Session: 07-12-01: Optimization, Uncertainty and Probability

Paper Number: 111874

111874 - Random Vibrations of Laminated Planar Frames 

In the aerospace and construction industries, planar frames often form part of the basic infrastructure for many systems (examples include, bridges, skeletal frames and deployable booms). In instances where weight becomes a critical parameter, selecting fiber reinforced composites over their metallic counterparts, can reduce the overall weight of the frame whilst still meeting strength and stiffness requirements. In some environments, laminated planar frames can be subjected to severe random excitation and it therefore, becomes necessary to reliably predict their response to avoid adverse effects such as, fatigue and excessive noise.

Historically, much of the published literature regarding the random excitation of beam structures and more so, the influence of modal cross-correlations on their response, implicitly targets isotropic metals such as steel and aluminum alloys. By comparison, the random vibration analysis of fiber reinforced composite beams have received less attention. In this work, the random vibration of a generalized laminated planar frame is investigated using the normal mode method. To the best of the authors’ knowledge, the title problem has not been studied in literature and the results presented herein, specifically with respect to the response characteristics of laminated frames, are novel. Treating the frame as a series of connected one-dimensional beam segments, the equations of in-plane motion are derived with the effects of shear deformation, rotary inertia and elastic coupling due to structural anisotropy being accounted for.

The free vibration characteristics are discussed and an expression for the orthogonality condition formulated. Applying the normal mode method, expressions for the mean square transverse, longitudinal and rotational displacements, in terms of the input spectral density are derived. The efficacy of the model is illustrated by performing extensive numerical analysis on point-driven two-member and three-member inclined laminated frames. It is shown that the contribution of the cross-correlation terms to the overall response of the frame can be significant depending on the frame angle, damping and boundary conditions. More so, it is demonstrated that the frequency spacing of the natural modes is dependent on the frame angle. Consequently, the influence of the cross correlation terms can be much greater for certain frame angles compared to others, even in cases where the damping ratio is relatively small. In instances where the boundary conditions of the frame are symmetric, and the contribution of the cross-correlation terms to the overall response is negligible, it is shown that the spatial response of both the longitudinal and transverse displacements are nearly symmetric about the center point of the frame. This result is an extension of the phenomenon observed by Crandall [1-2] and Elishakoff [3] for point-driven flat beams.

In this work, the effect of bending-extension material-coupling on the frame’s response is also investigated. By analyzing symmetrically and asymmetrically laminated clamped-free two-member inclined frames, it is shown that the tip response of the latter is significantly enhanced when material coupling is introduced. The numerical results presented herein are verified with independent finite element simulations conducted in the software package, Ansys® Parametric Design Language (APDL).

 

References

[1] S.H. Crandall, Random vibration of one- and two- dimensional structures, Developments in Statistics (1979) 1-82, https://doi.org/10.1016/B978-0-12-426602-5.50007-4.

[2] S.H. Crandall, Localized Response Reductions in Wide-Band Random Vibration of Uniform Structures, Ingenieur-Archiv 49 (1980) 347-359, https://doi.org/10.1007/BF02426913.

[3] I. Elishakoff, Probabilistic Theory of Structures, second ed., Dover, New York, 1999.

Presenting Author: Richard Bachoo University of the West Indies

Presenting Author Biography: Dr. Richard Bachoo is currently a Lecturer in the Department of Mechanical and Manufacturing Engineering at The University of the West Indies (UWI), St. Augustine. He obtained a Doctor of Philosophy in Mechanical Engineering from UWI in 2013. Dr. Bachoo has served as a Mechanical and Piping Engineer with the international oil and gas consultancy firm, WorleyParsons for several years. He worked on a wide range of CAPEX and OPEX projects during this time, before returning to academia in 2017. His research interests include Flow Induced Vibration, High Frequency Structural Vibration and Probabilistic Structural Dynamics.

Authors:

Richard Bachoo University of the West Indies
Isaac Elishakoff Florida Atlantic University