Simple frequency expression for the in‐plane vibration of thick circular rings

1976 ◽  
Vol 59 (1) ◽  
pp. 86-89 ◽  
Author(s):  
J. Kirkhope
Keyword(s):  
Plane Vibration ◽  
Circular Rings

A NEW METHOD FOR IN-PLANE VIBRATION ANALYSIS OF CIRCULAR RINGS WITH WIDELY DISTRIBUTED DEVIATION

2002 ◽  
Vol 254 (4) ◽  
pp. 787-800 ◽  
Author(s):  
Y.J. YOON ◽  
J.M. LEE ◽  
S.W. YOO ◽  
H.G. CHOI
Keyword(s):  
Vibration Analysis ◽  
New Method ◽  
Plane Vibration ◽  
Circular Rings

In-Plane Vibration of Simply Supported-Simply Supported Circular Ring Segments

1991 ◽  
Author(s):  
S. Azimi
Keyword(s):  
Natural Frequencies ◽  
Equations Of Motion ◽  
Circular Ring ◽  
Mode Shapes ◽  
Simply Supported ◽  
Plane Vibration ◽  
Ring Segment ◽  
Linear Spring ◽  
Circular Rings ◽  
Elastic Constraints

Abstract The general in-plane vibration problem of circular ring segments having linear and torsional elastic constraints at the ends has been studied. One of the interesting cases of concern for which there exists an exact solution is the case where the linear and torsional spring stiffnesses in the circumferential direction become zero (Ku = 0, Kt = 0) and the linear spring stiffness in the radial direction becomes infinity (Kw = ∞). This case is the so-called simply supported-simply supported case. The general form of the equations of motion of circular rings with the proper boundary conditions at the ends have been employed to investigate the vibration of the ring segment. Results for natural frequencies and mode shapes for different angles of the segment have been presented.

Modeling and analysis of the in-plane vibration of a complex cable-stayed bridge

2012 ◽  
Vol 331 (26) ◽  
pp. 5685-5714 ◽  
Author(s):  
D.Q. Cao ◽  
M.T. Song ◽  
W.D. Zhu ◽  
R.W. Tucker ◽  
C.H.-T. Wang
Keyword(s):  
Modeling And Analysis ◽  
Plane Vibration ◽  
Cable Stayed Bridge

scholarly journals Parametric Instability of a Traveling Plate Partially Supported by a Laterally Moving Elastic Foundation

2008 ◽  
Vol 130 (5) ◽  
Author(s):  
V. Kartik ◽  
J. A. Wickert
Keyword(s):  
Data Storage ◽  
Parametric Instability ◽  
Primary Resonance ◽  
Free Edge ◽  
Moving Plate ◽  
Torsional Mode ◽  
Plane Vibration ◽  
Out Of Plane ◽  
Axially Moving ◽  
The Stability

The parametric excitation of an axially moving plate is examined in an application where a partial foundation moves in the plane of the plate and in a direction orthogonal to the plate’s transport. The stability of the plate’s out-of-plane vibration is of interest in a magnetic tape data storage application where the read/write head is substantially narrower than the tape’s width and is repositioned during track-following maneuvers. In this case, the model’s equation of motion has time-dependent coefficients, and vibration is excited both parametrically and by direct forcing. The parametric instability of out-of-plane vibration is analyzed by using the Floquet theory for finite values of the foundation’s range of motion. For a relatively soft foundation, vibration is excited preferentially at the primary resonance of the plate’s fundamental torsional mode. As the foundation’s stiffness increases, multiple primary and combination resonances occur, and they dominate the plate’s stability; small islands, however, do exist within unstable zones of the frequency-amplitude parameter space for which vibration is marginally stable. The plate’s and foundation’s geometry, the foundation’s stiffness, and the excitation’s amplitude and frequency can be selected in order to reduce undesirable vibration that occurs along the plate’s free edge.

scholarly journals Semi-Analytical Solution for Free Vibration Differential Equations of Curved Girders

2017 ◽  
Vol 63 (1) ◽  
pp. 115-132
Author(s):  
Y. Song ◽  
X. Chai
Keyword(s):  
Analytical Solution ◽  
Differential Equations ◽  
Free Vibration ◽  
Coupling Effect ◽  
Longitudinal Vibration ◽  
Synthesis Method ◽  
Variable Separation ◽  
Element Analysis ◽  
Plane Vibration ◽  
Curved Girders

Abstract In this paper, a semi-analytical solution for free vibration differential equations of curved girders is proposed based on their mathematical properties and vibration characteristics. The solutions of in-plane vibration differential equations are classified into two cases: one only considers variable separation of non-longitudinal vibration, while the other is a synthesis method addressing both longitudinal and non-longitudinal vibration using Rayleigh’s modal assumption and variable separation method. A similar approach is employed for the out of- plane vibration, but further mathematical operations are conducted to incorporate the coupling effect of bending and twisting. In this case study, the natural frequencies of a curved girder under different boundary conditions are obtained using the two proposed methods, respectively. The results are compared with those from the finite element analysis (FEA) and results show good convergence.

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