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

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 Refinement of Mindlin Plate Theory Using Simultaneous Rotary Inertia and Shear Correction Factors

2018 ◽  
Vol 140 (3) ◽  
Author(s):  
Andrew N. Norris
Keyword(s):  
High Frequency ◽  
Plate Theory ◽  
Low Frequency ◽  
Rotary Inertia ◽  
Mindlin Plate ◽  
Flexural Wave ◽  
Correction Factors ◽  
Flexural Mode ◽  
Mode Dispersion ◽  
Mindlin Plate Theory

We revisit Mindlin's theory for flexural dynamics of plates using two correction factors, one for shear and one for rotary inertia. Mindlin himself derived and considered his equations with both correction factors, but never with the two simultaneously. Here, we derive optimal values of both factors by matching the Mindlin frequency–wavenumber branches with the exact Rayleigh–Lamb dispersion relations. The thickness shear resonance frequency is obtained if the factors are proportional but otherwise arbitrary. This degree-of-freedom allows matching of the main flexural mode dispersion with the exact Lamb wave at either low or high frequency by choosing the shear correction factor as a function of Poisson's ratio. At high frequency, the shear factor takes the value found by Mindlin, while at low frequency, it assumes a new explicit form, which is recommended for flexural wave modeling.

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.

Sharp Corner Functions for Mindlin Plates

2005 ◽  
Vol 72 (1) ◽  
pp. 1-9 ◽  
Author(s):  
O. G. McGee ◽  
J. W. Kim ◽  
A. W. Leissa
Keyword(s):  
Plate Theory ◽  
Thin Plates ◽  
Mode Shapes ◽  
Mindlin Plate ◽  
Transverse Displacement ◽  
Thick Plates ◽  
Thin Plate Theory ◽  
Mindlin Plate Theory ◽  
Moderately Thick Plates ◽  
Sharp Corners

Transverse displacement and rotation eigenfunctions for the bending of moderately thick plates are derived for the Mindlin plate theory so as to satisfy exactly the differential equations of equilibrium and the boundary conditions along two intersecting straight edges. These eigenfunctions are in some ways similar to those derived by Max Williams for thin plates a half century ago. The eigenfunctions are called “corner functions,” for they represent the state of stress currently in sharp corners, demonstrating the singularities that arise there for larger angles. The corner functions, together with others, may be used with energy approaches to obtain accurate results for global behavior of moderately thick plates, such as static deflections, free vibration frequencies, buckling loads, and mode shapes. Comparisons of Mindlin corner functions with those of thin-plate theory are made in this work, and remarkable differences are found.

Nonlinear vibration of piezoelectric nanoplates using nonlocal Mindlin plate theory

2016 ◽  
Vol 25 (15-16) ◽  
pp. 1252-1264 ◽  
Author(s):  
Chen Liu ◽  
Liao-Liang Ke ◽  
Jie Yang ◽  
Sritawat Kitipornchai ◽  
Yue-Sheng Wang
Keyword(s):  
Nonlinear Vibration ◽  
Plate Theory ◽  
Mindlin Plate ◽  
Mindlin Plate Theory
Sign in / Sign up

Export Citation Format

Share Document