scholarly journals FREE VIBRATION ANALYSIS OF SPIRAL THICK CYLINDRICAL SHELLS USING THE RAYLEIGH-RITZ METHOD

2014 ◽  
Vol 79 (698) ◽  
pp. 463-470
Author(s):  
Kazunori ITAKURA
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Cylindrical Shells ◽  
Ritz Method ◽  
Free Vibration Analysis

Vibration Analysis for Rotating Ring-Stiffened Cylindrical Shells With Arbitrary Boundary Conditions

2013 ◽  
Vol 135 (6) ◽  
Author(s):  
Lun Liu ◽  
Dengqing Cao ◽  
Shupeng Sun
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Vibration Analysis ◽  
Cylindrical Shells ◽  
Ritz Method ◽  
Free Vibration Analysis ◽  
Arbitrary Boundary ◽  
Arbitrary Boundary Conditions ◽  
Classical Boundary ◽  
Stiffened Cylindrical Shells

The free vibration analysis of rotating ring-stiffened cylindrical shells with arbitrary boundary conditions is investigated by employing the Rayleigh–Ritz method. Six sets of characteristic orthogonal polynomials satisfying six classical boundary conditions are constructed directly by employing Gram–Schmidt procedure and then are employed to represent the general formulations for the displacements in any axial mode of free vibrations for shells. Employing those formulations during the Rayleigh–Ritz procedure and based on Sanders' shell theory, the eigenvalue equations related to rotating ring-stiffened cylindrical shells with various classical boundary conditions have been derived. To simulate more general boundaries, the concept of artificial springs is employed and the eigenvalue equations related to free vibration of shells under elastic boundary conditions are derived. By adjusting the stiffness of artificial springs, those equations can be used to investigate the vibrational characteristics of shells with arbitrary boundaries. By comparing with the available analytical results for the ring-stiffened cylindrical shells and the rotating shell without stiffeners, the method proposed in this paper is verified. Strong convergence is also observed from convergence study. Further, the effects of parameters, such as the stiffness of artificial springs, the rotating speed of the ring-stiffened shell, the number of ring stiffeners and the depth to width ratio of ring stiffeners, on the natural frequencies are studied.

1D-Hierarchical Ritz and 2D-GDQ Formulations for the free vibration analysis of circular/elliptical cylindrical shells and beam structures

2021 ◽  
Vol 258 ◽  
pp. 113338
Author(s):  
Fiorenzo A. Fazzolari ◽  
Matteo Viscoti ◽  
Rossana Dimitri ◽  
Francesco Tornabene
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Cylindrical Shells ◽  
Free Vibration Analysis ◽  
Beam Structures
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