Transverse Vibration of a Rectangularly Orthotropic Spinning Disk, Part 2: Forced Vibration and Critical Speeds

1999 ◽  
Vol 121 (3) ◽  
pp. 280-285 ◽  
Author(s):  
A. Phylactopoulos ◽  
G. G. Adams
Keyword(s):  
Forced Vibration ◽  
Angular Speed ◽  
Point Load ◽  
Fourier Component ◽  
Amplitude Response ◽  
Disk Radius ◽  
Critical Speeds ◽  
Spinning Disk ◽  
Time Invariant ◽  
Orthotropic Disk

The transverse forced vibration of a rectangularly orthotropic spinning disk is investigated. The disk is subjected to a constant stationary point-load. Although the deflection of an isotropic disk under these loading conditions is time-invariant in a space-fixed coordinate system, the orthotropic disk undergoes time-dependent oscillatory motion. This phenomenon occurs as a result of the continually changing orientation of material properties with respect to the load. The disk deflection under-the-load is determined as a function of time. Also the deflection along a disk radius and circle containing the load are determined at a fixed instant of time. The occurrence of critical speeds is also investigated. Without damping, virtually any angular speed of the orthotropic disk is found to be critical. This behavior is due to the occurrence of more than one Fourier component in each of the eigenfunctions of the free vibration problem. With damping included, a large amplitude response is found at a speed much less than the lowest classical critical speed of an isotropic disk.

Dynamics Behavior of a Guided Spline Spinning Disk, Subjected to Conservative In-Plane Edge Loads, Analytical and Experimental Investigation

2016 ◽  
Vol 138 (4) ◽  
Author(s):  
Ahmad Mohammadpanah ◽  
Stanley G. Hutton
Keyword(s):  
Degrees Of Freedom ◽  
Natural Frequencies ◽  
Linear Equations ◽  
Transverse Motion ◽  
Stable Operation ◽  
Lateral Direction ◽  
Critical Speeds ◽  
Spinning Disk ◽  
Inner Radius ◽  
Work Done

The governing linear equations of transverse motion of a spinning disk with a splined inner radius and constrained from lateral motion by guide pads are derived. The disk is driven by a matching spline arbor that offers no restraint to the disk in the lateral direction. Rigid body translational and tilting degrees-of-freedom are included in the analysis of total motion of the spinning disk. The disk is subjected to lateral constraints and loads. Also considered are applied conservative in-plane edge loads at the outer and inner boundaries. The numerical solution of these equations is used to investigate the effect of the loads and constraints on the natural frequencies, critical speeds, and stability of a spinning disk. The sensitivity of eigenvalues of spline spinning disk to the in-plane edge loads is analyzed by taking the derivative of the spinning disk's eigenvalues with respect to the loads. An expression for the energy induced in the spinning disk by the in-plane loads, and their interaction at the inner radius, is derived by computation of the rate of work done by the lateral component of the edge loads. Experimental idling and cutting tests for a guided spline saw are conducted at the critical speed, super critical speeds, and at the flutter instability speed. The cutting results at different speeds are compared to show that the idling results of a guided spline disk can be used to predict stable operation speeds of the system during cutting.

The Vibration Response of a Linear Undamped System Resting on a Nonlinear Spring

1960 ◽  
Vol 27 (2) ◽  
pp. 272-274 ◽  
Author(s):  
P. R. Paslay ◽  
M. E. Gurtin
Keyword(s):  
Steady State ◽  
Linear System ◽  
Fourier Component ◽  
Vibration Response ◽  
Displacement Amplitude ◽  
Amplitude Response ◽  
Nonlinear Spring ◽  
Third Harmonic ◽  
Force Displacement ◽  
Force Excitation

The steady-state, undamped-displacement-amplitude response of a linear system on a single nonlinear spring due to a force excitation which varies sinusoidally with time is investigated. The force-displacement relation of the spring is F=k(x+εx3)(1) The Fourier component of the displacement-amplitude response of the system at the forcing frequency and its third harmonic are considered.

Critical Speeds of a Wind Tunnel Fan Shaft

1936 ◽  
Vol 40 (308) ◽  
pp. 557-560
Author(s):  
J. Morris
Keyword(s):  
Wind Tunnel ◽  
Forced Vibration ◽  
Forced Vibrations ◽  
Running Speed ◽  
Critical Speeds ◽  
Set Up ◽  
Dynamic Unbalance

In the design of a fan drive regard should be had to possible critical or resonant speeds which may result in failure of the system. It is not sufficient to arrange for the ordinary whirling speed to be well above the maximum running speed. In whirling the forced vibration arises from static or dynamic unbalance of fan and/or its shaft and the frequency of the forced vibration is the frequency of revolution of the fan shaft. Other important forced vibrations may however be set up.

Whirling with Spring Bearings and Rough Snubbers

1963 ◽  
Vol 67 (625) ◽  
pp. 66-67
Author(s):  
B. Irons
Keyword(s):  
Gas Turbine ◽  
High Speed ◽  
Critical Speed ◽  
Peak Amplitude ◽  
Amplitude Response ◽  
Critical Speeds ◽  
Bearing Load

To an increasing extent, aero gas turbine manufacturers are supporting high speed rotors on spring bearings, in order to escape the consequences of lightly damped and inconveniently placed critical speeds. While experience has been generally good, engineering doubts periodically arise.(a) By introducing the flexible bearings, the critical speed is reduced, say, from 9,000 r.p.m. to 3,000 r.p.m. At 3,000 r.p.m. a peak amplitude response is experienced, although the bearing load is comparatively low. (Some spring bearing designs incorporate damping as an accidental feature, many do not, and very few have damping designed into them.) The peak amplitude at 3,000 r.p.m. can rub the seals or overstress the spring, and to prevent this the bearing amplitude is restricted by a circular stop known here as the “snubber.”

The Influence of Nonlinear Air Drag on Microbeam Response for Noncontact Atomic Force Microscopy

2007 ◽  
Author(s):  
O. Gottlieb ◽  
A. Hoffman ◽  
W. Wu ◽  
R. Maimon ◽  
R. Edrei ◽  
...  
Keyword(s):  
Free Vibration ◽  
Frequency Response ◽  
Forced Vibration ◽  
Continuum Model ◽  
Viscoelastic Damping ◽  
Nonlinear Frequency ◽  
Amplitude Response ◽  
Atomic Force ◽  
Backbone Curves ◽  
Nonlinear Geometric

In this paper we formulate and analyze a continuum model for the vibration of a noncontacting atomic force microscope (AFM) microbeam in air that consistently incorporates nonlinear geometric and inertia effects, localized atomic interaction, viscoelastic damping and quadratic drag. We investigate a controlled set of experiments that include both free vibration decay of a large Silicon beam and forced vibration response of an AFM Silicon microbeam mapping a Silicon sample for various initial interaction distances. Nonlinear frequency and damping backbone curves are obtained from free vibration decay data and equivalent damping ratios are deduced from forced vibration frequency response. Estimation of the system linear viscoelastic parameters and nonlinear drag parameters is enabled by comparison of the experimental backbone curves with those of a nonlinear modal dynamical system deduced from the continuum model. The calibration results without sample interaction include both a slight softening effect for small amplitude response due to nonlinear inertia and viscoelastic damping and a hardening effect for large amplitude response governed by nonlinear geometric effects and drag. Validation of the nonlinear model is enabled by comparison with the measured forced vibration AFM frequency response below the dynamic jump-to-contact threshold.

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