scholarly journals Mathematical modeling in problems about dynamics and stability of elastic elements of wing profiles

2021 ◽  
pp. 201-212
Author(s):  
Petr A. Velmisov ◽  
Andrey V. Ankilov
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Linear Models ◽  
Numerical Study ◽  
Deformable Body ◽  
Initial Boundary ◽  
Stability Conditions ◽  
Partial Differential ◽  
Aeroelastic System ◽  
Elastic Elements

The mathematical models describing the dynamics of elastic elements of wing structures and representing the initial-boundary value problems for systems of partial differential equations are proposed. The dynamics and stability of elastic elements of wings, flown around by a gas or liquid stream in a model of an incompressible medium, are investigated. To study the dynamics of elastic elements and a gas-liquid medium, both linear and nonlinear models of the mechanics of a solid deformable body and linear models of the mechanics of liquid and gas are used. On the basis of the constructed functionals for partial differential equations, the sufficient stability conditions are obtained in analytical form. The conditions impose restrictions on the parameters of mechanical systems. The obtained stability conditions are necessary for solving the problems of controlling the parameters of the aeroelastic system. On the basis of the Galerkin method, a numerical study of the dynamics of elastic elements was carried out, the reliability of which is confirmed by the obtained analytical results.

Systematic Construction of Neural Forms for Solving Partial Differential Equations Inside Rectangular Domains, Subject to Initial, Boundary and Interface Conditions

2020 ◽  
Vol 29 (05) ◽  
pp. 2050009
Author(s):  
Pola Lydia Lagari ◽  
Lefteri H. Tsoukalas ◽  
Salar Safarkhani ◽  
Isaac E. Lagaris
Keyword(s):  
Neural Network ◽  
Heat Conduction ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Systematic Approach ◽  
Thermal Contact ◽  
Initial Boundary ◽  
Spatial Domain ◽  
Interface Conditions ◽  
Partial Differential

A systematic approach is developed for constructing proper trial solutions to Partial Differential Equations (PDEs) of up to second order, using neural forms that satisfy prescribed initial, boundary and interface conditions. The spatial domain considered is of the rectangular hyper-box type. On each face either Dirichlet or Neumann conditions may apply. Robin conditions may be accommodated as well. Interface conditions that induce discontinuities, have not been treated to date in the relevant neural network literature. As an illustration a common problem of heat conduction through a system of two rods in thermal contact is considered.

scholarly journals Exact, approximate solutions and error bounds for coupled implicit systems of partial differential equations

1992 ◽  
Vol 15 (4) ◽  
pp. 663-672
Author(s):  
Lucas Jódar
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Initial Boundary ◽  
Approximate Solutions ◽  
Value Systems ◽  
Finite Domain ◽  
Partial Differential ◽  
Implicit Systems ◽  
Initial Boundary Value ◽  
The Given

In this paper coupled implicit initial-boundary value systems of second order partial differential equations are considered. Given a finite domain and an admissible errorϵan analytic approximate solution whose error is upper bounded byϵin the given domain is constructed in terms of the data.

scholarly journals Role of Slip Velocity in a Magneto-Micropolar Fluid Flow from a Radiative Surface with Variable Permeability: A Numerical Study

2017 ◽  
Vol 22 (3) ◽  
pp. 637-651
Author(s):  
B.K. Sharma ◽  
V. Tailor ◽  
M. Goyal
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Micropolar Fluid ◽  
Numerical Study ◽  
Slip Flow ◽  
Skin Friction Coefficient ◽  
Convection Flow ◽  
Partial Differential ◽  
Linear Partial Differential Equations ◽  
Variable Permeability

AbstractAn analysis is presented to describe the hydromagnetic mixed convection flow of an electrically conducting micropolar fluid past a vertical plate through a porous medium with radiation and slip flow regime. A uniform magnetic field has been considered in the study which absorbs the micropolar fluid with a varying suction velocity and acts perpendicular to the porous surface of the above plate. The governing non-linear partial differential equations have been transformed into linear partial differential equations, which are solved numerically by applying the explicit finite difference method. The numerical results are presented graphically in the form of velocity, micro-rotation, concentration and temperature profiles, the skin-friction coefficient, the couple stress coefficient, the rate of heat and mass transfers at the wall for different material parameters.

scholarly journals Method of functional parametrization for solving a semi-periodic initial problem for fourth-order partial differential equations

2020 ◽  
Vol 100 (4) ◽  
pp. 5-16
Author(s):  
A.T. Assanova ◽  
◽  
Zh.S. Tokmurzin ◽  
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Fourth Order ◽  
Periodic Problem ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Hyperbolic Type ◽  
Order System ◽  
Partial Differential ◽  
Initial Boundary Value

A semi-periodic initial boundary-value problem for a fourth-order system of partial differential equations is considered. Using the method of functional parametrization, an additional parameter is carried out and the studied problem is reduced to the equivalent semi-periodic problem for a system of integro-differential equations of hyperbolic type second order with functional parameters and integral relations. An interrelation between the semi-periodic problem for the system of integro-differential equations of hyperbolic type and a family of Cauchy problems for a system of ordinary differential equations is established. Algorithms for finding of solutions to an equivalent problem are constructed and their convergence is proved. Sufficient conditions of a unique solvability to the semi-periodic initial boundary value problem for the fourth-order system of partial differential equations are obtained.

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