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.

Effect of Transverse Shear and Rotatory Inertia on Large Amplitude Vibration of Anisotropic Skew Plates: Part 2—Numerical Results

1980 ◽  
Vol 47 (1) ◽  
pp. 133-138 ◽  
Author(s):  
M. Sathyamoorthy ◽  
C. Y. Chia
Keyword(s):  
Transverse Shear ◽  
Large Amplitude ◽  
Numerical Procedure ◽  
Orientation Angle ◽  
Single Mode ◽  
Mode Analysis ◽  
Skew Angle ◽  
Nonlinear Bending ◽  
Amplitude Vibration ◽  
Large Amplitude Vibration

Based on the single-mode analysis, solutions to the governing equations developed in Part 1 of this paper are presented for various boundary conditions by use of Galerkin’s method and the Runge-Kutta numerical procedure. Excellent agreement is found between the present results and those available for nonlinear bending and large amplitude vibration of skew plates. The present results for moderately thick anisotropic skew plates indicate significant influences of the transverse shear deformation, orientation angle, skew angle, and side ratio on the large amplitude vibration behavior of certain fiber-reinforced composite skew plates.

Effect of Transverse Shear and Rotatory Inertia on Large Amplitude Vibration of Anisotropic Skew Plates: Part 1—Theory

1980 ◽  
Vol 47 (1) ◽  
pp. 128-132 ◽  
Author(s):  
M. Sathyamoorthy ◽  
C. Y. Chia
Keyword(s):  
Boundary Conditions ◽  
Transverse Shear ◽  
Large Amplitude ◽  
Transverse Shear Deformation ◽  
Rotatory Inertia ◽  
Inertia Effects ◽  
Various Boundary Conditions ◽  
Amplitude Vibration ◽  
Large Amplitude Vibration ◽  
Anisotropic Elastic

A nonlinear vibration theory for anisotropic elastic skew plates is developed with the aid of Hamilton’s principle. The effects of transverse shear deformation and rotatory inertia are included in the analysis. The differential equations formulated here readily reduce to the dynamic von Karman-type equations of skew plates when the shear and rotatory inertia effects are neglected. Solutions to these equations are presented for various boundary conditions in the second part of the paper.

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.

Nonlocal large-amplitude vibration of embedded higher-order shear deformable multiferroic composite rectangular nanoplates with different edge conditions

2017 ◽  
Vol 29 (5) ◽  
pp. 944-968 ◽  
Author(s):  
R Gholami ◽  
R Ansari ◽  
Y Gholami
Keyword(s):  
Boundary Conditions ◽  
Shear Deformation ◽  
Large Amplitude ◽  
Higher Order ◽  
Small Scale ◽  
Nonlinear Frequency ◽  
Amplitude Vibration ◽  
Large Amplitude Vibration ◽  
Multiferroic Composite ◽  
Shear Deformable

Based on the nonlocal elasticity theory, a unified nonlocal, nonlinear, higher-order shear deformable nanoplate model is developed to investigate the size-dependent, large-amplitude, nonlinear vibration of multiferroic composite rectangular nanoplates with different boundary conditions resting on an elastic foundation. By considering a unified displacement vector and using von Kármán’s strain tensor, the strain–displacement components are obtained. Using coupled nonlocal constitutive relations, the coupled ferroelastic, ferroelectric, ferromagnetic, and thermal properties of multiferroic composite materials and small-scale effect are taken into account. The electric and magnetic potential distributions in the nanoplate are calculated via Maxwell’s electromagnetic equations. Furthermore, Hamilton’s principle is utilized to obtain the mathematical formulation associated with the coupled governing equations of motions and boundary conditions. The developed model enables us to consider the effects of rotary inertia and transverse shear deformation without using any shear correction factor. Also, it can be degenerated to the models based on the Kirchhoff and existing shear deformation plate theories. To solve the large-amplitude vibration problem, an efficient multistep numerical solution approach is utilized. Effects of various important parameters such as the type of the plate theory, and parameters of nonlocality and coupled fields on the nonlinear frequency response are investigated.

Shear and Rotatory Inertia Effects on the Large Amplitude Vibration of the Initially Imperfect Plates

1980 ◽  
Vol 47 (3) ◽  
pp. 662-666 ◽  
Author(s):  
Z. Celep
Keyword(s):  
Transverse Shear ◽  
Vibration Mode ◽  
Initial Imperfection ◽  
Flexural Vibration ◽  
Rotatory Inertia ◽  
Inertia Effects ◽  
Amplitude Vibration ◽  
Large Amplitude Vibration ◽  
Elastic Rectangular Plate ◽  
Modal Equation

In this paper, the free flexural vibration of an elastic rectangular plate having initial imperfection is investigated including the effects of transverse shear and rotatory inertia. It is assumed that the vibration occurs with large amplitudes which leads to nonlinear differantial equations. On the basis of an assumed vibration mode, the modal equation of the plate is obtained and solved numerically.

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