EXPLANATION OF FREQUENCY CROSS OVERS AND CORRESPONDING MODE SHAPE CHANGES IN THE FREE VIBRATION PROBLEM OF CLAMPED CYLINDRICAL PANELS

2003 ◽  
Vol 259 (3) ◽  
pp. 724-732 ◽  
Author(s):  
B. SIVASUBRAMONIAN ◽  
A.M. KULKARNI ◽  
G. VENKATESWARA RAO
Keyword(s):  
Free Vibration ◽  
Mode Shape ◽  
Vibration Problem ◽  
Cylindrical Panels ◽  
Shape Changes

Influence of Adhesive Dimensions on the Transverse Free Vibration of Single-Lap Adhesive Cantilevered Beams

2011 ◽  
Vol 393-395 ◽  
pp. 149-152
Author(s):  
Bao Ying Xing ◽  
Xiao Cong He ◽  
Mo Sheng Feng
Keyword(s):  
Stress Concentration ◽  
Free Vibration ◽  
Dynamic Response ◽  
Significant Influence ◽  
Mode Shape ◽  
Natural Frequencies ◽  
Mode Shapes ◽  
Lap Joint ◽  
Adhesive Layers ◽  
Cantilevered Beams

This paper studies the influence of adhesive dimensions on the transverse free vibration of the single-lap adhesive cantilevered beams. The researches are performed by employing software ansys .Efficient analytic results of natural frequencies and mode shapes of transverse free vibration of the beams are provided, corresponding to different adhesive dimensions of bonded thicknesses and bondlines length. Bondlines length has more significant influence on the transverse natural frequencies and the lap joint’s mode shapes of the beams than bonded thickness. The transverse natural frequencies decrease with a decrease in the bondlines length of adhesive, but do not appear to variation observably with a decrease in the bonded thickness. Bondlines length shorting, the lap joint has a sharper mode shape. Simultaneously, the lap joint of even mode shapes influences the dynamic response of the beams significantly. These results indicate a local crack in adhesive layers because of the existence of stress concentration.

Contribution to the free vibration problem of a free-free beam with large end masses

2018 ◽  
Vol 98 (5) ◽  
pp. 840-847
Author(s):  
Slaviša Šalinić ◽  
Aleksandar Obradović ◽  
Momčilo Dunjić ◽  
Dragan Sekulić ◽  
Željko Lazarević
Keyword(s):  
Free Vibration ◽  
Vibration Problem ◽  
Free Beam

scholarly journals Closed-form solutions for the free-vibration problem of multilayered piezoelectric shells

2006 ◽  
Vol 84 (22-23) ◽  
pp. 1506-1518 ◽  
Author(s):  
M. D’Ottavio ◽  
D. Ballhause ◽  
B. Kröplin ◽  
E. Carrera
Keyword(s):  
Free Vibration ◽  
Closed Form ◽  
Closed Form Solutions ◽  
Vibration Problem

FREE VIBRATION RESPONSE OF CYLINDRICAL PANELS WITH HIGHER ORDER SHEAR DEFORMATION THEORY

2005 ◽  
Vol 05 (03) ◽  
pp. 409-434 ◽  
Author(s):  
HUMAYUN R. H. KABIR ◽  
HASAN ASKAR
Keyword(s):  
Finite Element ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Free Vibration ◽  
Boundary Conditions ◽  
Shear Deformation ◽  
Shell Theory ◽  
Fourier Series Expansion ◽  
Partial Differential ◽  
Cylindrical Panels

Presented here is an analytical solution to the free vibration problem of an isotropic cylindrical panel with SS2-type simply supported boundary conditions based on Reddy's third order shear deformation shell theory. Using the principle of virtual work, the Reddy's shell theory generates five highly coupled partial differential equations in terms of three unknown displacements and two unknown rotations. The partial differential equations in conjunction with the prescribed boundary conditions are solved using displacement functions expressed in terms of double Fourier series expansion. Cylindrical panels with various aspect and thickness ratios are considered in the study of convergence behavior and parametric variation of the eigenvalues. The eigenvalues and mode shapes obtained in this study are compared with those obtained from the finite element software package ANSYS. The hitherto unavailable analytical solutions can be used as benchmarks for checking the accuracy of various approximate methods such as the Rayleigh–Ritz, finite element and finite difference methods.

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