Free vibration frequencies of a circular thin plate with nonlinearly perturbed parameters

This paper analyzes the free vibration frequencies of a beam on a Winkler–Pasternak foundation via the original Timoshenko–Ehrenfest theory, a truncated version of the Timoshenko–Ehrenfest equation, and a new model based on slope inertia. We give a detailed comparison between the three models in the context of six different sets of boundary conditions. In particular, we analyze the most common combinations of boundary conditions deriving from three typical end constraints, namely the simply supported end, clamped end, and free end. An interesting intermingling phenomenon is presented for a simply-supported (S-S) beam together with proof of the ‘non-existence’ of zero frequencies for free-free (F-F) and simply supported-free (S-F) beams on a Winkler–Pasternak foundation.

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Effect of Centrifugal Force on Frequency Characteristic of Rotating Hollow Cylinders Using a Newly Designed Cylindrical Super Element

Dynamic Systems and Control, Parts A and B ◽

10.1115/imece2006-14415 ◽

2006 ◽

Cited By ~ 1

Author(s):

M. Bonakdar ◽

M. T. Ahmadian

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Free Vibration ◽

Centrifugal Force ◽

Natural Frequencies ◽

Rotating Cylinder ◽

Finite Cylinder ◽

Vibration Frequencies ◽

Hollow Cylinders ◽

Special Case

A sixteen node cylindrical super element is presented for evaluating the free vibration characteristics of a rotating laminated cylinder with conventional boundary conditions. It is shown that the natural frequencies are affected considerably when the centrifugal force is also taken into account. The vibration frequencies of rotating finite cylinder, obtained by conventional finite element are used to evaluate the accuracy of this approach. The special case of a stationary cylinder with zero spinning velocity is also considered as a check on this method. Results indicate only few number of cylindrical super elements are capable of predicting the natural frequency of the rotating cylinder within the same limit as many elements used in the conventional finite element method.

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Thermoelastic damping in the contour-mode vibrations of micro- and nano-electromechanical circular thin-plate resonators

Journal of Sound and Vibration ◽

10.1016/j.jsv.2007.11.035 ◽

2008 ◽

Vol 313 (1-2) ◽

pp. 77-96 ◽

Cited By ~ 41

Author(s):

Zhili Hao

Keyword(s):

Thin Plate ◽

Thermoelastic Damping ◽

Contour Mode ◽

Circular Thin Plate

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The Main Effect of Design Variables for a Safety Valve on a Fracture Pressure

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.345-346.1581 ◽

2007 ◽

Vol 345-346 ◽

pp. 1581-1584

Author(s):

Sang Woo Lee ◽

Dae Young Shin ◽

Kyoung Jin Chun

Keyword(s):

Finite Element Analysis ◽

Finite Element ◽

Thin Plate ◽

Safety Valve ◽

Analysis Method ◽

Element Analysis ◽

Finite Element Analysis Method ◽

Fracture Pressure ◽

Design Variables ◽

Circular Thin Plate

The safety valve has been designed to protect high pressure vessels. A fracture plate made of a circular thin plate is located within the safety valve. The circular thin plate has an outlet for fluid release and to help decrease the pressure. As such, fracture of the circular thin plate can occur at the appointed pressure. In this study, design variables of the safety valve were used to control fracture pressure so that it was easy to apply in the development of a new model of a safety valve. Design variables were fluid diameter of the safety valve, thickness of the fracture plate, filet radius of the clamping bolt, fracture pressure, and clamped torque of the clamping bolt. Design variables were selected, since the fracture experiment indicated that these variables might play a critical role in the fracture of the circular thin plate. Fracture pressure was calculated by the finite element analysis method and analyzed to affect the design variables on the fracture pressure. Using regression analysis, main design variables such as the fluid diameter, the thickness and the fillet were selected and the relationships of the variables were expressed by a regression equation. Furthermore, finite element analysis method and the regression equation were verified comparing with the experiment result.

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