Stress Superposition Method and free vibration of corner tensioned rectangular thin membranes

2020 ◽  
pp. 107201
Author(s):  
Bingyan Li ◽  
Rongqiang Liu ◽  
Qiang Cong ◽  
Hongwei Guo ◽  
Qiuhong Lin
Keyword(s):  
Free Vibration ◽  
Superposition Method ◽  
Thin Membranes ◽  
Stress Superposition

Accurate Analytical-Type Solutions for the Free Vibration of Simply-Supported Parallelogram Plates

1991 ◽  
Vol 58 (1) ◽  
pp. 203-208 ◽  
Author(s):  
D. J. Gorman
Keyword(s):  
Free Vibration ◽  
Equal Length ◽  
Superposition Method ◽  
Vibration Modes ◽  
Type Solution ◽  
Simply Supported ◽  
Wide Range ◽  
Plate Geometry ◽  
Special Case ◽  
Comprehensive Study

A comprehensive study of the free vibration of simply-supported parallelogram plates is conducted. Solutions are obtained by utilizing the superposition method and by taking advantage of symmetry inherent in the problem. Toward this end a new alternating Le´vy-type solution is introduced. Verification tests are conducted by comparing computed eigenvalues with those of rhombic plates in the special case where all plate edges are of equal length. Eigenvalues are stored for eight vibration modes and for a wide range of plate geometry.

scholarly journals A Highly Accurate and Efficient Analytical Approach to Bridge Deck Free Vibration Analysis

2000 ◽  
Vol 7 (6) ◽  
pp. 399-412 ◽  
Author(s):  
D.J. Gorman ◽  
L. Garibaldi
Keyword(s):  
Free Vibration ◽  
Bridge Deck ◽  
Bridge Decks ◽  
Free Vibration Analysis ◽  
Free Edge ◽  
Mode Shapes ◽  
Superposition Method ◽  
Type Solution ◽  
Edge Type ◽  
Edge Conditions

The superposition method is employed to obtain an accurate analytical type solution for the free vibration frequencies and mode shapes of multi-span bridge decks. Free edge conditions are imposed on the long edges running in the direction of the deck. Inter-span support is of the simple (knife-edge) type. The analysis is valid regardless of the number of spans or their individual lengths. Exact agreement is found when computed results are compared with known eigenvalues for bridge decks with all spans of equal length. Mode shapes and eigenvalues are presented for typical bridge decks of three and four span lengths. In each case torsional and non-torsional modes are studied.

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