scholarly journals INFLUENCE OF ICE COVER ON KELVIN AND POINCARE WAVES

2019 ◽  
Vol 47 (3) ◽  
pp. 72-79 ◽  
Author(s):  
S. V. Muzylev ◽  
T. B. Tsybaneva
Keyword(s):  
Boundary Conditions ◽  
Ice Cover ◽  
Thin Elastic Plate ◽  
Explicit Solutions ◽  
Normal Velocity ◽  
Unified Theory ◽  
Uniform Thickness ◽  
Dynamic Boundary Conditions ◽  
Poincare Waves ◽  
Theoretical Foundations

This work presents theoretical foundations of Kelvin and Poincare waves in the homogeneous ocean under an ice cover. The ice is considered as thin elastic plate of uniform thickness, with constant values of Young’s modulus, Poisson’s ratio, density, and compressive stress. The boundary conditions are such that the normal velocity at the bottom is zero, and at the undersurface of the ice the linearized kinematic and dynamic boundary conditions are satisfied. We present and analyze explicit solutions for the Kelvin and Poincare waves and the dispersion equations. The problem is examined in the context of a unified theory and without the hydrostatic assumption.

scholarly journals Linear evolution equations on the half-line with dynamic boundary conditions

2021 ◽  
pp. 1-33
Author(s):  
D. A. SMITH ◽  
W. Y. TOH
Keyword(s):  
Boundary Conditions ◽  
Heat Equation ◽  
Evolution Equations ◽  
Half Line ◽  
Robin Problem ◽  
Dynamic Boundary Conditions ◽  
Transform Method ◽  
Linear Evolution ◽  
Robin Condition ◽  
Linear Evolution Equations

The classical half-line Robin problem for the heat equation may be solved via a spatial Fourier transform method. In this work, we study the problem in which the static Robin condition $$bq(0,t) + {q_x}(0,t) = 0$$ is replaced with a dynamic Robin condition; $$b = b(t)$$ is allowed to vary in time. Applications include convective heating by a corrosive liquid. We present a solution representation and justify its validity, via an extension of the Fokas transform method. We show how to reduce the problem to a variable coefficient fractional linear ordinary differential equation for the Dirichlet boundary value. We implement the fractional Frobenius method to solve this equation and justify that the error in the approximate solution of the original problem converges appropriately. We also demonstrate an argument for existence and unicity of solutions to the original dynamic Robin problem for the heat equation. Finally, we extend these results to linear evolution equations of arbitrary spatial order on the half-line, with arbitrary linear dynamic boundary conditions.

The coupled Cahn–Hilliard/Allen–Cahn system with dynamic boundary conditions

2021 ◽  
pp. 1-27
Author(s):  
Ahmad Makki ◽  
Alain Miranville ◽  
Madalina Petcu
Keyword(s):  
Fractal Dimension ◽  
Boundary Conditions ◽  
Well Posedness ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Dynamic Boundary Conditions ◽  
Finite Dimensional ◽  
Dynamic Boundary ◽  
Long Time ◽  
Finite Fractal Dimension

In this article, we are interested in the study of the well-posedness as well as of the long time behavior, in terms of finite-dimensional attractors, of a coupled Allen–Cahn/Cahn–Hilliard system associated with dynamic boundary conditions. In particular, we prove the existence of the global attractor with finite fractal dimension.

scholarly journals An inverse problem of radiative potentials and initial temperatures in parabolic equations with dynamic boundary conditions

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
El Mustapha Ait Ben Hassi ◽  
Salah-Eddine Chorfi ◽  
Lahcen Maniar
Keyword(s):  
Inverse Problem ◽  
Boundary Conditions ◽  
Parabolic Equations ◽  
Stability Result ◽  
Stability Estimate ◽  
Lipschitz Stability ◽  
Dynamic Boundary Conditions ◽  
Logarithmic Convexity ◽  
Dynamic Boundary ◽  
Logarithmic Stability

Abstract We study an inverse problem involving the restoration of two radiative potentials, not necessarily smooth, simultaneously with initial temperatures in parabolic equations with dynamic boundary conditions. We prove a Lipschitz stability estimate for the relevant potentials using a recent Carleman estimate, and a logarithmic stability result for the initial temperatures by a logarithmic convexity method, based on observations in an arbitrary subdomain.

Updating Substructure Models With Dynamic Boundary Conditions

1995 ◽  
Author(s):  
Michael Link ◽  
Zheng Qian
Keyword(s):  
Boundary Conditions ◽  
Dynamic Stiffness ◽  
Design Parameters ◽  
Physical Parameters ◽  
Model Parameters ◽  
Dynamic Boundary Conditions ◽  
Main Structure ◽  
Modal Data ◽  
Residual Structure ◽  
Dynamic Boundary

Abstract In recent years procedures for updating analytical model parameters have been developed by minimizing differences between analytical and preferably experimental modal analysis results. Provided that the initial analysis model contains parameters capable of describing possible damage these techniques could also be used for damage detection. In this case the parameters are updated using test data before and after the damage. Looking at complex structures with hundreds of parameters one generally has to measure the modal data at many locations and try to reduce the number of unknown parameters by some kind of localization technique because the measurement information is generally not sufficient to identify all the parameters equally distributed all over the structure. Another way of reducing the number of parameters shall be presented here. This method is based on the idea of measuring only a part of the structure and replacing the residual structure by dynamic boundary conditions which describe the dynamic stiffness at the interfaces between the measured main structure and the remaining unmeasured residual structure. This approach has some advantage since testing could be concentrated on critical areas where structural modifications are expected either due to damage or due to intended design changes. The dynamic boundary conditions are expressed in Craig-Bampton (CB) format by transforming the mass and stiffness matrices of the unmeasured residual structure to the interface degrees of freedom (DOF) and to the modal DOFs of the residual structure fixed at the interface. The dynamic boundary stiffness concentrates all physical parameters of the residual structure in only a few parameters which are open for updating. In this approach damage or modelling errors within the unmeasured residual structure are taken into account only in a global sense whereas the measured main structure is parametrized locally as usual by factoring mass and stiffness submatrices defining the type and the location of the physical parameters to be identified. The procedure was applied to identify the design parameters of a beam type frame structure with bolted joints using experimental modal data.

scholarly journals Analysis of Monolithic and Sandwich Panels Subjected To Non-Uniform Thickness-Wise Boundary Conditions

2016 ◽  
Vol 5 (1) ◽  
pp. 232-249
Author(s):  
Riccardo Vescovini ◽  
Lorenzo Dozio
Keyword(s):  
Finite Element ◽  
Boundary Conditions ◽  
Sandwich Plate ◽  
Sandwich Plates ◽  
Vibration Frequencies ◽  
Thickness Direction ◽  
Finite Element Analyses ◽  
Uniform Thickness ◽  
Bending Problems ◽  
High Degree

Abstract The analysis of monolithic and sandwich plates is illustrated for those cases where the boundary conditions are not uniform along the thickness direction, and run at a given position along the thickness direction. For instance, a sandwich plate constrained at the bottom or top face can be considered. The approach relies upon a sublaminate formulation,which is applied here in the context of a Ritz-based approach. Due to the possibility of dividing the structure into smaller portions, viz. the sublaminates, the constraints can be applied at any given location, providing a high degree of flexibility in modeling the boundary conditions. Penalty functions and Lagrange multipliers are introduced for this scope. Results are presented for free-vibration and bending problems. The close matching with highly refined finite element analyses reveals the accuracy of the proposed formulation in determining the vibration frequencies, as well as the internal stress distribution. Reference results are provided for future benchmarking purposes.

scholarly journals Asymptotic Behavior of Solutions to Reaction-Diffusion Equations with Dynamic Boundary Conditions and Irregular Data

2018 ◽  
Vol 2018 ◽  
pp. 1-13
Author(s):  
Yonghong Duan ◽  
Chunlei Hu ◽  
Xiaojuan Chai
Keyword(s):  
Asymptotic Behavior ◽  
Boundary Conditions ◽  
Reaction Diffusion ◽  
Large Time Behavior ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Asymptotic Behavior Of Solutions ◽  
Time Behavior ◽  
Dynamic Boundary Conditions ◽  
Dynamic Boundary

This paper is concerned with the asymptotic behavior of solutions to reaction-diffusion equations with dynamic boundary conditions as well as L1-initial data and forcing terms. We first prove the existence and uniqueness of an entropy solution by smoothing approximations. Then we consider the large-time behavior of the solution. The existence of a global attractor for the solution semigroup is obtained in L1(Ω¯,dν). This extends the corresponding results in the literatures.

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