Wave Interaction With Floating Elastic Plate Based on the Timoshenko–Mindlin Plate Theory

2019 ◽  
Vol 142 (1) ◽  
Author(s):  
K. M. Praveen ◽  
D. Karmakar ◽  
C. Guedes Soares
Keyword(s):  
Dispersion Relation ◽  
Elastic Plate ◽  
Plate Theory ◽  
Wave Interaction ◽  
Bending Moment ◽  
Expansion Method ◽  
Wave Theory ◽  
Mindlin Plate ◽  
Floating Elastic Plate ◽  
Mindlin Plate Theory

In the present study, the wave interaction with the very large floating structures (VLFSs) is analyzed considering the small amplitude wave theory. The VLFS is modeled as a 2D floating elastic plate with infinite width based on Timoshenko–Mindlin plate theory. The eigenfunction expansion method along with mode-coupling relation is used to analyze the hydroelastic behavior of VLFSs in finite water depth. The contour plots for the plate covered dispersion relation are presented to illustrate the complexity in the roots of the dispersion relation. The wave scattering behavior in the form of reflection and transmission coefficients are studied in detail. The hydroelastic performance of the elastic plate interacting with the ocean wave is analyzed for deflection, strain, bending moment, and shear force along the elastic plate. Further, the study is extended for shallow water approximation, and the results are compared for both Timoshenko–Mindlin plate theory and Kirchhoff’s plate theory. The significance and importance of rotary inertia and shear deformation in analyzing the hydroelastic characteristics of VLFSs are presented. The study will be helpful for scientists and engineers in the design and analysis of the VLFSs.

The Bending Singularity at the Apex of V-Notch in an Anisotropic Thick Plate

2017 ◽  
Vol 735 ◽  
pp. 95-99
Author(s):  
Chung De Chen
Keyword(s):  
Eigenfunction Expansion ◽  
Thick Plate ◽  
Plate Theory ◽  
Expansion Method ◽  
Numerical Results ◽  
The Other ◽  
Mindlin Plate ◽  
Eigenfunction Expansion Method ◽  
Singularity Order ◽  
Mindlin Plate Theory

In this paper, the bending singularity at the apex of V-notch in an anisotropic thick plate is investigated. The Stroh-like formalism is used to model the anisotropy of the material. Based on the Ressiner-Mindlin plate theory and the eigenfunction expansion method, the characteristic equation for bending singularity order is derived and the order can be determined numerically. The numerical results show that the singularity orders strongly depend on the plate angle a. In addition, the singularity orders also depend on the principal orientation of the anisotropic material. The singularity orders for the case of are stronger than for that of. In the case of, to reduce the anisotropy is helpful to release the singularity at the notch tip. For the other case of, it is preferable to increase the anisotropy to reduce the singularity. The disappearance conditions of the bending singularity can be found based on the numerical results.

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.

scholarly journals Wave interaction with Floating platform of different shapes and supports using BEM approach

2017 ◽  
Vol 14 (2) ◽  
pp. 115-133
Author(s):  
Anoop I. Shirkol ◽  
Nasar Thuvanismail
Keyword(s):  
Numerical Model ◽  
Elastic Plate ◽  
Wave Interaction ◽  
Wave Force ◽  
Ocean Waves ◽  
Wave Forces ◽  
Thin Elastic Plate ◽  
Floating Platform ◽  
Floating Elastic Plate ◽  
Different Shapes

Wave interaction with a floating thin elastic plate which can be used as floating platform is analyzed using Boundary Element Method (BEM) for different shapes such as rectangular, circular and triangular. Different support conditions are considered and the performance of the floating platform under the action of ocean waves is explored. The study is performed under the assumption of linearized water wave theory and the floating elastic plate is modelled based on the Euler-Bernoulli beam theory. Using Galerkin’s approach, a numerical model has been developed and the hydrodynamic loading on the floating elastic plate of shallow draft (thickness) is investigated. The wave forces are generated by the numerical model for the analysis of the floating plate. The resulting bending moment and optimal deflection due to encountering wave force is analysed. The present study will be helpful in design and analysis of the large floating platform in ocean waves.

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.

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