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.

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.

Transverse Vibrations of Beams, Exact Versus Approximate Solutions

1981 ◽  
Vol 48 (4) ◽  
pp. 923-928 ◽  
Author(s):  
J. R. Hutchinson
Keyword(s):  
Exact Solution ◽  
Timoshenko Beam ◽  
Natural Frequencies ◽  
Circular Cross Section ◽  
Approximate Solutions ◽  
Approximate Methods ◽  
Transverse Vibrations ◽  
Elasticity Equations ◽  
Beam Approximation ◽  
Free Beam

An exact solution for the natural frequencies of vibration of a finite length free-free beam with a circular cross section is found and compared to approximate solutions. This exact solution is a series solution of the general linear elasticity equations which converges to correct natural frequencies. Correctness of the frequencies is established by comparison to previous experiments. Comparison of the exact to approximate solutions is made with the Pochhammer-Chree approximation, the Timoshenko beam approximation and the Pickett approximation. The comparisons clearly show the range of applicability of the approximate methods as well as their accuracy. The correct shear coefficient for use in the Timoshenko beam approximation is investigated and conclusions which differ with, yet at the same time complement, those of previous researchers are reached.

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.

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.

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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