Recent Advances in Approximate Methods for Predicting Nonlinear Vibrations in Cantilever Beams and Plates: A Review
DOI:
https://doi.org/10.23918/eajse.v11i2p11Keywords:
Nonlinear Vibration, Cantilever Beam, Approximate Methods, Galerkin Method, Lindstedt-Poincaré MethodAbstract
This study provides a comprehensive overview of the significance of studying the nonlinear vibration characteristics of beam-like structures, such as cantilever pillars and plates, that have non-linear vibration characteristics that deserve special attention. Furthermore, beam-like members such as radio wires, rotor edges, airplane wings, supersonic airfoils of high rises, and others are used in building construction works, and they are engineered strategically to withstand bowing sideways. However, dynamic analysis when these structures is highly subjected to alternating and large axial strains, complex and often nonlinear, and these analyses may demand advanced modelling and analytical techniques which do not exist. The dynamic behavior of flexible structures is described using a set of equations that includes non-linear ordinary differential equations and such equations are tackled by the Ritz-Galerkin approach which will be covered in this paper, in comparison with the Galerkin and Lindstedt-Poincaré techniques, it demonstrates higher accuracy and lower cost, thus providing essential additional information on how to construct models of nonlinear vibrational systems properly. This study has addressed the limitations of the applicability of linear beam theory and pointed out the importance of nonlinearities for the dynamic behavior of beam-like structures. It discusses various types of nonlinearities that significantly affect the beam model motion equations, which are extremely useful for engineers and scientists. The research concentrated on the utilization of approximation techniques, namely the Galerkin method and the Lindstedt-Poincaré approach, in the analysis of beam vibration issues characterized by nonlinearity. This thoroughly examines the problem of nonlinear vibrations in cantilever beams and plates. It examined recent efforts in the advancement of approximation approaches for forecasting and assessing the nonlinear dynamic behavior of structural components.
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