Semi-analytical solutions for buckling and free vibration of composite anisogrid lattice cylindrical panels

2021 ◽  
pp. 114422
Author(s):  
M.M. Mobasheri Zafarabadi ◽  
M.M. Aghdam
Keyword(s):  
Free Vibration ◽  
Analytical Solutions ◽  
Cylindrical Panels

Vibration of Beams with a Single Delamination under Axial Loading

2011 ◽  
Vol 675-677 ◽  
pp. 477-480
Author(s):  
Dong Wei Shu
Keyword(s):  
Free Vibration ◽  
Natural Frequency ◽  
Analytical Solutions ◽  
Axial Load ◽  
Natural Frequencies ◽  
Axial Loading ◽  
Composite Beams ◽  
Mode Shapes ◽  
Equilibrium Conditions ◽  
Monotonic Relation

In this work analytical solutions are developed to study the free vibration of composite beams under axial loading. The beam with a single delamination is modeled as four interconnected Euler-Bernoulli beams using the delamination as their boundary. The continuity and the equilibrium conditions are satisfied between the adjoining beams. The studies show that the sizes and the locations of the delaminations significantly influence the natural frequencies and mode shapes of the beam. A monotonic relation between the natural frequency and the axial load is predicted.

Hamilton, Ritz, and Elastodynamics

1976 ◽  
Vol 43 (4) ◽  
pp. 684-688 ◽  
Author(s):  
C. D. Bailey
Keyword(s):  
Approximate Solution ◽  
Differential Equations ◽  
Free Vibration ◽  
Exact Solutions ◽  
Analytical Solutions ◽  
Vibration Modes ◽  
Cantilever Beams ◽  
Transient Motion ◽  
Linear Elastodynamics ◽  
The Law

The theory of Ritz is applied to the equation that Hamilton called the “Law of Varying Action.” Direct analytical solutions are obtained for the transient motion of beams, both conservative and nonconservative. The results achieved are compared to exact solutions obtained by the use of rigorously exact free-vibration modes in the differential equations of Lagrange and to an approximate solution obtained through the application of Gurtin’s principles for linear elastodynamics. A brief discussion of Hamilton’s law and Hamilton’s principle is followed by examples of results for both free-free and cantilever beams with various loadings.

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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