Out-of-plane free vibration of a circular arch with uniform cross-section: Exact solution

2006 ◽  
Vol 291 (3-5) ◽  
pp. 525-538 ◽  
Author(s):  
Ekrem Tufekci ◽  
O. Yasar Dogruer
Keyword(s):  
Exact Solution ◽  
Free Vibration ◽  
Cross Section ◽  
Circular Arch ◽  
Out Of Plane ◽  
Uniform Cross Section

IN-PLANE VIBRATION OF CIRCULAR ARCHES WITH VARYING CROSS-SECTIONS

2013 ◽  
Vol 13 (01) ◽  
pp. 1350003 ◽  
Author(s):  
EKREM TUFEKCI ◽  
OZNUR OZDEMIRCI YIGIT
Keyword(s):  
Exact Solution ◽  
Cross Section ◽  
Cross Sections ◽  
Free Vibrations ◽  
Transverse Shear Deformation ◽  
Mode Transition ◽  
Rotatory Inertia ◽  
Initial Value ◽  
Inertia Effects ◽  
Circular Arch

The in-plane free vibration of circular arches with continuously varying cross-sections is studied by means of the exact solution. The exact solution can be obtained only for a circular arch with constant cross-section. As an approximation, the circular arch with varying cross-sections is divided into a number of arch elements with constant cross-sections. The cross-section of each arch element is determined by averaging the upper and lower cross-sections. Then, the exact solution of free vibrations for each arch element can be obtained by using the initial value method. The axial extension, transverse shear deformation and rotatory inertia effects are included in the analysis. As the number of the arch elements increases, the fast convergence of the frequencies to those of the original arch is observed. Clamped–clamped (CC), hinged–hinged (HH), hinged–clamped (HC), clamped–free (CF) and free–free (FF) boundary conditions are studied for different opening angles, taper types and taper ratios. A detailed parametric study is performed, by which the mode transition phenomenon is observed. The results obtained are compared with those available in the literature.

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.

Sign in / Sign up

Export Citation Format

Share Document