On exact solution of kármán's equations of rigid clamped circular plate and shallow spherical shell under a concentrated load

1987 ◽  
Vol 8 (11) ◽  
pp. 1057-1068 ◽  
Author(s):  
Zheng Xiao-jing ◽  
Zhou You-he
Keyword(s):  
Exact Solution ◽  
Spherical Shell ◽  
Circular Plate ◽  
Shallow Spherical Shell ◽  
Concentrated Load

Free Vibration of Shallow-Spherical Shell

2014 ◽  
Vol 578-579 ◽  
pp. 890-894
Author(s):  
Xian Qin Hou
Keyword(s):  
Exact Solution ◽  
Free Vibration ◽  
Spherical Shell ◽  
Solution Method ◽  
Shallow Spherical Shell ◽  
Frequency Curve ◽  
Third Order ◽  
Practical Solution ◽  
Clamped Edge

Shallow spherical shell is one of the structure shapes and is adopted extensively in engineering. Based on the exact solution of free vibration of the shallow-spherical shell, the frequency equations of the shallow spherical shell with clamped edge are derived and calculated numerically. Then the first third-order frequency curve and modal curve and solved. Comparing these with the results of the exact-solution method, the range of of the shallow-spherical shell when calculated by use of practical-solution method can be derived.

Zero Gravity Validation of Smart Aperture Antennas

1999 ◽  
Author(s):  
Hwan-Sik Yoon ◽  
Gregory Washington
Keyword(s):  
Spherical Shell ◽  
Analytical Model ◽  
Stress Function ◽  
Spherical Shape ◽  
Element Model ◽  
Shallow Spherical Shell ◽  
Zero Gravity ◽  
Governing Equations ◽  
Homogeneous Solutions ◽  
Calculated Stress

Abstract In this study, a smart aperture antenna of spherical shape is modeled and experimentally verified. The antenna is modeled as a shallow spherical shell with a small hole at the apex for mounting. Starting from five governing equations of the shallow spherical shell, two governing equations are derived in terms of a stress function and the axial deflection using Reissner’s approach. As actuators, four PZT strip actuators are attached along the meridians separated by 90 degrees respectively. The forces developed by the actuators are considered as distributed pressure loads on the shell surface instead of being applied as boundary conditions like previous studies. This new way of applying the actuation force necessitates solving for the particular solutions in addition to the homogeneous solutions for the governing equations. The amount of deflections is evaluated from the calculated stress function and the axial deflection. In addition to the analytical model, a finite element model is developed to verify the analytical model on the various surface positions of the reflector. Finally, an actual working model of the reflector is built and tested in a zero gravity environment, and the results of the theoretical model are verified by comparing them to the experimental data.

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