Description of G2DMULT moment method algorithm for calculating spectral Green's functions of cylindrical multiconductor structures of arbitrary cross section

2003 ◽  
Author(s):  
P.-S. Kidal
Keyword(s):  
Cross Section ◽  
Moment Method ◽  
Green's Functions ◽  
Green’S Functions ◽  
Arbitrary Cross Section

scholarly journals Closed-form solutions for vibrations of a magneto-electro-elastic beam with variable cross section by means of Green’s functions

2018 ◽  
Vol 30 (1) ◽  
pp. 82-99 ◽  
Author(s):  
Xuan Ling Zhang ◽  
Xiao Chao Chen ◽  
Echuan Yang ◽  
Hai Feng Li ◽  
Jian Bo Liu ◽  
...  
Keyword(s):  
Boundary Conditions ◽  
Cross Section ◽  
Electric Potential ◽  
Green's Functions ◽  
Green’S Functions ◽  
Elastic Beam ◽  
Variable Cross Section ◽  
Variable Cross ◽  
Cross Sectional ◽  
Closed Form Solutions

In this article, closed-form solutions are obtained for vibrations of a magneto-electro-elastic beam with variable cross section. Based on Timoshenko beam assumptions, governing equation for the non-uniform beam with exponentially varying width is obtained. Laplace transform approach applied to the governing equation results in the corresponding Green’s functions for the beams with various boundary conditions. The equations, which are solved to obtain Green’s functions, are degenerated for the analyses of the characters of free vibration. For free vibrations of the beams under different mechanical boundary conditions, the effects of the non-uniformly cross-sectional parameters and magneto-electric boundary conditions on the dynamic characters are studied. In addition, the magneto-electric potential modal variables’ distributions through the thickness are presented. In the discussions of forced vibration, two points in the beam are selected to investigate frequency responses in terms of displacement and magneto-electric potential. Moreover, the influences of excitation frequency and cross-sectional parameter on through-the-thickness distributions of electric potentials are investigated.

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