Abstract
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.
Highlights
Introduction to Refined Beam TheoriesIn engineering practice, problems involving non-structural masses are of special interest [1]
The analyses demonstrate the ineffectiveness of classical theories in dealing with torsional, coupling, and local effects that may occur when localized inertia is considered
Non-structural masses are commonly used in finite element (FE) models to incorporate the weight of the engines, fuel, and payload, see, for example, [2,3,4,5]
Summary
Problems involving non-structural masses are of special interest [1]. For instance, (2) in order to have null transverse strain component (γxy = (∂u/∂y)+(∂V/∂x)) at x = ±(b/2) This leads to the third-order displacement field known as the Reddy-Valsov beam theory [10] as follows: V. where f1(x) and g1(x) are cubic functions of the x coordinate. According to (4), a linear distribution of transverse displacement components is needed to detect the rigid rotation of the cross-section about the beam axis. According to CUF, the generic displacement field can be expressed in a compact manner as an N-order expansion in terms of generic functions, Fτ, as follows:. In this class of models, Lagrange-like polynomials are used to discretize the displacement field on the cross-section These models are referred to as LE (Lagrange Expansion) and they have been used to develop a component-wise (CW) modelling approach in some recent works.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
