scholarly journals An Analytical Method for Evaluating the Dynamic Response of Plates Subjected to Underwater Shock Employing Mindlin Plate Theory and Laplace Transforms

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Zhenyu Wang ◽  
Xu Liang ◽  
Guohua Liu
Keyword(s):  
Dynamic Response ◽  
Response Time ◽  
Analytical Method ◽  
Extreme Values ◽  
Plate Theory ◽  
Underwater Explosion ◽  
Mindlin Plate ◽  
Time Histories ◽  
Mindlin Plate Theory ◽  
Benchmark Solutions

It is often in the interest of a designer to know the transient state of stress in a plate subjected to an underwater explosion. In this paper, an analytical method based on Taylor’s fluid-solid interaction (FSI) model, Mindlin plate theory, Laplace transform, and its inversion is proposed to examine the elastic dynamic response of a plate subjected to an underwater explosion. This analytical method includes shear deformation, the moments and membrane stress in the plate, and the FSI effect and considers a full profile of possibilities. The results of the response-time histories and the response distribution on the plate in terms of displacements and stresses from the analytical method are compared with finite element analysis (FEA) to validate this method, and the comparison indicates good agreement. Comparison of the acceleration at the center of an air-backed plate between the analytical method and the experiment from relevant literature, shows good agreements, and the analytical method and its FSI model are validated. The influence of the FSI is investigated in detail. All extreme values of the response-time histories decrease as the thickness increases for the non-FSI case. The results can be used as benchmark solutions in further research.

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
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