulations in Ansys® APDL are used to verify all results. [ABSTRACT FROM AUTHOR]