Symbolic Manipulation

1986 ◽  
pp. 61-78
Author(s):  
Harley Flanders
Keyword(s):  
Symbolic Manipulation

A Multi-Mode Approach for the Nonlinear Vibrations of Circular Cylindrical Shells

2001 ◽  
Author(s):  
Francesco Pellicano ◽  
Marco Amabili ◽  
Michael P. Païdoussis
Keyword(s):  
Degrees Of Freedom ◽  
Nonlinear Vibrations ◽  
Shell Theory ◽  
Cylindrical Shells ◽  
Nonlinear Behavior ◽  
Symbolic Manipulation ◽  
Comparison Functions ◽  
Circular Cylindrical Shells ◽  
Multi Mode

Abstract The nonlinear vibrations of simply supported, circular cylindrical shells, having geometric nonlinearities is analyzed. Donnell’s nonlinear shallow-shell theory is used, and the partial differential equations are spatially discretized by means of the Galerkin procedure, using a large number of degrees of freedom. A symbolic manipulation code is developed for the discretization, allowing an unlimited number of modes. In the displacement expansion particular care is given to the comparison functions in order to reduce as much as possible the dimension of the dynamical system, without losing accuracy. Both driven and companion modes are included, allowing for traveling-wave response of the shell. The fundamental role of the axisymmetric modes, which are included in the expansion, is confirmed and a convergence analysis is performed. The effect of the geometric shell characteristics, radius, length and thickness, on the nonlinear behavior is analyzed.

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