Coupled axial-flexural-torsional vibration of Timoshenko frames

Abstract

In this study, free in-plane and out-of-plane bending vibrations of frame structures have been analyzed together with torsional vibration. Axial extension, rotational inertia and shear effects have also been considered. The frame structure has been designed to have two beams with doubly symmetric cross sections that are connected at various angles to each other. Natural frequencies have been obtained analytically by solving simultaneous linear equations of complex coefficients. Finite element and experimental modal analysis have also been conducted to verify the analytical results. The agreement among the results from the various methods has been found to be good.

Dynamic Analysis of Composite Wind Turbine Blades as Beams: An Analytical and Numerical Study

“…Here, the coordinate system is attached to , the centre of mass (CM); the ′ ′ ′ coordinate system is attached to , the shear centre (SC); and are distances between ( , ), i.e., the coordinates of the centre of mass, and ( , ), coordinates of the shear centre. In the analytical formulation, the equilibrium and compatibility equations in Reference [27] are modified for the beam, which has a nonuniform and asymmetrical cross section. The equilibrium equations are…”

“…(1) In the analytical formulation, the equilibrium and compatibility equations in Reference [27] are modified for the beam, which has a nonuniform and asymmetrical cross section. The equilibrium equations are…”

“…Although the wind turbine blades usually undergo large deformations, the most common beam formulations, namely the Euler-Bernoulli and Timoshenko beam theories for straight and uniform beams, only include small displacements. Under these assumptions, performing analytical solutions even for frames are possible [27]. To build accurate models of the wind turbine blades, more general formulations that can take into account the characteristics of the blades must be considered, both geometrically and material-wise [28,29].…”

Free vibrations of spatial frame structures: Analytical modelling and solution

“…Beams, with various geometric and material characteristics, are one of the most common load-carrying members that are used in many engineering structures such as shafts of rotating machinery, turbine blades, vehicle chassis, buildings, marine structures, etc. (Chaker and Cherifati, 1999; Chen and Zhu, 2021; Ibrahim et al, 1996; Tüfekci et al, 2020a, 2020b; Tuzzi et al, 2020; Woo, 1986; Yucel et al, 2014; Zhu et al, 2016). Beams usually have predictable mechanical characteristics due to their geometric simplicity, which allows certain assumptions to be made.…”

“…As assemblies of multiple beams, frame structures display similar behaviour to the beams but with a more complex nature. The complexity is, of course, caused by the interaction of the axial-flexural-torsional deformations of individual beams belonging to the frame structure (Ng and Kuang, 2000; Yucel et al, 2014). Alongside these couplings, preloading is a common issue with the frame structures.…”