Free vibrations of arches with inclusion of axial extension, shear deformation and rotatory inertia in Cartesian coordinates

2004 ◽  
Vol 8 (1) ◽  
pp. 43-48 ◽  
Author(s):  
Byoung Koo Lee ◽  
Tae Eun Lee ◽  
Dae Soon Ahn
Keyword(s):  
Shear Deformation ◽  
Free Vibrations ◽  
Rotatory Inertia ◽  
Cartesian Coordinates ◽  
Axial Extension

Free Vibration of Damaged Frame Structures Considering the Effects of Axial Extension, Shear Deformation and Rotatory Inertia: Exact Solution

2017 ◽  
Vol 17 (10) ◽  
pp. 1750111
Author(s):  
Ugurcan Eroglu ◽  
Ekrem Tufekci
Keyword(s):  
Exact Solution ◽  
Free Vibration ◽  
Shear Deformation ◽  
Natural Frequencies ◽  
Plane Motion ◽  
Mode Shapes ◽  
Frame Structures ◽  
Crack Identification ◽  
Rotatory Inertia ◽  
Axial Extension

In this paper, a procedure based on the transfer matrix method for obtaining the exact solution to the equations of free vibration of damaged frame structures, considering the effects of axial extension, shear deformation, rotatory inertia, and all compliance components arising due to the presence of a crack, is presented. The crack is modeled by a rotational and/or translational spring based on the concept of linear elastic fracture mechanics. Only the in-plane motion of planar structures is considered. The formulation is validated through some examples existing in the literature. Additionally, the mode shapes and natural frequencies of a frame with pitched roof are provided. The variation of natural frequencies with respect to the crack location is presented. It is concluded that considering the axial compliance, and axial-bending coupling due to the presence of a crack results in different dynamic characteristics, which should be considered for problems where high precision is required, such as for the crack identification problems.

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.

Axisymmetric Free Vibrations of Conical Shells

1964 ◽  
Vol 31 (3) ◽  
pp. 458-466 ◽  
Author(s):  
Hyman Garnet ◽  
Joseph Kempner
Keyword(s):  
Shear Deformation ◽  
Transverse Shear ◽  
Thin Shell ◽  
Shell Theory ◽  
Free Vibrations ◽  
Transverse Shear Deformation ◽  
Rotatory Inertia ◽  
Conical Shells ◽  
Thin Shell Theory ◽  
Thickness Parameter

The lowest axisymmetric modes of vibration of truncated conical shells are studied by means of a Rayleigh-Ritz procedure. Transverse shear deformation and rotatory inertia effects are accounted for, and the results are compared with those predicted by the classical thin-shell theory. Additionally, the results are compared when either of these theories is formulated in two ways: First, in the manner of Love’s first approximation in the classical thin-shell theory, and then by including the influence of the change of the element of arc length through the thickness. It was found that the Love and the more complex formulation yielded results which differed negligibly in either theory. The results predicted by the shear deformation-rotatory inertia theory differed significantly from those predicted by the classical thin-shell theory within a range of parameters which characterize short thick cones. These differences resulted principally from the influence of the transverse shear deformation. It was also found that within this short-cone range an increase in the shell thickness parameter was accompanied by an increase in the natural frequency. Moreover, the increase in frequency with increasing thickness parameter became less severe as the length-to-mean radius ratio was increased. For the longer cones, the frequency was virtually independent of the thickness.

Influences of Large Amplitudes, Transverse Shear Deformation, and Rotatory Inertia on Lateral Vibrations of Transversely Isotropic Plates

1969 ◽  
Vol 36 (2) ◽  
pp. 254-260 ◽  
Author(s):  
Cheng-Ih Wu ◽  
J. R. Vinson
Keyword(s):  
Shear Deformation ◽  
Transverse Shear ◽  
Large Amplitude ◽  
Pyrolytic Graphite ◽  
Flexural Vibration ◽  
Transversely Isotropic ◽  
Free Vibrations ◽  
Transverse Shear Deformation ◽  
Rotatory Inertia ◽  
Special Case

In the present paper, using an improved Reissner’s variational theorem along with Berger’s hypothesis, a set of governing equations which include the effects of transverse shear deformation and rotatory inertia is derived for the large amplitude free vibrations of plates composed of a transversely isotropic material. Applying the possibility of neglecting the rotatory inertia in primarily flexural vibration (discussed in the previous work [1]2), the lateral free vibrations of simply supported plates are treated in detail and the solution is compared with those of previous investigators. The free vibration of beams is studied as a special case of plates, while the small amplitude vibrations are treated as a special case of large amplitude vibrations. The numerical results show that the effect of transverse shear deformation is significant when applying to the plate constructions made of pyrolytic graphite-type materials.

Symmetric Flexural Vibrations of a Clamped Circular Disk

1956 ◽  
Vol 23 (2) ◽  
pp. 319
Author(s):  
H. Deresiewicz
Keyword(s):  
Shear Deformation ◽  
Frequency Spectrum ◽  
Transverse Shear ◽  
Circular Disk ◽  
Transverse Shear Deformation ◽  
Axially Symmetric ◽  
Rotatory Inertia ◽  
Flexural Vibrations ◽  
Clamped Edges

Abstract The frequency spectrum is computed for the case of free, axially symmetric vibrations of a circular disk with clamped edges, using a theory which includes the effects of rotatory inertia and transverse shear deformation.

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