scholarly journals Free Vibration Analysis of Axially Functionally Graded (AFG) Cantilever Columns of a Regular Polygon Cross-Section with Constant Volume

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 319
Author(s):  
Joon Kyu Lee ◽  
Byoung Koo Lee
Keyword(s):  
Free Vibration ◽  
Cross Section ◽  
Regular Polygon ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Constant Volume ◽  
Integral Approach ◽  
Element Analysis ◽  
Direct Integral ◽  
Material Inhomogeneity

This paper deals with the transverse free vibration of axially functionally graded (AFG) cantilever columns under the influence of axial compressive load. The columns possessing a regular polygon in their cross-section are tapered and their material properties vary along the axis of the column. An emphasis is placed on the columns with constant volume for admissible geometries and materials. The governing differential equation of the problem is derived and solved using the direct integral approach in conjunction with the determinant search technique. The obtained results are in good agreement with those in the available literature and computed by finite element analysis. Numerical examples for the natural frequency and mode shape of the columns are presented to investigate the effects of parameters related to geometrical nonuniformity and material inhomogeneity.

scholarly journals Free Vibration of AFG Circular Arch with Symmetric and Anti-symmetric Boundary Conditions at Mid-Arc

Symmetry ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 417 ◽  
Author(s):  
Joon Kyu Lee ◽  
Byoung Koo Lee
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Cross Section ◽  
Solution Method ◽  
Regular Polygon ◽  
Axial Direction ◽  
Functionally Graded ◽  
Material Parameters ◽  
Finite Element Software ◽  
Uniform Cross Section

This paper studies the in-plane free vibration of axially functionally graded (AFG) circular arches with non-uniform cross-section. The geometric and material properties of circular arches with regular polygon cross-section vary symmetrically about the mid-arc along the axial direction in quadratic polynomial form. The governing differential equations of the motion are derived, and the symmetric and anti-symmetric boundary conditions of the arches are developed for applying initial and boundary value problems in the solution method. The computed results agree well with the results of the finite element software ADINA. The effects of geometrical and material parameters on the natural frequency and mode shape of AFG circular arches are investigated.

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