Effects of transverse shear and rotatory inertia on large amplitude vibration of composite plates and shells

Sadhana ◽  
1987 ◽  
Vol 11 (3-4) ◽  
pp. 367-377
Author(s):  
M Sathyamoorthy
Keyword(s):  
Transverse Shear ◽  
Large Amplitude ◽  
Composite Plates ◽  
Rotatory Inertia ◽  
Amplitude Vibration ◽  
Plates And Shells ◽  
Large Amplitude Vibration

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 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.

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.

Large-amplitude vibration of imperfect angle-ply laminated rectangular plates for various materials

2015 ◽  
Vol 12 (4) ◽  
pp. 313-318
Author(s):  
He Huang ◽  
David Hui
Keyword(s):  
Large Amplitude ◽  
Fiber Strength ◽  
Composite Plates ◽  
Rectangular Plates ◽  
Modulus Ratio ◽  
Backbone Curve ◽  
Fiber Volume ◽  
Runge Kutta Method ◽  
Amplitude Vibration ◽  
Large Amplitude Vibration

This paper deals with the solution of modified-Duffing ordinary differential equation for large-amplitude vibration of imperfect angle-ply rectangular composite plates. The boundary condition is simply supported and in-plane movable. The initial condition for the vibration is an initial vibration amplitude. This vibration problem is solved numerically by Runge-Kutta method. The effect of plate imperfection is studied and proved that a typical backbone curve will show up in case of a relatively large imperfection. Three different composite materials are then chosen to reveal the influence of young’s modulus ratio. Four fiber volumes are assumed to study its effect on the vibration mode. It turns out that either increasing the fiber strength or increasing the fiber volume in a composite will lead to an increase of its overall strength. And this will further trigger the plate vibration to behave more nonlinearly.

Boundary Control of Large Amplitude Vibration of Anisotropic Composite Laminated Plates

2010 ◽  
Vol 132 (6) ◽  
Author(s):  
Hossein Rastgoftar ◽  
Mohammad Eghtesad ◽  
Alireza Khayatian
Keyword(s):  
Boundary Control ◽  
Large Amplitude ◽  
Control Method ◽  
Composite Plates ◽  
Laminated Plates ◽  
Composite Laminated Plates ◽  
Anisotropic Composite ◽  
Amplitude Vibration ◽  
Large Amplitude Vibration ◽  
Control Forces

This paper presents a solution to the stabilization problem of large amplitude vibration of the anisotropic composite laminated plates when the Kirchhoff theorem is used to model geometric equations of strain. Because of the large displacement in the normal direction to the plate, the plate displacements in in-plane directions are not dispensable, and strains and governing equations for transverse vibration and in-plane motions are nonlinear; therefore, the nonlinear boundary control method is proposed to be utilized to stabilize the plate vibration. The boundary control forces consist of feedback of the velocities and slope at the boundary of the plate. By applying the proposed method, it is possible to asymptotically stabilize large amplitude vibration of anisotropic composite plates with simply supported boundary conditions without resorting to truncation of the model and without the use of in-domain measuring and actuating devices.

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.

Modeling of Large Amplitude Vibration Control of Beams and Cylindrical Deformations of Plates and Shells With Distributed Piezoelectric Actuators

2001 ◽  
Author(s):  
R. Schmidt
Keyword(s):  
Vibration Control ◽  
Large Amplitude ◽  
Virtual Work ◽  
Curved Beams ◽  
Piezoelectric Layers ◽  
Amplitude Vibration ◽  
Plates And Shells ◽  
Large Amplitude Vibration ◽  
Strain Measures ◽  
Principle Of Virtual Displacements

Abstract The paper deals with the geometrically nonlinear theory and finite element method for the simulation of large amplitude vibration control of straight and curved beams, or what is equivalent, cylindrical deformations of plates and shells, consisting of a master structure with integrated thin piezoelectric layers or patches. The theory is based on the Bernoulli or Kirchhoff-Love hypothesis, respectively, and constitutes an entirely Lagrangean displacement formulation for small strains with no restrictions imposed on the magnitude of rotations or displacements. Based on modified strain measures the strain-displacement relations are only quadratic in terms of displacements and their gradients. Work-conjugate stress resultants and stress couples are derived from the internal virtual work associated with the first approximation of the strain energy density. Based on the principle of virtual displacements the FE equations for the simulation of static and dynamic response control are derived.

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