scholarly journals A PRACTICAL METHOD FOR CALCULATING NATURAL BENDING FREQUENCIES OF UNIFORM ELASTIC BEAMS CONSIDERING ROTATORY INERTIA AND SHEAR DEFORMATION

2022 ◽  
Vol 87 (791) ◽  
pp. 72-82
Author(s):  
Yudai YAMAGUCHI ◽  
Daiki SATO ◽  
Tetsuro TAMURA
Keyword(s):  
Shear Deformation ◽  
Practical Method ◽  
Rotatory Inertia ◽  
Elastic Beams

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.

Effect of Shear Deformation and Rotatory Inertia on Dynamic Buckling of Elastic Plates

1988 ◽  
Vol 110 (3) ◽  
pp. 282-286
Author(s):  
V. Birman
Keyword(s):  
Dynamic Response ◽  
Shear Deformation ◽  
Plate Theory ◽  
Deformation Mode ◽  
Dynamic Buckling ◽  
Rectangular Plates ◽  
Elastic Plates ◽  
Rotatory Inertia ◽  
Qualitative Effect

The influence of shear deformation and rotatory inertia on dynamic response of elastic rectangular plates subject to in-plane loads increasing with time is discussed using Mindlin’s plate theory. The qualitative effect of those factors on transverse displacements is estimated. It is shown that this effect becomes essential only if the plate is thick and the number of half-waves along the plate axes in the deformation mode is large.

scholarly journals Out-plane Vibrations of Curved Bars Considering Shear Deformation and Rotatory Inertia

1981 ◽  
Vol 24 (193) ◽  
pp. 1206-1213
Author(s):  
Katsuyoshi SUZUKI ◽  
Shin TAKAHASHI
Keyword(s):  
Shear Deformation ◽  
Rotatory Inertia

On the Importance of Shear Deformation, Rotatory Inertia, and Coriolis Forces in Turbine Blade Vibrations

1986 ◽  
Vol 108 (2) ◽  
pp. 319-324 ◽  
Author(s):  
K. A. Ansari
Keyword(s):  
Shear Deformation ◽  
Turbine Blade ◽  
Normal Modes ◽  
Functional Method ◽  
Lumped Parameter Model ◽  
Rotatory Inertia ◽  
Blade Vibration ◽  
Coriolis Forces ◽  
Analysis Technique ◽  
Blade Vibrations

This paper is concerned with the significance of the effects of shear deformation, rotatory inertia, and Coriolis forces in the analysis of turbine blade vibrations. Since these are quite pronounced at the high frequency ranges encountered in turbine blade vibration problems, they should not be overlooked although their inclusion paves the way for a complicated nonlinear analysis. An approximate analysis technique is presented which involves an application of the stationary functional method using the normal modes of a discretized model. Numerical results for a typical blade are obtained and discussed. An advantage of this analysis as applied to a lumped parameter model is that nonlinear modes higher than the fundamental can also be easily computed and assessed.

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.

Global Bending Response Analysis of Elastic and Viscoplastic Nuclear Shipping Cask Structures Subjected to Impact Loading

1980 ◽  
Vol 102 (1) ◽  
pp. 33-39
Author(s):  
R. C. Shieh
Keyword(s):  
Strain Rate ◽  
Shear Deformation ◽  
Strain Rate Sensitivity ◽  
Rate Sensitivity ◽  
Design Analysis ◽  
Response Analysis ◽  
Material Strength ◽  
Lumped Mass ◽  
Rotatory Inertia ◽  
Analysis Techniques

Within the framework of lumped mass upgraded beam theory in which rotatory and elastic shear deformation effects are considered, the title analysis is made for the case of large realistic lead-shielded, cylindrical stainless steel shipping casks equipped with end impact limiters. A computerized study developed elsewhere for the dynamic response analysis of elastic and elastic/viscoplastic beams and frames is first extended to include shear deformation and rotatory inertia effects and subsequently used in the cask impact response analysis study. Three types of impact limiter reaction force pulses are considered and three simplified analysis techniques (i.e., quasi-static, dynamic amplification factor and elementary beam analysis techniques) used in shipping cask design are evaluated. In particular, effects of shear deformation and rotatory inertia on impact responses and strain rate sensitivity effects on inelastic dynamic cask response behavior are studied. Appropriate guidelines are formulated for: 1) general use of these techniques in impact design analysis, and 2) treating strain rate sensitivity effects on material strength properties in conjunction with use of elastic, limit and elastic-plastic design analysis methods.

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.

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