Free Vibrations of Noncircular Cylindrical Shells Having Circumferentially Varying Thickness

1985 ◽  
Vol 52 (1) ◽  
pp. 149-154 ◽  
Author(s):  
K. Suzuki ◽  
A. W. Leissa
Keyword(s):  
Power Series ◽  
Free Vibration ◽  
Cylindrical Shells ◽  
Free Vibrations ◽  
Mode Shapes ◽  
Thickness Variation ◽  
Series Expansions ◽  
Varying Thickness ◽  
Power Series Expansions ◽  
Vibration Problems

An exact method using power series expansions is presented for solving free vibration problems for noncircular cylindrical shells having circumferential thickness variation. The method is used to obtain the first known results for this class of problems. Frequencies and mode shapes are presented for a set of elliptical cylindrical shells having second degree thickness variation in each quadrant.

Free Vibrations of Longitudinally Stiffened Cylindrical Shells

1974 ◽  
Vol 41 (4) ◽  
pp. 1087-1093 ◽  
Author(s):  
J. T. S. Wang ◽  
S. A. Rinehart
Keyword(s):  
Experimental Data ◽  
Free Vibration ◽  
Cylindrical Shells ◽  
Free Vibrations ◽  
Mode Shapes ◽  
Structural System ◽  
Isotropic Cylinder ◽  
Simply Supported ◽  
Thin Walled ◽  
Stiffened Cylindrical Shells

This study is concerned with the free-vibration characteristics of thin cylindrical shells reinforced by longitudinal stringers for any edge boundary conditions. The structural system is treated as an isotropic cylinder interacting with a set of discrete thin-walled stringers. Frequencies of simply supported shells obtained according to the present analysis compare favorably with Ritz solution and existing experimental data. For mode shapes, the present analysis often yields much better results than Ritz solution. Numerical results for frequencies and mode shapes for clamped-clamped cylindrical shells are included, and frequencies of a shell with very flexible stiffeners compare favorably with frequencies of an unstiffened shell.

scholarly journals Parallel Software to Offset the Cost of Higher Precision

2021 ◽  
Vol 40 (2) ◽  
pp. 59-64
Author(s):  
Jan Verschelde
Keyword(s):  
Power Series ◽  
Parallel Algorithms ◽  
Series Expansions ◽  
Use Case ◽  
Double Precision ◽  
Algebraic Space ◽  
Space Curves ◽  
Computational Overhead ◽  
Power Series Expansions ◽  
The Cost

Hardware double precision is often insufficient to solve large scientific problems accurately. Computing in higher precision defined by software causes significant computational overhead. The application of parallel algorithms compensates for this overhead. Newton's method to develop power series expansions of algebraic space curves is the use case for this application.

Free vibration characteristics of delaminated composite pretwisted stiffened cylindrical shell

2017 ◽  
Vol 232 (4) ◽  
pp. 595-611 ◽  
Author(s):  
Mrutyunjay Rout ◽  
Sasank Shekhara Hota ◽  
Amit Karmakar
Keyword(s):  
Free Vibration ◽  
Dynamic Equilibrium ◽  
Twist Angle ◽  
Cylindrical Shells ◽  
Shell Element ◽  
Vibration Characteristics ◽  
Mode Shapes ◽  
Iteration Algorithm ◽  
Lagrange’S Equation ◽  
Benchmark Solutions

Effects of delamination on free vibration characteristics of laminated stiffened cylindrical shells with pretwist are analyzed by finite element method. The investigation is carried out using an eight-noded quadratic isoparametric shell element, which incorporates the transverse shear deformation and rotary inertia along with a three-noded beam element for the stiffener. The multipoint constraint algorithm has been included to guarantee the compatibility of deformation, equilibrium of resultant forces, and moments at delamination crack tip. The general dynamic equilibrium equation is derived from Lagrange’s equation of motion for moderate rotational speeds for which the Coriolis effect is neglected. The standard eigenvalue problem is solved utilizing QR iteration algorithm. The accuracy of the present formulation is validated with benchmark solutions is available in the literature. The present work concerns about the effects of delamination, fiber orientation, twist angle, stiffener depth-to-shell thickness ratio, and rotational speed on the fundamental frequency of shallow cylindrical shells with stiffener. Representative mode shapes for some typical case of the stiffened shell for different twist angles and rotational speeds are also presented.

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