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Nonlinear Static Analysis and Superharmonic Influence on Nonlinear Forced Vibration of Timoshenko Beams
Abstract In the present work, static analysis and subsequently superharmonic influence on the nonlinear dynamic behavior of externally excited thick beams are investigated. Energy equations are derived considering Timoshenko beam theory. For the static analysis, classical Ritz method is followed. Nonlinear load–deflection response is obtained considering various geometric parameters such as length-to-depth ratio and load application points. For the vibration analysis, differential equations are obtained considering the Lagrange’s equation. Subsequently, harmonic balance method is employed for multi-DOF systems, which reduce the differential equations into nonlinear set of algebraic equation. These equations are tackled by enforcing an iterative scheme based on modified direct substitution method. Simple harmonic assumption although provides a very good prediction for small amplitude vibration problem. However, it is inadequate for the system having large amplitude vibration. It is shown that for accurate solution higher-order harmonics must be considered.
Nonlinear Static Analysis and Superharmonic Influence on Nonlinear Forced Vibration of Timoshenko Beams
Abstract In the present work, static analysis and subsequently superharmonic influence on the nonlinear dynamic behavior of externally excited thick beams are investigated. Energy equations are derived considering Timoshenko beam theory. For the static analysis, classical Ritz method is followed. Nonlinear load–deflection response is obtained considering various geometric parameters such as length-to-depth ratio and load application points. For the vibration analysis, differential equations are obtained considering the Lagrange’s equation. Subsequently, harmonic balance method is employed for multi-DOF systems, which reduce the differential equations into nonlinear set of algebraic equation. These equations are tackled by enforcing an iterative scheme based on modified direct substitution method. Simple harmonic assumption although provides a very good prediction for small amplitude vibration problem. However, it is inadequate for the system having large amplitude vibration. It is shown that for accurate solution higher-order harmonics must be considered.
Nonlinear Static Analysis and Superharmonic Influence on Nonlinear Forced Vibration of Timoshenko Beams
Panigrahi, Brajesh (Autor:in) / Pohit, Goutam (Autor:in)
01.01.2019
20 pages
Aufsatz/Kapitel (Buch)
Elektronische Ressource
Englisch
Nonlinear Dynamic Analysis of Timoshenko Beams
| Springer Verlag | 2010
Nonlinear Dynamic Analysis of Timoshenko Beams
| British Library Conference Proceedings | 2011
Forced motion of Timoshenko beams
| Engineering Index Backfile | 1953
Geometrically Nonlinear Analysis of Timoshenko Beams under Thermomechanical Loadings
| British Library Online Contents | 2003