Effect of large displacements on the linearized vibration of composite beams

• Published in: International journal of non-linear mechanics Vol. 120; p. 103390
• Main Authors: Carrera, E., Pagani, A., Augello, R.
• Format: Journal Article
• Language: English
• Published: New York Elsevier Ltd 01.04.2020; Elsevier BV
• Subjects: Algorithms; Boundary conditions; Carrera unified formulation; Composite beams; Equations of motion; Geometrical nonlinear analysis; Linearization; Mode aberration; Nonlinear equations; Nonlinear phenomena; Nonlinear vibration; Postbuckling; Resonant frequencies; Static equilibrium; Vibration analysis; Vibration mode; Mode aberration; Composite beams; Carrera unified formulation; Nonlinear vibration; Geometrical nonlinear analysis
• ISSN: 0020-7462; 1878-5638
• DOI: 10.1016/j.ijnonlinmec.2019.103390

Natural frequencies and mode shapes are functions of the equilibrium state. In the large displacement regime, pre-stresses may modify significantly the modal behaviour of structures. In this work, a geometrical nonlinear total Lagrangian formulation that includes cross-sectional deformations is developed to analyse the vibration modes of composite beams structures in the nonlinear regime. Equations of motion are solved around nonlinear static equilibrium states, which are identified using a Newton–Raphson algorithm along with a path-following method of arc-length type. Different boundary conditions and stacking sequences are analysed. It is shown that vibration modes are strongly modified by nonlinear phenomena. Moreover, models that do not describe those effects accurately may results in misleading results, especially if compression is dominant. In fact, results show a crossing phenomenon in the post-buckling regime of an asymmetric cross-ply beam, whereas it is completely unforeseen by the linearized analysis. •Effect of large displacements on mode aberration of composite beams are studied.•The Carrera unified formulation is used to implement layerwise models.•Post-buckling and large displacements equilibrium states are investigated.•Internal stress states play an important role on the linearized vibration.•Trivial linearized solutions may bring to inaccurate results.