Nonlinear Flexural Vibration of an Elastic Ring

1978 ◽  
Vol 45 (2) ◽  
pp. 428-429 ◽  
Author(s):  
A. Maewal
Keyword(s):  
Free Vibration ◽  
Galerkin Method ◽  
Flexural Vibration ◽  
Circular Ring ◽  
Elastic Ring ◽  
Nonlinear Free Vibration ◽  
The Galerkin Method

Nonlinear free vibration of a thin, elastic, circular ring is analyzed using an asymptotic technique and results are compared with previous solutions obtained through the Galerkin method.

Inplane Vibrations of Circular Rings With a Radially Variable Thickness

1983 ◽  
Vol 105 (1) ◽  
pp. 137-143 ◽  
Author(s):  
H. Lecoanet ◽  
J. Piranda
Keyword(s):  
Experimental Data ◽  
Galerkin Method ◽  
Variable Thickness ◽  
Circular Ring ◽  
Constant Thickness ◽  
Circular Rings ◽  
The Galerkin Method ◽  
Good Agreement

This paper gives some results on inplane vibrations of circular ring with a radially variable thickness. The problem is solved with the Galerkin method [1] making use of the eigenfunctions of a constant thickness ring. Good agreement is obtained between the approximate results and those of the exact calculus or experimental data.

scholarly journals Nonlinear Free Vibration for Viscoelastic Moderately Thick Laminated Composite Plates with Damage Evolution

2010 ◽  
Vol 2010 ◽  
pp. 1-15 ◽  
Author(s):  
Y. F. Zheng ◽  
L. Q. Deng
Keyword(s):  
Free Vibration ◽  
Transverse Shear ◽  
Superposition Principle ◽  
Laminated Composite ◽  
Composite Plates ◽  
Laminated Plates ◽  
Damage Effect ◽  
Laminated Composite Plates ◽  
Nonlinear Free Vibration ◽  
The Galerkin Method

The nonlinear free vibration for viscoelastic cross-ply moderately thick laminated composite plates under considering transverse shear deformation and damage effect is investigated. Based on the Timoshenko-Mindlin theory, strain-equivalence hypothesis, and Boltzmann superposition principle, the nonlinear free vibration governing equations for viscoelastic moderately thick laminated plates with damage are established and solved by the Galerkin method, Simpson integration, Newton-Cotes, Newmark, and iterative methods. In the numerical results, the effects of transverse shear, material viscoelasticity, span-thickness ratio, aspect ratio, and damage effect on the nonlinear free vibrating frequency of the viscoelastic cross-ply moderately thick laminated plates are discussed.

Free Vibration Analysis of Truncated Conical Composite Shells using the Galerkin Method

2012 ◽  
Vol 12 (7) ◽  
pp. 698-701 ◽  
Author(s):  
Faramarz Ashenai Ghasemi ◽  
Reza Ansari ◽  
Rahim Bakhoday Paskiaby
Keyword(s):  
Free Vibration ◽  
Galerkin Method ◽  
Vibration Analysis ◽  
Free Vibration Analysis ◽  
Composite Shells ◽  
The Galerkin Method

The Fundamental Flexural Vibration of a Cantilever Beam of Rectangular Cross Section with Uniform Taper

1965 ◽  
Vol 16 (2) ◽  
pp. 139-144 ◽  
Author(s):  
J. S. Rao
Keyword(s):  
Galerkin Method ◽  
Natural Frequency ◽  
Cantilever Beam ◽  
Cross Section ◽  
Rectangular Cross Section ◽  
Flexural Vibration ◽  
The Other ◽  
Correction Factors ◽  
Flexural Mode ◽  
The Galerkin Method

SummaryAn attempt has been made to determine the natural frequency of fundamental flexural mode of a cantilever beam with uniform taper by the Galerkin method. The method suggested considerably reduces the calculations as compared with the other methods available and the results are checked with the correction factors derived by Martin.

scholarly journals Free vibration and chatter stability of a rotating thin-walled composite bar

2018 ◽  
Vol 10 (9) ◽  
pp. 168781401879826 ◽  
Author(s):  
Jingmin Ma ◽  
Yongsheng Ren
Keyword(s):  
Time Delay ◽  
Free Vibration ◽  
Galerkin Method ◽  
Lagrange Equation ◽  
Chatter Stability ◽  
Milling Force ◽  
Thin Walled ◽  
The Stability ◽  
The Time Domain ◽  
The Galerkin Method

The free vibration and chatter stability of a rotating thin-walled composite bar under the action of regenerative milling force were investigated in this article. The free vibration equations of the rotating thin-walled composite bar were presented and solved by the Galerkin method according to the derived Lagrange equation for the rotating thin-walled composite bar, and the influences of the taper ratio, ply angle, and mode number on the first natural frequency were analyzed. In order to study the chatter stability of the rotating thin-walled composite bar, the time-delay motion equation of the system was derived with consideration of the effects of regenerative milling force and internal/external damping. The two-mode Galerkin method was used to discretize the time-delay free vibration equations, and the semi-discrete method in the time domain was employed to predict the stability lobes. Finally, the correctness of the method was validated, and the stability analysis of the rotating thin-walled composite bar was conducted. Emphatically, the influences of the ply angle, taper ratio, and internal/external damping on the chatter stability of the rotating thin-walled composite bar were analyzed.

Nonlinear Free Flexural Vibration of Oval Rings

2003 ◽  
Vol 70 (5) ◽  
pp. 774-777 ◽  
Author(s):  
M. Ganapathi ◽  
B. P. Patel ◽  
D. P. Makhecha
Keyword(s):  
Free Vibration ◽  
Flexural Vibration ◽  
Beam Element ◽  
Vibration Characteristics ◽  
Curved Beam ◽  
Total Response ◽  
Nonlinear Free Vibration ◽  
B Spline ◽  
Curved Beam Element

In this article, the nonlinear free vibration characteristics of isotropic oval rings are analyzed using a shear flexible cubic B-spline curved beam element. The amplitude-frequency relationships are estimated from the response history. The participation of various modes in the total response is highlighted.

Sign in / Sign up

Export Citation Format

Share Document