Response of a Stationary, Damped, Circular Plate Under a Rotating Slider Bearing System

1993 ◽  
Vol 115 (1) ◽  
pp. 65-69 ◽  
Author(s):  
I. Y. Shen
Keyword(s):  
Circular Plate ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Slider Bearing ◽  
Numerical Examples ◽  
Elastic Circular Plate ◽  
Parametric Resonances ◽  
Supercritical Speed ◽  
Bearing System

This paper is to demonstrate that axisymmetric plate damping will suppress unbounded response of a stationary, elastic, circular plate excited by a rotating slider. Use of the method of multiple scales shows that the axisymmetric plate damping will suppress parametric resonances excited by slider stiffness and slider inertia at supercritical speed. In addition, the plate damping will increase the onset speed above which slider damping destabilizes the elastic circular plate. Moreover, numerical examples show that the plate damping could stabilize the plate/slider system at discrete rotation speeds above the onset speed.

Stability and Vibration of a Rotating Circular Plate Subjected to Stationary In-Plane Edge Loads

1996 ◽  
Vol 63 (1) ◽  
pp. 121-127 ◽  
Author(s):  
I. Y. Shen ◽  
Y. Song
Keyword(s):  
Circular Plate ◽  
Rotational Speed ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Parametric Instability ◽  
Single Mode ◽  
Equation Of Motion ◽  
Asymmetric Membrane ◽  
Parametric Resonances ◽  
Hill’S Equations

This paper predicts transverse vibration and stability of a rotating circular plate subjected to stationary, in-plane, concentrated edge loads. First of all, the equation of motion is discretized in a plate-based coordinate system resulting in a set of coupled Hill’s equations. Through use of the method of multiple scales, stability of the rotating plate is predicted in closed form in terms of the rotational speed and the in-plane edge loads. The asymmetric membrane stresses resulting from the stationary in-plane edge loads will transversely excite the rotating plates to single-mode parametric resonances as well as combination resonances at supercritical speed. In addition, introduction of plate damping will suppress the parametric instability when normalized edge loads are small. Moreover, the radial in-plane edge load dominates the rotational speed at which the instability occurs, and the tangential in-plane edge load dominates the width of the instability zones.

Bio-MEMS Circular Plate Sensors Under Electrostatic Hard Excitations: Frequency Response of Superharmonic Resonance of Fourth Order

2020 ◽  
Author(s):  
Julio Beatriz ◽  
Dumitru I. Caruntu
Keyword(s):  
Frequency Response ◽  
Circular Plate ◽  
Fourth Order ◽  
Multiple Scales ◽  
Superharmonic Resonance ◽  
Electrostatically Actuated ◽  
Amplitude Frequency Response ◽  
Elastic Circular Plate ◽  
Modes Of Vibration ◽  
The Difference

Abstract This paper investigates the frequency-amplitude response of electrostatically actuated Bio-MEMS clamped circular plates under superharmonic resonance of fourth order. The system consists of an elastic circular plate parallel to a ground plate. An AC voltage between the two plates will lead to vibrations of the elastic plate. Method of Multiple Scales, and Reduced Order Model with two modes of vibration are the two methods used in this work. The two methods show similar amplitude-frequency response, with an agreement in the low amplitudes. The difference between the two methods can be seen for larger amplitudes. The effects of voltage and damping on the amplitude-frequency response are reported. The steady-state amplitudes in the resonant zone increase with the increase of voltage and with the decrease of damping.

Dynamic Morphing of Elastic Plates via Principal Parametric Resonance

2020 ◽  
Author(s):  
Andrea Arena ◽  
Walter Lacarbonara
Keyword(s):  
Mechanical Model ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Parametric Instability ◽  
Equation Of Motion ◽  
Elastic Plates ◽  
Asymptotic Approach ◽  
Threshold Voltages ◽  
Parametric Resonances ◽  
Instability Regions

Abstract Principal parametric resonances of elastic plates actuated by periodic in-plane stresses effected by embedded piezoelectric wires are investigated to describe the morphing scenarios of flexible, ultra-lightweight panels. A mechanical model of elastic plate including geometric nonlinearities and the parametric actuation provided by the piezoelectric wires, is adopted to formulate the nonlinear equation of motion. A bifurcation analysis is carried out by means of an asymptotic approach based on the method of multiple scales leading to a comprehensive parametric study on the effect of the wires width on the morphing regions (i.e., parametric instability regions) associated with the principal parametric resonances. The threshold voltages triggering the onset of the principal parametric resonances of the lowest three symmetric modes are also calculated as a function of the wires size so as to determine the voltage requirements for the morphing activation.

scholarly journals The Combined Internal and Principal Parametric Resonances on Continuum Stator System of Asynchronous Machine

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Baizhou Li ◽  
Qichang Zhang
Keyword(s):  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Defense Industry ◽  
Response Curves ◽  
Shell System ◽  
State Response ◽  
Noise Characteristics ◽  
Runge Kutta Method ◽  
Nonlinear Dynamic Equations ◽  
Parametric Resonances

With the increasing requirement of quiet electrical machines in the civil and defense industry, it is very significant and necessary to predict the vibration and noise characteristics of stator and rotor in the early conceptual phase. Therefore, the combined internal and principal parametric resonances of a stator system excited by radial electromagnetic force are presented in this paper. The stator structure is modeled as a continuum double-shell system which is loaded by a varying distributed electromagnetic load. The nonlinear dynamic equations are derived and solved by the method of multiple scales. The influences of mechanical and electromagnetic parameters on resonance characteristics are illustrated by the frequency-response curves. Furthermore, the Runge-Kutta method is adopted to numerically analyze steady-state response for the further understanding of the resonance characteristics with different parameters.

Parametric Resonances at Subcritical Speeds in Discs with Rotating Frictional Loads

1994 ◽  
Vol 208 (6) ◽  
pp. 417-425 ◽  
Author(s):  
S N Chan ◽  
J E Mottershead ◽  
M P Cartmell
Keyword(s):  
State Space ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Follower Load ◽  
State Space Analysis ◽  
Eigenvalue Method ◽  
Parametric Resonances ◽  
Annular Disc ◽  
Multiple Scales Analysis ◽  
Mass Spring

This paper is concerned with the parametric resonances in a stationary classical annular disc when excited by a rotating mass-spring-damper system together with a frictional follower load. An analysis by the method of multiple scales is performed to reveal the existence of instabilities associated with subcritical parametric resonances, and other instabilities of the backward waves in modes with nodal diameters. The latter are shown to be driven by friction and not to be dependent upon the rotational speed. A state-space analysis, with truncated modes, is used to investigate the effect of varying the friction, stiffness, mass and damping prameters in a series of simulated problems. The results obtained from the state-space eigenvalue method tend to support the conclusions of the multiple scales analysis.

Transient Interaction of a Circular Plate and a Fluid Medium

1979 ◽  
Vol 46 (1) ◽  
pp. 26-30 ◽  
Author(s):  
J. W. Berglund
Keyword(s):  
Boundary Conditions ◽  
Circular Plate ◽  
Applied Pressure ◽  
Plate Boundary ◽  
Fluid Medium ◽  
Fluid Field ◽  
Elastic Circular Plate ◽  
Unstrained State ◽  
State Of Rest ◽  
Acoustic Fluid

The transient dynamic response of an elastic circular plate subjected to a suddenly applied pressure is determined for several edge boundary conditions. The plate boundary is attached to a semi-infinite, radially rigid tube which is filled with an acoustic fluid, and pressure is applied to the in-vacuo side of the plate. The transient solution is determined by using a technique in which the plate is subjected to a periodic pressure function constructed of appropriately signed and time-shifted Heaviside step functions, and by relying on a physical mechanism which returns the plate and fluid near the plate to an unstrained state of rest between pulses. The plate response is presented for a number of radius-to-thickness ratios and edge boundary conditions when interacting with water. Comparisons are also made with solutions obtained using a plane wave approximation to the fluid field.

On the modulation of water waves on shear flows

1976 ◽  
Vol 347 (1651) ◽  
pp. 537-546 ◽  
Keyword(s):  
Water Waves ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Vries Equation ◽  
Harmonic Wave ◽  
Short Wave ◽  
Long Wave ◽  
Stokes Waves ◽  
The Stability ◽  
Wave Limit

The method of multiple scales is used to examine the slow modulation of a harmonic wave moving over the surface of a two dimensional channel. The flow is assumed inviscid and incompressible, but the basic flow takes the form of an arbitrary shear. The appropriate nonlinear Schrödinger equation is derived with coefficients that depend, in a complicated way, on the shear. It is shown that this equation agrees with previous work for the case of no shear; it also agrees in the long wave limit with the appropriate short wave limit of the Korteweg-de Vries equation, the shear being arbitrary. Finally, it is remarked that the stability of Stokes waves over any shear can be examined by using the results derived here.

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