Three dimensional dynamics of rotating structures under mixed boundary conditions

Abstract

This paper presents the spectral-Tchebychev (ST) technique for solution of three dimensional (3D) dynamics of rotating structures. In particular, structures that exhibit coupled dynamic response require a 3D modeling approach to capture their dynamic behavior. Rotational motions further complicate this behavior, inducing coriolis, centrifugal softening, and (nonlinear) stress-stiffening effects. Therefore, a 3D solution approach is needed to accurately capture the rotational dynamics. The presented 3D-ST technique provides a fast-converging and precise solution approach for rotational dynamics of structures with complex geometries and mixed boundary conditions. Specifically, unlike finite elements techniques, the presented technique uses a series expansion approach considering distributed-parameter system equations: The integral boundary value problem for rotating structures is discretized using the spectral-Tchebychev approach. To simplify the domain of the structures, cross-sectional and rotational transformations are applied to problems with curved cross-section and pretwisted geometry. The nonlinear terms included in the integral boundary value problem are linearized around an equilibrium solution using the quasi-static method.

Free vibration analysis of a rotating pre-twisted beam subjected to tendon-induced axial loading

“…Therefore, the model does not take into account the transverse shear deformation, rotary inertia effects, warping and material diversity of a typical rotorcraft blade. This may certainly be seen as a limitation with regards to rotorcraft blade modelling, which is usually made of composites may be more accurately modelled using more sophisticated approaches such as geometrically-exact, fully intrinsic composite blade theory [8] or three-dimensional linear elasticity-based model [36,37]. However, it is believed that the main findings made for the beam-tendon system presented in this paper, such as the frequency reduction and frequency loci veering, would be also present if a different beam model was used.…”

Vibration Response of Steam Turbine Healthy and Cracked Blade under the Stress Stiffening and Spin Softening Effects

“…Bediz et al 43 presented a 3D methodology for rotating structures' dynamics (nonlinear stress-stiffness, centrifugal softening, Coriolis) with complex geometries and mixed boundary conditions such as a pretwisted cantilever beam using the spectral-Tchebychev (ST) technique. Zeng et al 44 discussed a cracked compressor blade's dynamic characteristics during the run-up process (RUP) considering angular acceleration effect, crack factors and aerodynamic force amplitude and exhibited that crack-breathing behaviour dominated by aerodynamic force and centrifugal force at low speed and high speed respectively.…”

The effect of nonlinear temperature distribution on the vibrational behavior of a size‐dependent FG laminated rectangular plates undergoing prescribed overall motion

“…A similar approach was taken by Ramamurti and Kielb [19] to determine the modal properties of twisted rotating plates. Vibration of composite rotating plates has been considered in some of the previous studies [20][21][22][23][24][25].…”