Abstract
Free vibration analysis of prestressed, homogenous, Fiber-Metal Laminated (FML) and composite beams subjected to axial force and end moment is revisited. Finite Element Method (FEM) and frequency-dependent Dynamic Finite Element (DFE) models are developed and presented. The frequency results are compared with those obtained from the conventional FEM (ANSYS, Canonsburg, PA, USA) as well as the Homogenization Method (HM). Unlike the FEM, the application of the DFE formulation leads to a nonlinear eigenvalue problem, which is solved to determine the system’s natural frequencies and modes. The governing differential equations of coupled flexural–torsional vibrations, resulting from the end moment, are developed using Euler–Bernoulli bending and St. Venant torsion beam theories and assuming linear harmonic motion and linearly elastic materials. Illustrative examples of prestressed layered, FML, and unidirectional composite beam configurations, exhibiting geometric bending-torsion coupling, are studied. The presented DFE and FEM results show excellent agreement with the homogenization method and ANSYS modeling results, with the DFE’s rates of convergence surpassing all. An investigation is also carried out to examine the effects of various combined axial loads and end moments on the stiffness and fundamental frequencies of the structure. An illustrative example, demonstrating the application of the presented methods to the buckling analysis of layered beams is also presented.
Highlights
Vibration is one of the main causes of structural failure, which makes it one of the most important and ongoing research fields in structural modelling and analysis
Fiber-Metal Laminated (FML) materials consist of layers of metal sheet and unidirectional fiber layers embedded in an adhesive system
Numerical tests were performed to confirm the predictability, accuracy and practical applicability of the proposed methods. Both the layered beam conventional FEM (LBFEM) and Layered Beam Dynamic Finite Element (LBDFE) formulations were first validated using the limited available experimental data [35] and numerical examples of prestressed multi-layer beams presented in earlier works by authors [29,30]
Summary
Vibration is one of the main causes of structural failure, which makes it one of the most important and ongoing research fields in structural modelling and analysis. Analytical solutions have been formulated for the vibration analysis of various beam configurations [11,15] and Banerjee et al [18] presented a Dynamic Stiffness Matrix (DSM) for coupled bending– torsion beam elements. Cortés and Sarría [24] presented a dynamic analysis of 3-Layer sandwich beams with thick viscoelastic damping core for FEM applications They introduced a modified RKU model [25]. The coupled free vibration analysis of homogeneous beams subjected to combined axial force and end moment has only been investigated in a few semi-analytical studies [12–14]. The coupled flexural–torsional vibration of axially-loaded layered beams, caused by the end moment is investigated and two formulations are presented.
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