Axisymmetrical Snapping of a Spinning Nonflat Disk

Abstract

In this paper we study the steady-state deflection of a spinning nonflat disk, both theoretically and experimentally. Both the initial and the deformed shapes of the disk are assumed to be axisymmetrical. Von Karman’s plate model is adopted to formulate the equations of motion, and Galerkin’s method is employed to discretize the partial differential equations. In the case when the initial height of the nonflat disk is sufficiently large, multiple equilibrium positions can exist, among them the two stable one-mode solutions P01 and P03 are of particular interest. Theoretical investigation shows that if the disk is initially in the stressed position P03, it will be snapped to position P01 when the rotation speed reaches a critical value. Experiments on a series of copper disks with different initial heights are conducted to verify the theoretical predictions. Generally speaking, the experimental measurements agree well with theoretical predictions when the initial height is small. For the disks with large initial heights, on the other hand, the measured snapping speeds are significantly below the theoretical predictions. The circumferential waviness of the copper disks induced in the manufacturing process and the aerodynamic force at high rotation speed are two possible factors causing this discrepancy.

Deformation and reverse snapping of a circular shallow shell under uniform edge tension

“…Moreover, the flattened-out disk remains on the same side of the base plane throughout. The main features of the results reported in Chen and Lin (2005) apparently contradict the predictions presented in Akkas and Odeh (2001). It remains unknown whether the differences in these main features are due to the different loading mechanisms in the two problems, or simply because one of the conclusions is incorrect.…”

“…We use solid and dashed lines to represent stable and unstable solutions. The stability of these positions is determined by the usual perturbation technique, for example, see Chen and Lin (2005). If only the axisymmetrical assumed modes (u m0 ) are used in the expansion, the apex position will trace the locus ABCD, and snap-through will occur at point B (q = 1571).…”

“…In another study on the possibility of snap-through buckling of shallow shells under in-plane loading, Chen and Lin (2005) investigated the deformation of a spinning annular non-flat disk. The in-plane loading in this case is the centrifugal force.…”

Vibration Characteristics of Rotating Thin Disks—Part I: Experimental Results

“…They did not consider the effect of large deformation on the frequency response characteristics of the disks tested. Chen et al [2] used the nonlinear governing equations of motion to investigate the impact of symmetrical initial runout on the amplitude of spinning disk deflection. They concluded that, depending on the shape and level of initial nonfiatness, the disk may exhibit snap through buckling.…”

Vibration of a rotating flexible ferromagnetic disc subjected to a solenoid electromagnet

“…A solenoid electromagnet is placed above the disc surface position (r s , s ) in a polar coordinate system (r,) fixed on the ground, and the electromagnet induces a transverse resultant force F m acting on the disc. Including the initial unstressed transverse runoutw [9][10][11][12][13], the governing equation of the rotating flexible disc with viscous damping c subjected to the solenoid electromagnet is established as…”