Free vibration and stability of hybrid nanocomposite-reinforced shallow toroidal shells using an extended closed-form formula based on the Galerkin method

2021 ◽  
pp. 1-17
Author(s):  
Mohammad Amin Shahmohammadi ◽  
Sayed Mohamad Mirfatah ◽  
Hamzeh Salehipour ◽  
Mojtaba Azhari ◽  
Ömer Civalek
Keyword(s):  
Free Vibration ◽  
Galerkin Method ◽  
Closed Form ◽  
Hybrid Nanocomposite ◽  
The Galerkin Method ◽  
Closed Form Formula ◽  
Toroidal Shells

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

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.

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.

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