Natural Frequencies of Thick Rotating Annular Discs Using an Integrated Method

2003 ◽  
Author(s):  
Yuan Mao Huang ◽  
C. C. Lai
Keyword(s):  
Natural Frequencies ◽  
Plate Theory ◽  
Outer Radius ◽  
Interactive Software ◽  
The Finite Element Method ◽  
First Order ◽  
Integrated Method ◽  
Subspace Iteration ◽  
Inner Radius ◽  
Existing Data

An integrated method that combines the first order plate theory, Hamilton’s principle, the finite element method and the subspace iteration method is used to calculate the natural frequencies of thick rotating annular discs. The shear deformation and the rotary inertia of elastic discs with the uniform thickness are considered. Interactive software is generated for personal computers, and the effects of the disc rotational speed, the ratio of the disc thickness to the disc outer radius and the ratio of the disc inner radius to the disc outer radius on natural frequencies are analyzed. Comparison of calculated natural frequencies of discs shows good correlation with existing data. It is expected that this method can provide more accurate results compared with existing methods.

On the Vibration of a Rotating Disk

1972 ◽  
Vol 39 (4) ◽  
pp. 1143-1144 ◽  
Author(s):  
S. Barasch ◽  
Y. Chen
Keyword(s):  
Approximate Calculation ◽  
Initial Conditions ◽  
Rotating Disk ◽  
Equation Of Motion ◽  
Outer Radius ◽  
Order Equation ◽  
System Of Differential Equations ◽  
Fourth Order Equation ◽  
First Order ◽  
Inner Radius

The equation of motion of a rotating disk, clamped at the inner radius and free at the outer radius, is solved by reducing the fourth-order equation of motion to a set of four first-order equations subject to arbitrary initial conditions. A modified Adams’ method is used to numerically integrate the system of differential equations. Results show that Lamb-Southwell’s approximate calculation of the frequency is justified.

Buckling of Functionally Graded Circular/Annular Plates Based on the First-Order Shear Deformation Plate Theory

2004 ◽  
Vol 261-263 ◽  
pp. 609-614 ◽  
Author(s):  
L.S. Ma ◽  
Tie Jun Wang
Keyword(s):  
Shear Deformation ◽  
Material Properties ◽  
Volume Fraction ◽  
Plate Theory ◽  
Plate Thickness ◽  
Shear Deformation Theory ◽  
Outer Radius ◽  
Functionally Graded ◽  
First Order ◽  
Annular Plates

Based on the first-order shear deformation theory of plate, governing equations for the axisymmetric buckling of functionally graded circular/annular plates are derived. The coupled deflections and rotations in the pre-buckling state of the plates are neglected in analysis. The material properties vary continuously through the thickness of the plate, and obey a power law distribution of the volume fraction of the constituents. The resulting differential equations are numerically solved by using a shooting method. The critical buckling loads of circular and annular plates are obtained, which are compared with those obtained from the classical plate theory. Effects of material properties, ratio of inter to outer radius, ratio of plate thickness to outer radius, and boundary conditions on the buckling behavior of FGM plates are discussed.

scholarly journals Voltage-Induced Wrinkling in a Constrained Annular Dielectric Elastomer Film

2017 ◽  
Vol 85 (1) ◽  
Author(s):  
Kai Li ◽  
Wanfang Wu ◽  
Ziyang Jiang ◽  
Shengqiang Cai
Keyword(s):  
Applied Voltage ◽  
Plate Theory ◽  
Critical Value ◽  
Dielectric Elastomer ◽  
Outer Radius ◽  
Material Failure ◽  
System Failure ◽  
Mechanical Forces ◽  
Inner Radius ◽  
Deformation Modes

Wrinkles can be often observed in dielectric elastomer (DE) films when they are subjected to electrical voltage and mechanical forces. In the applications of DEs, wrinkle formation is often regarded as an indication of system failure. However, in some scenarios, wrinkling in DE does not necessarily result in material failure and can be even controllable. Although tremendous efforts have been made to analyze and calculate a variety of deformation modes in DE structures and devices, a model which is capable of analyzing wrinkling phenomena including the critical electromechanical conditions for the onset of wrinkles and wrinkle morphology in DE structures is currently unavailable. In this paper, we experimentally demonstrate controllable wrinkling in annular DE films with the central part being mechanically constrained. By changing the ratio between the inner radius and outer radius of the annular films, wrinkles with different wavelength can be induced in the films when externally applied voltage exceeds a critical value. To analyze wrinkling phenomena in DE films, we formulate a linear plate theory of DE films subjected to electromechanical loadings. Using the model, we successfully predict the wavelength of the voltage-induced wrinkles in annular DE films. The model developed in this paper can be used to design voltage-induced wrinkling in DE structures for different engineering applications.

INFLUENCE OF IN-PLANE AXIAL AND SHEAR LOADING ON THE VIBRATION OF METALLIC PLATES

2011 ◽  
Vol 03 (03) ◽  
pp. 447-467 ◽  
Author(s):  
E. CARRERA ◽  
S. LECCA ◽  
P. NALI ◽  
M. SOAVE
Keyword(s):  
Boundary Conditions ◽  
Natural Frequencies ◽  
Plate Theory ◽  
Shear Loading ◽  
Shear Locking ◽  
The Finite Element Method ◽  
Third Order ◽  
Carrera Unified Formulation ◽  
Shear Deformation Theories ◽  
Metallic Plates

This work deals with the vibration problem of metallic plates subjected to combined axial, biaxial and shear in-plane loading. Various type of boundary conditions are considered. Results related to thin plate theories and shear deformation theories are compared to a third-order plate theory including the thickness stretching effects. The Finite Element Method (FEM) is applied on the basis of Carrera Unified Formulation kinematic assumptions. FE matrices are computed by referring to the four-node element. The mixed interpolation of tensorial components technique is used in order to contrast the shear locking for both classical and refined theories. The influence of the in-plane loading (combined axial, biaxial and shear) on plate undamped natural frequencies is illustrated and discussed. Various plate geometries and boundary conditions are considered.

Vibration behavior of a radially functionally graded annular disc with variable geometry

2014 ◽  
Vol 21 (3) ◽  
pp. 453-461 ◽  
Author(s):  
Hasan Çallıoğlu ◽  
Ersin Demir ◽  
Yasin Yılmaz ◽  
Zekeriya Girgin
Keyword(s):  
Natural Frequency ◽  
Elasticity Modulus ◽  
Plate Theory ◽  
Outer Radius ◽  
Functionally Graded ◽  
Mode Shapes ◽  
Variable Geometry ◽  
Vibration Behavior ◽  
Inner Radius ◽  
Annular Disc

AbstractIn this study, the free vibration behavior of an annular disc made of functionally graded material (FGM) with variable geometry is investigated. The elasticity modulus, density, and thickness of the disc are assumed to vary through the radial direction according to the power law so that the effects of their indexes on the natural frequency of the disc are investigated. The Poisson’s ratio is assumed as a constant. The natural frequencies of the disc are calculated for various boundary conditions by using classical plate theory, and the various types of mode shapes, which are described by the number of nodal diameters and nodal circles, are also discussed. Moreover, the effects of the ratio of the inner radius to the outer radius on the natural frequency are also considered. It is found that in order to increase the natural frequency, the elasticity modulus and thickness should be increased at the inner surface, whereas density should be increased at the outer surface. The natural frequency can also be increased by increasing the ratio of inner radius to outer radius. The results obtained are compared with the results of a finite-element-based commercial program, ANSYS®, and found to be consistent with each other.

The effect of bi-axial in-plane loads on the natural frequency of nano-plates

2017 ◽  
Vol 24 (19) ◽  
pp. 4513-4528 ◽  
Author(s):  
Seyed Ghasem Enayati ◽  
Morteza Dardel ◽  
Mohammad Hadi Pashaei
Keyword(s):  
Natural Frequency ◽  
Nonlocal Elasticity ◽  
Natural Frequencies ◽  
Plate Theory ◽  
Nonlocal Parameter ◽  
Nonlocal Elasticity Theory ◽  
Classical Plate Theory ◽  
First Order ◽  
Compressive Loads ◽  
Comprehensive Study

In this paper, natural frequencies of nano-plates subjected to two-sided in-plane tension or compressive loads, based on Eringen nonlocal elasticity theory and displacement field of first-order shear deformation plate theory (FSDT), are investigated. By considering total rotational variables as the two rotations due to bending and shear, another formulation form of FSDT nano-plate is achieved, that can simultaneously consider classical plate theory (CLPT) and FSDT. In a comprehensive study, the effects of different parameters such as a nonlocal parameter, aspect ratio, thickness to length ratio, mode number, boundary conditions and also length of nano-plate are examined on the dimensionless natural frequency. The results show that simultaneously applying two-sided tension and compressive in-plane loads changes frequency in a manner which is different to one-directional loading.

scholarly journals Effect of Membrane Components of Transverse Forces on Magnitudes of Total Transverse Forces in the Nonlinear Stability of Plate Structures

Materials ◽  
2020 ◽  
Vol 13 (22) ◽  
pp. 5262
Author(s):  
Zbigniew Kołakowski ◽  
Jacek Jankowski
Keyword(s):  
Shear Deformation ◽  
Deformation Theory ◽  
Plate Theory ◽  
Shear Deformation Theory ◽  
The Finite Element Method ◽  
Classical Plate Theory ◽  
Plate Structures ◽  
First Order ◽  
Membrane Components ◽  
Membrane Deformations

For an isotropic square plate subject to unidirectional compression in the postbuckling state, components of transverse forces in bending, membrane transverse components and total components of transverse forces were determined within the first-order shear deformation theory (FSDT), the simple first-order shear deformation theory (S-FSDT), the classical plate theory (CPT) and the finite element method (FEM). Special attention was drawn to membrane components of transverse forces, which are expressed with the same formulas for the first three theories and do not depend on membrane deformations. These components are nonlinearly dependent on the plate deflection. The magnitudes of components of transverse forces for the four theories under consideration were compared.

Free Flexural Vibrations of Bonded and Centrally Doubly Stiffened Composite Orthotropic Base Plates or Panels

Aerospace ◽  
2004 ◽  
Author(s):  
U. Yuceoglu ◽  
V. O¨zerciyes ◽  
K. C¸il
Keyword(s):  
Natural Frequencies ◽  
Plate Theory ◽  
Base Plate ◽  
Mode Shapes ◽  
Shear Stresses ◽  
Adhesive Layers ◽  
First Order ◽  
Flexural Vibrations ◽  
Interpolation Polynomials ◽  
Base Plates

The problem of the “Free Flexural Vibrations of Bonded and Centrally Doubly Stiffened Composite Orthotropic Base Plates or Panels” is formulated and investigated. The composite plate or panel system is made up of an orthtropic base plate reinforced or doubly stiffened by the upper and lower stiffening orthotropic plate strips. The stiffening plate strips are at the mid-center and are adhesively bonded to the base plate. The base plate and the stiffening plate strips are considered as dissimilar orthotropic Mindlin plates. Thus, the analysis is based on a “First Order Shear Deformation Plate Theory (FSDPT)” of Mindlin type. In the very thin, linearly elastic adhesive layers, the transverse normal and shear stresses are included. The sets of the dynamic equations and other equations of plates and adhesive layers are finally reduced to a “Governing System of the First Order Ordinary Differential Equations.” Then, this system is integrated by means of the “Modified Transfer Matrix Method (with Interpolation Polynomials and/or Chebyshev Polynomials).” The mode shapes and the associated natural frequencies are calculated and some parametric studies are presented. Also, the influences of the “hard” and the “soft” adhesive layers on the natural frequencies and the mode shapes are shown.

Delamination of Laminate Plates

2014 ◽  
Vol 969 ◽  
pp. 97-100 ◽  
Author(s):  
Eva Kormaníková
Keyword(s):  
Finite Element Analysis ◽  
Mixed Mode ◽  
Plate Theory ◽  
Laminate Plate ◽  
Element Analysis ◽  
Interface Elements ◽  
First Order ◽  
Plate Elements ◽  
Interface Modeling ◽  
Shear Deformable

The paper deals with numerical modeling of delamination of laminate plate consists of unidirectional fiber reinforced layers. The methodology adopts the first-order shear laminate plate theory and fracture and contact mechanics. There are described sublaminate modeling and delamination modeling by the help of finite element analysis. With the interface modeling there is calculated the energy release rate along the lamination front. Numerical results are given for mixed mode delamination problems by implementing the method in a 2D finite analysis, which utilizes shear deformable plate elements and interface elements. Numerical example is done by the commercial ANSYS code.

Sign in / Sign up

Export Citation Format

Share Document