Critical speed

About: Critical speed is a research topic. Over the lifetime, 2764 publications have been published within this topic receiving 31365 citations.

Transverse Vibration of Axially Moving Functionally Graded Materials Based on Timoshenko Beam Theory

Abstract: The transverse free vibration of an axially moving beam made of functionally graded materials (FGM) is investigated using a Timoshenko beam theory. Natural frequencies, vibration modes, and critical speeds of such axially moving systems are determined and discussed in detail. The material properties are assumed to vary continuously through the thickness of the beam according to a power law distribution. Hamilton’s principle is employed to derive the governing equation and a complex mode approach is utilized to obtain the transverse dynamical behaviors including the vibration modes and natural frequencies. Effects of the axially moving speed and the power-law exponent on the dynamic responses are examined. Some numerical examples are presented to reveal the differences of natural frequencies for Timoshenko beam model and Euler beam model. Moreover, the critical speed is determined numerically to indicate its variation with respect to the power-law exponent, axial initial stress, and length to thickness ratio.

Reverse roll coating flow

Abstract: The Galerkin finite element method of solution formulated by Coyle et al. is applied to analyse the coating flow field between two reverse rotating rolls. A wide range of operating conditions that are of practical importance were studied. Many quantitative results that can benefit a practising engineer are presented and physical insight is gained by the analysis of the data. It is shown that the reverse roll coating process is affected by various factors, among which the roll speed ratio is the most significant. Regardless of other parameters chosen, a critical speed ratio always exists at which the metered film thickness experiences a minimum. At this critical speed ratio, the dynamic contact line is exactly located at the centre of the gap between the two rolls. The significance of the Reynolds and the Capillary numbers increases with increasing speed ratio. For speed ratios beyond the critical value, a thinner metered film can be achieved by means of either increasing the film thickness of the entering layer or by decreasing the principal roll radius. Furthermore, the computational predictions indicate that changing the roll radius ratio has no obvious effect on reverse roll coating and that gravity effects, quantified by the Stokes number, can be ignored under normal operating conditions. Copyright © 1999 John Wiley & Sons, Ltd.

The Influence of Shaft’s Bending on the Coupling Vibration of a Flexible Blade-Rotor System

Abstract: The influence of shaft bending on the coupling vibration of rotor-blades system is nonignorable. Therefore, this paper analyzed the influence of shaft bending on the coupling vibration of rotor-blades system. The vibration mode function of shaft under elastic supporting condition was also derived to ensure accuracy of the model as well. The influence of the number of blades, the position of disk, and the support stiffness of shaft on critical speed of system was analyzed. The numerical results show that there were two categories of coupling mode shapes which belong to a set where the blade’s first two modes predominate in the system: shaft-blade (SB) mode and interblade (BB) mode due to the coupling between blade and shaft. The BB mode was of repeated frequencies of () multiplicity for number blades, and the SB mode was of repeated frequencies of () multiplicity for number blades. What is more, with the increase of the number of blades, natural frequency of rotor was decreasing linearly, that of BB mode was constant, and that of SB mode was increasing linearly. Natural frequency of BB mode was not affected while that of rotor and SB mode was affected (changed symmetrically with the center of shaft) by the position of disk. In the end, vibration characteristics of coupling mode shapes were analyzed.

Geometrical nonlinear aeroelastic stability analysis of a composite high-aspect-ratio wing

Abstract: A composite high-aspect-ratio wing of a high-altitude long-endurance (HALE) aircraft was modeled with FEM by MSC/NASTRAN, and the nonlinear static equilibrium state is calculated under design load with follower force effect, but without load redistribution. Assuming the little vibration amplitude of the wing around the static equilibrium state, the system is linearized and the natural frequencies and mode shapes of the deformed structure are obtained. Planar doublet lattice method is used to calculate unsteady aerodynamics in frequency domain ignoring the bending effect of the deflected wing. And then, the aeroelastic stability analysis of the system under a given load condition is successively carried out. Comparing with the linear results, the nonlinear displacement of the wing tip is higher. The results indicate that the critical nonlinear flutter is of the flap/chordwise bending type because of the chordwise bending having quite a large torsion component, with low critical speed and slowly growing damping, which dose not appear in the linear analysis. Furthermore, it is shown that the variation of the nonlinear flutter speed depends on the scale of the load and on the chordwise bending frequency. The research work indicates that, for the very flexible HALE aircraft, the nonlinear aeroelastic stability is very important, and should be considered in the design progress. Using present FEM software as the structure solver (e.g. MSC/NASTRAN), and the unsteady aerodynamic code, the nonlinear aeroelastic stability margin of a complex system other than a simple beam model can be determined.