Natural Frequencies of Thick Annular Plates

1982 ◽  
Vol 49 (3) ◽  
pp. 633-638 ◽  
Author(s):  
T. Irie ◽  
G. Yamada ◽  
K. Takagi
Keyword(s):  
Boundary Conditions ◽  
Natural Frequencies ◽  
Plate Theory ◽  
Mindlin Plate ◽  
Annular Plates ◽  
Mindlin Plate Theory

The natural frequencies of vibration based on the Mindlin plate theory are tabulated for uniform annular plates under nine combinations of boundary conditions.

Free Bending Vibrations of Adhesively Bonded Orthotropic Plates With a Single Lap Joint

1996 ◽  
Vol 118 (1) ◽  
pp. 122-134 ◽  
Author(s):  
U. Yuceoglu ◽  
F. Toghi ◽  
O. Tekinalp
Keyword(s):  
Boundary Conditions ◽  
Natural Frequencies ◽  
Plate Theory ◽  
Mode Shapes ◽  
Mindlin Plate ◽  
Lap Joint ◽  
Orthotropic Plates ◽  
Adhesively Bonded ◽  
Bending Vibrations ◽  
Free Bending

This study is concerned with the free bending vibrations of two rectangular, orthotropic plates connected by an adhesively bonded lap joint. The influence of shear deformation and rotatory inertia in plates are taken into account in the equations according to the Mindlin plate theory. The effects of both thickness and shear deformations in the thin adhesive layer are included in the formulation. Plates are assumed to have simply supported boundary conditions at two opposite edges. However, any boundary conditions can be prescribed at the other two edges. First, equations of motion at the overlap region are derived. Then, a Levy-type solution for displacements and stress resultants are used to formulate the problem in terms of a system of first order ordinary differential equations. A revised version of the Transfer Matrix Method together with the boundary and continuity conditions are used to obtain the frequency equation of the system. The natural frequencies and corresponding mode shapes are obtained for identical and dissimilar adherends with different boundary conditions. The effects of some parameters on the natural frequencies are studied and plotted.

High-frequency vibrations of circular and annular plates with the Mindlin plate theory

2020 ◽  
Vol 90 (5) ◽  
pp. 1025-1038
Author(s):  
Hui Chen ◽  
Rongxing Wu ◽  
Longtao Xie ◽  
Jianke Du ◽  
Lijun Yi ◽  
...  
Keyword(s):  
High Frequency ◽  
Plate Theory ◽  
Mindlin Plate ◽  
Annular Plates ◽  
Mindlin Plate Theory ◽  
High Frequency Vibrations

Vibrations of Thick Free Circular Plates, Exact Versus Approximate Solutions

1984 ◽  
Vol 51 (3) ◽  
pp. 581-585 ◽  
Author(s):  
J. R. Hutchinson
Keyword(s):  
Exact Solution ◽  
Natural Frequencies ◽  
Plate Theory ◽  
Approximate Solutions ◽  
Mindlin Plate ◽  
Circular Plates ◽  
Shear Coefficient ◽  
Elasticity Equations ◽  
Mindlin Plate Theory ◽  
Plate Solution

An exact solution for the natural frequencies of a thick free circular plate is compared to approximate solutions. The exact solution is a series solution of the general linear elasticity equations that converges to the correct natural frequencies. The approximate solutions to which this exact solution is compared are the Mindlin plate theory and a modification of a solution method proposed by Pickett. The comparisons clearly show the range of applicability of the approximate solutions as well as their accuracy. The choice of a best shear coefficient for use in the Mindlin plate theory is considered by evaluating the shear coefficient that would make the exact and modified Pickett method match the Mindlin plate solution.

A Cell-Based Smoothed Finite Element Method for Free Vibration Analysis of a Rotating Plate

2019 ◽  
Vol 16 (05) ◽  
pp. 1840003 ◽  
Author(s):  
C. F. Du ◽  
D. G. Zhang ◽  
G. R. Liu
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Plate Theory ◽  
Free Vibration Analysis ◽  
Mindlin Plate ◽  
Smoothed Finite Element Method ◽  
A Cell ◽  
Mindlin Plate Theory ◽  
Rotating Plate

A cell-based smoothed finite element method (CS-FEM) is formulated for nonlinear free vibration analysis of a plate attached to a rigid rotating hub. The first-order shear deformation theory which is known as Mindlin plate theory is used to model the plate. In the process of formulating the system stiffness matrix, the discrete shear gap (DSG) method is used to construct the strains to overcome the shear locking issue. The effectiveness of the CS-FEM is first demonstrated in some static cases and then extended for free vibration analysis of a rotating plate considering the nonlinear effects arising from the coupling of vibration of the flexible structure with the undergoing large rotational motions. The nonlinear coupling dynamic equations of the system are derived via employing Lagrange’s equations of the second kind. The effects of different parameters including thickness ratio, aspect ratio, hub radius ratio and rotation speed on dimensionless natural frequencies are investigated. The dimensionless natural frequencies of CS-FEM are compared with those other existing method including the FEM and the assumed modes method (AMM). It is found that the CS-FEM based on Mindlin plate theory provides more accurate and “softer” solution compared with those of other methods even if using coarse meshes. In addition, the frequency loci veering phenomena associated with the mode shape interaction are examined in detail.

Natural Frequencies of Mindlin Circular Plates

1980 ◽  
Vol 47 (3) ◽  
pp. 652-655 ◽  
Author(s):  
T. Irie ◽  
G. Yamada ◽  
S. Aomura
Keyword(s):  
Natural Frequencies ◽  
Plate Theory ◽  
Mindlin Plate ◽  
Circular Plates ◽  
Simply Supported ◽  
Mindlin Plate Theory ◽  
Clamped Edges

The natural frequencies of vibration based upon the Mindlin plate theory are tabulated for uniform circular plates with free, simply supported, and clamped edges for the first several tens modes.

Coupled Extensional and Flexural Motions of a Two-Layer Plate With Interface Slip

2018 ◽  
Vol 141 (2) ◽  
Author(s):  
Peng Li ◽  
Feng Jin ◽  
Weiqiu Chen ◽  
Jiashi Yang
Keyword(s):  
Plate Theory ◽  
Cutoff Frequency ◽  
Great Influence ◽  
Imperfect Interface ◽  
Mindlin Plate ◽  
Finite Plate ◽  
Mindlin Plate Theory ◽  
Interface Elasticity ◽  
Propagating Shear ◽  
Perfect Interface

The effect of imperfect interface on the coupled extensional and flexural motions in a two-layer elastic plate is investigated from views of theoretical analysis and numerical simulations. A set of full two-dimensional equations is obtained based on Mindlin plate theory and shear-slip model, which concerns the interface elasticity and tangential discontinuous displacements across the bonding imperfect interface. Some numerical examples are processed, including the propagation of straight-crested waves in an unbounded plate, the buckling of a finite plate, as well as the deflection of a finite plate under uniform load. It is revealed that the bending-evanescent wave in the composites with a perfect interface eventually cuts-on to a propagating shear-like wave with cutoff frequency when the two sublayers imperfectly bonded. The similar phenomenon has been verified once again for coupled face-shear and thickness-shear waves. It also has been pointed out that the interfacial parameter has a great influence on the performance of static buckling, in which the outcome can be reduced to classical buckling load of a simply supported plate when the interface is perfect.

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