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Shock and Vibration
Volume 2014 (2014), Article ID 141982, 16 pages
Research Article

Influence of Non-Structural Localized Inertia on Free Vibration Response of Thin-Walled Structures by Variable Kinematic Beam Formulations

1Department of Mechanical and Aerospace Engineering, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy
2School of Aerospace, Mechanical and Manufacturing Engineering, Royal Melbourne Institute of Technology, Bundoora, VIC 3083, Australia

Received 4 February 2014; Accepted 28 March 2014; Published 27 April 2014

Academic Editor: Tony Murmu

Copyright © 2014 Alfonso Pagani et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Variable kinematic beam theories are used in this paper to carry out vibration analysis of isotropic thin-walled structures subjected to non-structural localized inertia. Arbitrarily enriched displacement fields for beams are hierarchically obtained by using the Carrera Unified Formulation (CUF). According to CUF, kinematic fields can be formulated either as truncated Taylor-like expansion series of the generalized unknowns or by using only pure translational variables by locally discretizing the beam cross-section through Lagrange polynomials. The resulting theories were, respectively, referred to as TE (Taylor Expansion) and LE (Lagrange Expansion) in recent works. If the finite element method is used, as in the case of the present work, stiffness and mass elemental matrices for both TE and LE beam models can be written in terms of the same fundamental nuclei. The fundamental nucleus of the mass matrix is opportunely modified in this paper in order to account for non-structural localized masses. Several beams are analysed and the results are compared to those from classical beam theories, 2D plate/shell, and 3D solid models from a commercial FEM code. The analyses demonstrate the ineffectiveness of classical theories in dealing with torsional, coupling, and local effects that may occur when localized inertia is considered. Thus the adoption of higher-order beam models is mandatory. The results highlight the efficiency of the proposed models and, in particular, the enhanced capabilities of LE modelling approach, which is able to reproduce solid-like analysis with very low computational costs.