The Effect of Rotatory Inertia and of Shear Deformation on the Frequency and Normal Mode Equations of Uniform Beams With Simple End Conditions

1961 ◽  
Vol 28 (4) ◽  
pp. 579-584 ◽  
Author(s):  
T. C. Huang
Keyword(s):  
Shear Deformation ◽  
Normal Mode ◽  
Transverse Shear ◽  
Transverse Shear Deformation ◽  
Rotatory Inertia ◽  
End Conditions ◽  
Flexural Vibrations

New frequency and normal mode equations for flexural vibrations of six common types of simple, finite beams are presented. The derivation includes the effect of rotatory inertia and transverse-shear deformation. A specific example is given.

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.

Large Amplitude Elliptical Plate Vibration With Transverse Shear and Rotatory Inertia Effects

1982 ◽  
Vol 104 (2) ◽  
pp. 426-431 ◽  
Author(s):  
M. Sathyamoorthy
Keyword(s):  
Shear Deformation ◽  
Transverse Shear ◽  
Large Amplitude ◽  
Mode Analysis ◽  
Transverse Shear Deformation ◽  
Rotatory Inertia ◽  
Semi Major Axis ◽  
Nonlinear Bending ◽  
Amplitude Vibration ◽  
Large Amplitude Vibration

An improved nonlinear vibration theory is used in the present analysis to study the effects of transverse shear deformation and rotatory inertia on the large amplitude vibration behavior of isotropic elliptical plates. When these effects are negligible the differential equations given here readily reduce to the well-known dynamic von Ka´rma´n equations. Based on a single-mode analysis, solutions to the governing equations are presented for immovably clamped elliptical plates by use of Galerkin’s method and the numerical Runge-Kutta procedure. An excellent agreement is found between the present results and those available for nonlinear bending and large amplitude vibration of elliptical plates. The present results for moderately thick elliptical plates indicate significant influences of the transverse shear deformation, axes ratio, and semi-major axis-to-thickness ratio on the large amplitude vibration of elliptical plates.

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.

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