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result(s) for
"Elastic plates"
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On Equilibrium Problem for T-Shape Elastic Structure
This paper is concerned with an equilibrium problem for an elastic structure consisting of a plate and an elastic beam connected to each other at a given point. We consider two cases: In the first one, the elastic beam is connected to a rigid part of the elastic plate; in the second case, contact occurs between two elastic bodies. The elastic plate may contain a thin rigid delaminated inclusion. Neumann-type boundary conditions are considered at the external boundary of the plate. The existence of a solution to the considered problems is proven. A sufficient and necessary condition imposed onto the external forces for the solvability of the problems is found. Passages to the limit with respect to the rigidity parameter of the elastic beam are justified. For all problems, we analyze variational statements as well as differential ones.
Journal Article
Composite wave models for elastic plates
The long-term challenge of formulating an asymptotically motivated wave theory for elastic plates is addressed. Composite two-dimensional models merging the leading or higher-order parabolic equations for plate bending and the hyperbolic equation for the Rayleigh surface wave are constructed. Analysis of numerical examples shows that the proposed approach is robust not only at low- and high-frequency limits but also over the intermediate frequency range.
Journal Article
Analytical modeling for nonlinear vibration analysis of partially cracked thin magneto-electro-elastic plate coupled with fluid
A nonlinear analytical model for the transverse vibration of cracked magneto-electro-elastic (MEE) thin plate is presented using the classical plate theory (CPT). The MEE plate material selected is fiber-reinforced
BaTiO
3
–
CoFe
2
O
4
composite, which contains a partial crack at the center. The CPT and the simplified line spring model for crack terms are modified to accommodate the effect of electric and magnetic field rigidities. The analysis considers in-plane forces for the MEE plate, which makes the model nonlinear. The derived governing equation is solved by expressing the transverse displacement in terms of modal coordinates. An approximate solution for forced vibration of cracked MEE plate is also obtained using a perturbation technique. The effect of part-through crack, volume fraction of the composite on the vibration frequencies and structure response is investigated. The frequency response curves presented shows the phenomenon of hard or soft spring. Furthermore, the devised model is extended to the case of cracked MEE plate submerged in fluid. Velocity potential function and Bernoulli’s equation are used to incorporate the inertia effect of surrounding fluid. Both partially and totally submerged plate configurations are considered. The validation of the present results is carried out for intact submerged plate as to the best of the author’s knowledge the literature lacks in results for submerged-cracked plates. New results for cracked MEE plate show that the vibration characteristics are affected by volume fraction, crack length, fluid level and depth of immersion.
Journal Article
Analytical Study of the Head-On Collision Process between Hydroelastic Solitary Waves in the Presence of a Uniform Current
The present study discusses an analytical simulation of the head-on collision between a pair of hydroelastic solitary waves propagating in the opposite directions in the presence of a uniform current. An infinite thin elastic plate is floating on the surface of water. The mathematical modeling of the thin elastic plate is based on the Euler–Bernoulli beam model. The resulting kinematic and dynamic boundary conditions are highly nonlinear, which are solved analytically with the help of a singular perturbation method. The Poincaré–Lighthill–Kuo method is applied to obtain the solution of the nonlinear partial differential equations. The resulting solutions are presented separately for the left- and right-going waves. The behavior of all the emerging parameters are presented mathematically and discussed graphically for the phase shift, maximum run-up amplitude, distortion profile, wave speed, and solitary wave profile. It is found that the presence of a current strongly affects the wavelength and wave speed of both solitary waves. A graphical comparison with pure-gravity waves is also presented as a particular case of our study.
Journal Article
Impact of a porous structure in mitigating wave effect on a floating elastic plate in a two-layer fluid
The interaction of oblique waves with a porous structure placed in front of a floating elastic plate, which is an idealization of a very large floating structure in a two-layer fluid, is examined in the context of linear water wave theory. The porous structure, treated as a breakwater, is placed at a finite distance from the floating elastic plate to mitigate the hydrodynamic response of the elastic plate. To address the associated boundary value problem, matched eigenfunction expansion method is employed. The solution is computed, and the impact of the porous structure on the hydrodynamic coefficients associated with the floating plate such as deflection of the plate, bending moment, shear force, mooring line effect, wave scattering and trapping is graphically illustrated. The suitable physical properties for ideal plate characteristics are shown by a comparison of various edge conditions. It is recommended that an appropriate breakwater width maximizes wave reflection and minimizes transmission. Waveload on the plate gets reduced by appropriate parameter values connected with the porous breakwater. The findings of this study are expected to have an effect on how marine infrastructures are to be designed to mitigate wave force.
Journal Article
Three-Dimensional and Oblique Wave-Current Interaction with a Floating Elastic Plate Based on an Analytical Approach
An analytical hydroelastic model formulation in three-dimensional and oblique wave cases is developed to analyze the dynamic response of a horizontal, floating elastic plate subject to wave-current interaction under linearized small-amplitude wave theory. The floating elastic plate is moored to the bottom bed and free to the channel walls. Green’s function’s technique is utilised to determine the dispersion relation in 3D, and the series form of Green’s function in different water depths is derived in the oblique wave case. Further, the comparative analysis of phase and group velocities for different wave angles, between the present the existing models, is discussed. The derived dispersion relation is used in the solution by applying the geometrical symmetry velocity decomposition method. The present theoretical results of wave quantities are validated with the recently published and existing numerical hydroelastic model. A comparative analysis revealed a 1.7% difference between the present model and the existing hydroelastic models, and a 7.7% difference when compared to the model’s limiting cases. Several numerical results of the wave quantities, wave force, and vertical displacements are conducted to investigate the influence of current velocity on the hydroelastic response in three dimensions. It has been noted that the value of reflection coefficient diminishes for larger values of current velocity and the vertical displacement correspondingly becomes greater. This analysis will inform the design of elastic plate-based wave energy converters and breakwaters by clarifying how current loads affect the hydroelastic of a floating elastic plate with an oblique angle and three dimensions.
Journal Article
First-Order Shape Derivative of the Energy for Elastic Plates with Rigid Inclusions and Interfacial Cracks
Within the framework of Kirchhoff–Love plate theory, we analyze a variational model for elastic plates with rigid inclusions and interfacial cracks. The main feature of the model is a fully coupled nonpenetration condition that involves both the normal component of the longitudinal displacements and the normal derivative of the transverse deflection of the crack faces. Without making any artificial assumptions on the crack geometry and shape variation, we prove that the first-order shape derivative of the potential deformation energy is well defined and provide an explicit representation for it. The result is applied to derive the Griffith formula for the energy release rate associated with crack extension.
Journal Article
Axisymmetric Forced Vibration of Hydro-Elastic System Consisting of Pre-Strained Highly Elastic Plate, Compressible Inviscid Fluid and Rigid Wall
The present paper studies the axisymmetric forced vibrations of the hydro-elastic system consisting of the plate made of a highly elastic material with axisymmetric finite initial strains, barotropic inviscid compressible fluid, and rigid wall restricting the fluid flow. The motion of the plate is described using the equations and relations of the three-dimensional linearized theory of elastic waves in bodies with initial stresses. However, the flow of the fluid is described by the linearized Euler equations for the inviscid compressible fluids. Guz’s presentations for the general solution of the mentioned linearized equations are used to solve these equations for the corresponding boundary and compatibility conditions. The corresponding equations concerning these transforms are solved analytically using the Hankel integral transform. The originals of the sought values are found numerically by employing the authors’ calculation algorithm and PC programs. Numerical results on the frequency response of the interface pressure are presented and discussed. In particular, it is established that the initial radial stretching of the plate leads to the decrease in the interface pressure.
Journal Article