A numerical method for analysis of free vibration of spherical shells.

AIAA Journal ◽  
1967 ◽  
Vol 5 (7) ◽  
pp. 1256-1261 ◽  
Author(s):  
M. S. ZARGHAMEE ◽  
A. R. ROBINSON
Keyword(s):  
Free Vibration ◽  
Numerical Method ◽  
Spherical Shells

scholarly journals Dynamic Response of Laminated FRP Composite Made Cracked Spherical Shells Subjected to Free Vibration

2014 ◽  
Vol 6 ◽  
pp. 1580-1587 ◽  
Author(s):  
R.R. Das ◽  
A. Chakraborty ◽  
A. Guchhait ◽  
A. Singla
Keyword(s):  
Free Vibration ◽  
Dynamic Response ◽  
Spherical Shells ◽  
Frp Composite

A numerical method for static and free-vibration analysis of non-uniform Timoshenko beam–columns

2006 ◽  
Vol 33 (3) ◽  
pp. 278-293 ◽  
Author(s):  
Z Canan Girgin ◽  
Konuralp Girgin
Keyword(s):  
Free Vibration ◽  
Numerical Method ◽  
Timoshenko Beam ◽  
Dynamic Stiffness ◽  
Geometrical Nonlinearity ◽  
Free Vibration Analysis ◽  
Winkler Foundation ◽  
Beam Columns ◽  
Geometrical Properties ◽  
Stiffness Matrices

A generalized numerical method is proposed to derive the static and dynamic stiffness matrices and to handle the nodal load vector for static analysis of non-uniform Timoshenko beam–columns under several effects. This method presents a unified approach based on effective utilization of the Mohr method and focuses on the following arbitrarily variable characteristics: geometrical properties, bending and shear deformations, transverse and rotatory inertia of mass, distributed and (or) concentrated axial and (or) transverse loads, and Winkler foundation modulus and shear foundation modulus. A successive iterative algorithm is developed to comprise all these characteristics systematically. The algorithm enables a non-uniform Timoshenko beam–column to be regarded as a substructure. This provides an important advantage to incorporate all the variable characteristics based on the substructure. The buckling load and fundamental natural frequency of a substructure subjected to the cited effects are also assessed. Numerical examples confirm the efficiency of the numerical method.Key words: non-uniform, Timoshenko, substructure, elastic foundation, geometrical nonlinearity, stiffness, stability, free vibration.

scholarly journals A numerical method for computing optimum radii of host stars and orbits of planets, with application to Kepler-11, Kepler-90, Kepler-215, HD 10180, HD 34445 and TRAPPIST-1

2020 ◽  
pp. 2150028
Author(s):  
V. S. Geroyannis
Keyword(s):  
Numerical Method ◽  
Planetary System ◽  
Hydrostatic Equilibrium ◽  
Polytropic Index ◽  
Spherical Shells ◽  
Polytropic Model ◽  
Emden Equation ◽  
Exoplanetary Systems ◽  
Planetary Orbits ◽  
Host Stars

In the so-called “global polytropic model”, we assume planetary systems in hydrostatic equilibrium and solve the Lane–Emden equation in the complex plane. We thus find polytropic spherical shells providing accommodation to planetary orbits. On the basis of this model, we develop a numerical method which can compute optimum values for the polytropic index of the global polytropic model that simulates the planetary system, for the orbits of the planets, and for the host star radius. We apply our method to the exoplanetary systems Kepler-11, Kepler-90, Kepler-215, HD 10180, HD 34445 and TRAPPIST-1.

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