Out-of-Plane Free Vibrations of a Uniform Circular Ring

1966 ◽  
Vol 33 (3) ◽  
pp. 708-709 ◽  
Author(s):  
J. L. Krahula
Keyword(s):  
Free Vibrations ◽  
Circular Ring ◽  
Out Of Plane

Modeling of a Rolling Flexible Circular Ring

2015 ◽  
Vol 82 (11) ◽  
Author(s):  
François Robert Hogan ◽  
James Richard Forbes
Keyword(s):  
Numerical Simulations ◽  
Dynamic Model ◽  
Lagrange Multipliers ◽  
Flat Surface ◽  
Ritz Method ◽  
Free Vibrations ◽  
Circular Ring ◽  
Ring Rolling ◽  
Motion Equations ◽  
Out Of Plane

The motion equations of a rolling flexible circular ring are derived using a Lagrangian formulation. The in-plane flexural and out-of-plane twist-bending free vibrations are modeled using the Rayleigh–Ritz method. The motion equations of a flexible circular ring translating and rotating in space are first developed and then constrained to roll on a flat surface by introducing Lagrange multipliers. The motion equations developed capture the nonholonomic nature of the circular ring rolling without slip on a flat surface. Numerical simulations are performed to validate the dynamic model developed and to investigate the effect of the flexibility of the circular ring on its trajectory. The vibrations of the circular ring are observed to impact the ring's motion.

On Free Vibrations of a Thin Spinning Disk Stiffened With an Outer Reinforcing Ring

1988 ◽  
Vol 110 (4) ◽  
pp. 507-514 ◽  
Author(s):  
S. K. Sinha
Keyword(s):  
Data Storage ◽  
Free Vibrations ◽  
Circular Ring ◽  
Outer Edge ◽  
Design Parameters ◽  
Computer Data ◽  
Storage Devices ◽  
Small Deflection ◽  
Deflection Theory ◽  
Annular Disks

Thin spinning annular disks, which have widely varying applications ranging from inertial wheels in spacecraft to computer data storage devices, experience some inherent vibration problems during operation. One of the techniques to control the vibrations of the disk, being analyzed in this paper, is to stiffen it by attaching a reinforcing ring at its outer edge. The present work considers the effect of adding such a ring and discusses the changes in the natural frequencies for a large range of design parameters. The classical plate bending equation based upon small deflection theory which includes the contribution of rotational membrane stresses has been used in the eigenvalue formulation. Numerical results presented in a nondimensional form should be useful in predicting the dynamic response of such a disk stiffened with a circular ring under the spinning conditions.

Free vibrations of rectangular cantilever plates. Part 1: out-of-plane motion

2004 ◽  
Vol 271 (1-2) ◽  
pp. 131-146 ◽  
Author(s):  
Jongwon Seok ◽  
H.F. Tiersten ◽  
H.A. Scarton
Keyword(s):  
Free Vibrations ◽  
Plane Motion ◽  
Out Of Plane

Theoretical Analysis of Free Vibrations Based on a New High Order Shell Theory for Cylindrical Shells Conveying Fluid

2017 ◽  
Author(s):  
Ming Ji ◽  
Kazuaki Inaba
Keyword(s):  
Boundary Conditions ◽  
Shell Theory ◽  
Natural Frequencies ◽  
Equations Of Motion ◽  
Cylindrical Shells ◽  
Fluid Pressure ◽  
Free Vibrations ◽  
High Order ◽  
Out Of Plane ◽  
Conveying Fluid

The natural frequencies of free vibrations for thick cylindrical shells with clamped-clamped ends conveying fluid are investigated. Equations of motion and boundary conditions are derived by Hamilton’s principle based on the new high order shell theory. The hydrodynamic force is derived from the linearized potential flow theory. Besides, fluid pressure acting on the shell wall is gotten by the assumption of non-penetration condition. The out-of-plane and in-plane vibrations are coupled together due to the existence of fluid-solid-interaction (FSI). Under the assumption of harmonic motion, the dispersion relationships are presented. Using the method of frequency sweeping, the natural frequencies of symmetric modes and asymmetric modes corresponding to each flow velocity are found by satisfying the dispersion relationship equations and boundary conditions. Several numerical examples with different flow velocities and thickness are presented compared with previous thin shell theory and FEM results and show reasonable agreement. The effects of thickness are discussed.

The linear theory of free vibrations of a suspended cable

1974 ◽  
Vol 341 (1626) ◽  
pp. 299-315 ◽  
Keyword(s):  
Linear Theory ◽  
Free Vibrations ◽  
Plane Motion ◽  
Suspended Cable ◽  
Out Of Plane

A linear theory is developed for the free vibrations of a uniform suspended cable in which the ratio of sag to span is about 1:8, or less. Both in-plane and out-of-plane motion is considered. It is shown that the analysis of the symmetric in-plane modes is heavily dependent on a parameter which allows for the effects of cable geometry and elasticity. The results of simple experiments are reported which establish the validity of the theory.

Out-of-plane free vibrations of curved beams with variable curvature

2008 ◽  
Vol 318 (1-2) ◽  
pp. 227-246 ◽  
Author(s):  
Byoung Koo Lee ◽  
Sang Jin Oh ◽  
Jeong Man Mo ◽  
Tae Eun Lee
Keyword(s):  
Free Vibrations ◽  
Curved Beams ◽  
Variable Curvature ◽  
Out Of Plane
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