Wide-band random vibration of the X-braced frame with and without lumped masses and concentrated rotary inertiae

Author Type

Outside Researcher

Co-Author Type 1

Faculty

Co-Author Type 2

Outside Researcher

Co-Author Type 3

Outside Researcher

College

Engineering and Computer Science

Department

Ocean and Mechanical Engineering

Document Type

Article

Publication/Event/Conference Title

Mechanics Research Communications

Publication Status

Version of Record

Abstract

An analytical model is developed to determine the vibration characteristics of a generalized X-braced frame excited by a random point force, whose time history corresponds to band-limited white noise. The model is based on the Timoshenko-Ehrenfest beam theory and facilitates the inclusion of multiple lumped masses with inherent rotary inertia. Analytical expressions for the mean square displacement and velocity are explicitly derived in terms of the modal autocorrelation and cross-correlation components. When a lightly damped beam is subjected to a broadband point load, it is well-known that the modal cross-correlation component of the response is negligible because of well-spaced natural modes. In this study, however, it is shown that modal cross-correlations can significantly influence the random response characteristics of the X-braced frame due to the presence of closely spaced natural frequencies. Moreover, it is demonstrated that the extent to which modal cross-correlations influence the random response of the frame depends on, (a) location of the point force, (b) relative thickness of the horizontal segment, (c) relative thickness of the internal bracings and (d) position and magnitude of the lumped element(s). In cases where cross-correlations are strong, the effect is to alter the spatial distribution of the response by introducing a substantial degree of asymmetry while increasing the magnitude of the drive-point response. Contrarily, when cross-correlations are negligible, the spatial distribution of the response is nearly symmetric about the center point of the frame. In this work, the results from the analytical model are verified using an independent finite element model developed in Ansys®.

DOI

10.1016/j.mechrescom.2026.104682

Publication Date

6-1-2026

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