Thin-walled Cross-section Beams Research Articles

Frequency and mode change in the large deflection and post-buckling of compact and thin-walled beams

This paper deals with the investigation of normal modes change of metallic structures, when subjected to geometrical nonlinearities in the large displacement/rotations field. Namely, a unified framework based on the Carrera Unified Formulation (CUF) and a total Lagrangian approach are employed to formulate higher order beam theories including geometric nonlinearities. Thus, a finite element approximation is used along with a path-following method to perform nonlinear analyses. Linearized vibration modes around equilibrium states and along the whole equilibrium path of structures subjected to bending and compression loadings are evaluated by solving a classical eigenvalue problem. In order to show the capabilities of the proposed methodology, both solid and thin-walled cross-section beams are considered. The analyses demonstrate that, with some differences depending on the geometry and both boundary and loading conditions, natural frequencies and modal shapes may change significantly as the structure is subjected to large displacements and rotations.

Linearized buckling analysis of isotropic and composite beam-columns by Carrera Unified Formulation and dynamic stiffness method

This article introduces a one-dimensional (1D) higher-order exact formulation for linearized buckling analysis of beam-columns. The Carrera Unified Formulation (CUF) is utilized and the displacement field is expressed as a generic N-order expansion of the generalized unknown displacement field. The principle of virtual displacements is invoked along with CUF to derive the governing equations and the associated natural boundary conditions in terms of fundamental nuclei, which can be systematically expanded according to N by exploiting an extensive index notation. After the closed form solution of the N-order beam-column element is sought, an exact dynamic stiffness (DS) matrix is derived by relating the amplitudes of the loads to those of the responses. The global DS matrix is finally processed through the application of the Wittrick-Williams algorithm to extract the buckling loads of the structure. Isotropic solid and thin-walled cross-section beams as well as laminated composite structures are analyzed in this article. The validity of the formulation and its broad range of applicability are demonstrated through comparisons of results from the literature and by using commercial finite element codes.

Vibration Control of Composite Spacecraft Booms Subjected to Solar Heating

In this paper, piezoelectric feedback control of vibration and instability of spacecraft booms modeled as circular thin-walled cross-section beams and subjected to solar radiant heating is investigated. Having in view that composite material systems are likely to play a great role in the design of these devices, the beam constituent materials encompass non-classical effects such as anisotropy and transverse shear. In addition, in order to induce beneficial elastic couplings, a special ply-angle distribution achieved via the usual helically wounding fiber-reinforced technology, the so called filament winding, is implemented. The dynamic governing equations including the temperature effects and the related boundary conditions are obtained via the application of Hamilton's principle. Toward the end of controlling the oscillations and prevent the occurrence of the thermal dynamic instability, a feedback control capability based on the use of the piezoelectric induced strain actuation is implemented. The performance of its implementation considered in conjunction with that of the structural tailoring are highlighted and pertinent conclusions are derived.