“Nonlinear dynamics of boussinesq convection in a deep rotating shell. Ill: Effects of velocity boundary conditions” by P. A. Gilman

1979 ◽  
Vol 14 (1) ◽  
pp. 251-252
Author(s):  
F. H. Busse
Keyword(s):  
Nonlinear Dynamics ◽  
Boundary Conditions ◽  
Rotating Shell

scholarly journals STABILITY OF ROTATING CIRCULAR CYLINDRICAL SHELL SUBJECT TO AN AXIAL AND ROTATIONAL FLUID FLOW

2017 ◽  
Vol 18 (9) ◽  
pp. 84-97
Author(s):  
S.A. Bochkarev ◽  
V.P. Matveenko
Keyword(s):  
Finite Element Method ◽  
Fluid Flow ◽  
Boundary Conditions ◽  
Circular Cylindrical Shell ◽  
Loss Of Stability ◽  
Rotating Fluid ◽  
The Finite Element Method ◽  
The Stability ◽  
Rotating Shell ◽  
Simultaneous Rotation

This paper is concerned with the stability analysis of rotating cylindrical shells conveying a co-rotating fluid. The problem is solved by the finite element method for shells subjected to different boundary conditions. It has been found that the loss of stability for a rotating shell under the action of the fluid having both axial and circumferential velocity components depends on the type of boundary conditions imposed on the shell ends. The results of numerical calculations have shown that for different variants of boundary conditions a simultaneous rotation of shell and the fluid causes an increase or decrease in the critical velocity of axial fluid flow.

Nonlinear Dynamics Analysis of a Printed Wiring Board With Simple and Clamped Boundary Conditions

2001 ◽  
Author(s):  
Xiaoling He
Keyword(s):  
Nonlinear Dynamics ◽  
Boundary Conditions ◽  
Equations Of Motion ◽  
Nonlinear Resonance ◽  
Failure Criteria ◽  
Dynamics Analysis ◽  
Printed Wiring Board ◽  
Resonance Behavior ◽  
Condition Effect ◽  
Wiring Board

Abstract Dynamic response of a printed wiring board (PWB) is analyzed in nonlinear dynamics approach. Equations of motion for the simply supported PWB and the clamped PWB are obtained by the Galerkin’s method. A 2-layer plastic PWB made of isotropic laminates is studied for its boundary condition effect on the vibratory behavior in deflection and stresses. Failure due to plane stress interaction is estimated based on the composite failure criteria. It is found that nonlinear resonance occurs almost periodically in both frequency and temporal domain. Load frequency and magnitude affect the deflection response under different boundary conditions. Resonance behavior is critical in PWB failure prediction based on the stress analysis. The analytical results can be extended to the nonlinear dynamics analysis of the thin laminated plate.

Nonlinear Shell Dynamics—Intrinsic and Semi-Intrinsic Approaches

1983 ◽  
Vol 50 (3) ◽  
pp. 531-536 ◽  
Author(s):  
A. Libai
Keyword(s):  
Nonlinear Dynamics ◽  
Boundary Conditions ◽  
Rotational Velocity ◽  
Equations Of Motion ◽  
Field Equations ◽  
Nonlinear Shell ◽  
Initial And Boundary Conditions ◽  
Shell Dynamics

The intrinsic approach to the nonlinear dynamics of shells, which was introduced in [6], is reviewed and extended by the addition of appropriate initial and boundary conditions of the dynamic and kinematic types to the field equations. The alternative semi-intrinsic velocity approaches (where the velocity components supply the connection between the equations of motion and the time rates of the metric and curvature) are also presented. Both linear and rotational velocity forms are included. The relative merits of these approaches to shell dynamics are discussed and compared with extrinsic approaches.

Nonlinear Dynamics of Stockbridge Dampers

2015 ◽  
Vol 137 (6) ◽  
Author(s):  
O. Barry ◽  
J. W. Zu ◽  
D. C. D. Oguamanam
Keyword(s):  
Nonlinear Dynamics ◽  
Boundary Conditions ◽  
Equations Of Motion ◽  
Frequency Equation ◽  
Mode Shapes ◽  
Nonlinear Frequency ◽  
Modulation Equations ◽  
Proposed Model ◽  
Cantilevered Beams ◽  
Stockbridge Damper

The present paper deals with the nonlinear dynamics of a Stockbridge damper. The nonlinearity is from damping and the geometric stretching of the messenger. The Stockbridge damper is modeled as two cantilevered beams with tip masses. The equations of motion and boundary conditions are derived using Hamilton’s principle. The model is valid for both symmetric and asymmetric Stockbridge dampers. Explicit expressions are presented for the frequency equation, mode shapes, nonlinear frequency, and modulation equations. Experiments are conducted to validate the proposed model.

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