Exact solution of free in-plane vibration of a stepped circular arch

2006 ◽  
Vol 295 (3-5) ◽  
pp. 725-738 ◽  
Author(s):  
Ekrem Tufekci ◽  
Oznur Ozdemirci
Keyword(s):  
Exact Solution ◽  
Plane Vibration ◽  
Circular Arch

EXACT SOLUTION OF FREE IN-PLANE VIBRATION OF SHALLOW CIRCULAR ARCHES

2001 ◽  
Vol 01 (03) ◽  
pp. 409-428 ◽  
Author(s):  
EKREM TÜFEKÇİ
Keyword(s):  
Exact Solution ◽  
Boundary Conditions ◽  
Shear Deformation ◽  
Slenderness Ratio ◽  
Mode Shapes ◽  
Rotatory Inertia ◽  
Shallow Arch ◽  
Inertia Effects ◽  
Plane Vibration ◽  
Axial Extension

The free in-plane vibration of a shallow circular arch with uniform cross-section is investigated by taking into account axial extension, shear deformation and rotatory inertia effects. The exact solution of the governing differential equations is obtained by the initial value method. By employing the same solution procedure, the solutions are also given for the other cases, in which each effect is considered alone, as well as no effect. The frequency coefficients are obtained for the lowest five vibration modes of arches with five combinations of classical boundary conditions, and various slenderness ratios and opening angles. The results show that the shear deformation and rotatory inertia effects are also very important as well as the axial extension effect, even if a slender shallow arch is considered. The discrepancies among the results of the five cases decrease, when opening angle increases for a constant radius and slenderness ratio. The effects of the boundary conditions and the slenderness ratio of the arch are investigated. The discrepancies among the results of the cases become much more important in higher modes. The mode shapes of a shallow arch are obtained for each case.

Exact solution for free in-plane vibration analysis of an eccentric elliptical plate

2013 ◽  
Vol 224 (8) ◽  
pp. 1609-1624 ◽  
Author(s):  
Seyyed M. Hasheminejad ◽  
Ali Ghaheri ◽  
Sajjad Vaezian
Keyword(s):  
Exact Solution ◽  
Vibration Analysis ◽  
Elliptical Plate ◽  
Plane Vibration

GEOMETRICALLY NON-LINEAR FREE IN-PLANE VIBRATION OF STEPPED CIRCULAR ARCH

2021 ◽  
Author(s):  
Omar Outassafte ◽  
Ahmed Adri ◽  
Yassine El Khouddar ◽  
Said Rifai ◽  
Rhali Benamar
Keyword(s):  
Plane Vibration ◽  
Circular Arch ◽  
Non Linear

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.

Exact solution of a four-site crystal model for an intermediate-valence system

1986 ◽  
Vol 47 (6) ◽  
pp. 1029-1034 ◽  
Author(s):  
J.C. Parlebas ◽  
R.H. Victora ◽  
L.M. Falicov
Keyword(s):  
Exact Solution ◽  
Intermediate Valence ◽  
Crystal Model
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