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Dynamic Stiffness Method for Exact Longitudinal Free Vibration of Rods and Trusses Using Simple and Advanced Theories by Xiang Liu; Yaxing Zhao; Wei Zhou; J. Ranjan Banerjee is a Engineering article available to read on EtoBox.

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Closed-form dynamic stiffness (DS) formulations coupled with an efficient eigen-solution technique are proposed for exact longitudinal free vibration analyses of rods and trusses by using classical, Rayleigh-Love, Rayleigh-Bishop and Mindlin-Hermann theories. First, the exact general solutions of the governing differential equations of the four rod theories are developed. Then the solutions are substituted into the generalized displacement and force boundary conditions (BCs), leading to the elemental DS matrices utilising symbolic computation. As an accurate and efficient modal solution technique, the Wittrick-Williams (WW) algorithm is applied. The J 0 count for the WW algorithm has been resolved for all four types of DS elements with explicit analytical expressions. The method is verified against some existing exact results for rods subjected to specific BCs. Comparisons of the natural frequencies and mode shapes for different theories and slenderness ratios are also made. Finally, benchmark solutions are provided for individual rods subject to different BCs, a stepped rod and a truss. This research provides an exact and highly efficient modal analysis tool for rods and trusses w

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Author

Xiang Liu; Yaxing Zhao; Wei Zhou; J. Ranjan Banerjee

Publisher

Elsevier BV

Published

2022

Language

EN

Field

Engineering (Physical Sciences)