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.

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.

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.

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.

Large-amplitude vibration of imperfect angle-ply laminated rectangular plate with viscous damping

2015 ◽  
Vol 12 (3) ◽  
pp. 207-214 ◽  
Author(s):  
He Huang ◽  
David Hui
Keyword(s):  
Boundary Conditions ◽  
Vibration Frequency ◽  
Large Amplitude ◽  
Plane Boundary ◽  
Damping Factor ◽  
Viscous Damping ◽  
Damped System ◽  
Amplitude Vibration ◽  
Out Of Plane ◽  
Large Amplitude Vibration

This paper solves the modified-Duffing ordinary differential equation for large-amplitude vibration of imperfect angle-ply rectangular composite plate. Viscous damping is then introduced in the derivation and analyzed under four different boundary conditions (combining two out-of-plane boundary conditions with two in-plane boundary conditions). It has been shown that even a small viscous damping factor, for example 0.1 from an ordinary damped system can largely decrease the vibration amplitude within several periods. Yet at the same time, the vibration frequency only changes slightly. Furthermore, viscous damping is proved to significantly affect the vibration frequency and the vibration mode from nonlinear to much more linear. This effect is irrelevant to boundary conditions and geometric imperfections.

Large Amplitude Free Vibration Study of Square Plates under Different Boundary Conditions Through a Static Analysis

2004 ◽  
Vol 10 (7) ◽  
pp. 1009-1028 ◽  
Author(s):  
K. N. Saha ◽  
D. Misra ◽  
G. Pohit ◽  
S. Ghosal
Keyword(s):  
Boundary Conditions ◽  
Large Amplitude ◽  
Static Problem ◽  
Mode Shapes ◽  
Linear Combinations ◽  
Isotropic Plates ◽  
Dimensionless Amplitude ◽  
Amplitude Vibration ◽  
Large Amplitude Vibration ◽  
Comparison Of The Results

The free v ibration problem of thin isotropic plates incorporating the effect. of geometric non-linearity is studied by developing a specific numerical methodology. The problem is formulated by using a variational method. The large amplitude vibration problem is addressed by solving the corresponding static problem first through an iterative schemne using a relaxation parameter. Subsequently. with the resulting displacement field, the dynamic problem is solved as a standard eigenvalue problem. The assumed deflection field, required for the analysis, is constituted through linear combinations of beam vibration modes corresponding to the specific boundary conditions of the plate. Typical results for the square plates, in the form of backbone curves, have been furnished in the dimensionless amplitude-frequency plane. Two different combinations of the boundary conditions for the purpose are chosen following an earlier benchmark work. Much insight on large amplitude dynamic behavior of the plate is obtained through the vibration mode shapes. presented for each case. A comparison of the results of the reduced problem with those of earlier studies indicates excellent agreement.

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