Flutter Analysis of Viscoelastic Sandwich Plate in Supersonic Flow

2005 ◽  
Author(s):  
B. A. Khudayarov
Keyword(s):  
Supersonic Flow ◽  
Differential Equations ◽  
Numerical Method ◽  
Quadrature Formula ◽  
Sandwich Plate ◽  
Galerkin Methods ◽  
Basic Direction ◽  
Partial Derivatives ◽  
Plate Flutter ◽  
Flutter Analysis

In this work is investigated the flutter of viscoelastic sandwich plate streamlined by gas current. The basic direction of work is consisted in taking into account of viscous-elastic material’s properties at supersonic speeds. The vibration equations relatively of deflection are described by Integro-Differential Equations (IDE) in partial derivatives. By Bubnov-Galerkin methods reduced the problems to investigation of system of ordinary IDE. The IDE are solved by numerical method, which based on using of quadrature formula. Critical speeds for sandwich plate flutter are defined.

scholarly journals INVESTIGATION OF THE NONLINEAR FLUTTER OF VISCOELASTIC PLATES IN A SUPERSONIC FLOW

2014 ◽  
pp. 42-45
Author(s):  
Bakhtiyar Khudayarov
Keyword(s):  
Differential Equation ◽  
Supersonic Flow ◽  
Differential Equations ◽  
Integration Method ◽  
Basic Direction ◽  
Partial Derivatives ◽  
Integro Differential Equation ◽  
Plate Flutter ◽  
Nonlinear Flutter ◽  
Nonlinear Viscoelastic

In this paper the flutter of nonlinear viscoelastic plates in a supersonic flow is investigated. The basic direction of work is consisted in taking into account of viscoelastic material’s properties at supersonic speeds. Quasi-steady aerodynamic panel loadings are determined using piston theory. The vibration equations relatively of deflection are described by Integrо-differential equations in partial derivatives. The plate nonlinear partial integro-differential equation is transformed info a set of nonlinear ordinary IDE through a Bubnov-Galerkin’s approach. The resulting system of IDE is solved through the Badalov-Eshmatov integration method. Critical speeds for plate flutter are defined.

scholarly journals MATHEMATICAL MODELLING OF PROBLEM ON NON-LINEAR FLUTTER OF VISCO-ELASTIC SHELLS

2014 ◽  
pp. 94-98
Author(s):  
Bakhtiyar Khudayarov
Keyword(s):  
Cylindrical Shell ◽  
Differential Equations ◽  
Mathematical Modelling ◽  
Numerical Solution ◽  
Viscoelastic Property ◽  
Critical Speed ◽  
Galerkin Methods ◽  
Basic Direction ◽  
Viscoelastic Cylindrical Shell ◽  
Current Value

In this work is investigated the flutter of viscoelastic cylindrical shell streamlined by gas current. The basic direction of work is consisted in taking into account of viscoelastic material’s properties at supersonic speeds. The vibration equations relatively of deflection are described by Integra-differential equations in partial derivatives. By Bubnov-Galerkin methods reduced the problems to investigation of system of ordinary Integro-Differential Equations (IDE). The IDE are solved by numerical method, which based on using of quadrature formula. The algorithm of the numerical solution on the basis of the method was described. Critical speeds for cylindrical shell flutter are defined. The influence of the viscoelastic property of the material, geometrical and aerodynamically non-linearity to the current value of critical speed and amplitude-frequency characteristics of the cylindrical shells was analyzed.

The Nonlinear Dynamical Analysis of a Sandwich Plate with In-Plane Loading in Supersonic Flow

2016 ◽  
Vol 26 (09) ◽  
pp. 1650144 ◽  
Author(s):  
Xiao-Dong Yang ◽  
Wei Zhang ◽  
Hong-Bo Wang ◽  
Ming-Hui Yao
Keyword(s):  
Supersonic Flow ◽  
Differential Equations ◽  
Sandwich Plate ◽  
Multiple Scales ◽  
Shear Deformation Theory ◽  
Dynamical Analysis ◽  
Nonlinear Dynamical ◽  
Periodic Loading ◽  
Fluctuation Amplitude ◽  
Nonlinear Dynamical Analysis

Nonlinear dynamics of a sandwich plate with viscoelastic soft core in supersonic flow are investigated by considering the in-plane periodic loading. Using Reddy’s third-order shear deformation theory and von Karman’s nonlinearity, the governing partial differential equations are derived by Hamilton’s principle and then truncated into a set of ordinary differential equations by Galerkin method. The critical speed for flutter is discussed by employing the linear theory. Further, the method of multiple scales is used in the nonlinear dynamical analysis of the truncated system. The Poincaré map is numerically calculated to identify dynamical behaviors. The bifurcation diagrams are presented for varying the dimensionless in-plane loading fluctuation amplitude and the Mach number related dimensionless parameter while other parameters are unchanged.

Steady-state modelling method for matrix-reactance frequency converter with boost topology

2011 ◽  
Vol 60 (2) ◽  
pp. 137-148
Author(s):  
Igor Korotyeyev ◽  
Beata Zięba
Keyword(s):  
Fourier Series ◽  
Steady State ◽  
Differential Equations ◽  
Numerical Method ◽  
Frequency Converter ◽  
Double Fourier Series ◽  
Galerkin’S Method ◽  
Galerkin's Method ◽  
Modelling Method ◽  
Three Phase

Steady-state modelling method for matrix-reactance frequency converter with boost topologyThis paper presents a method intended for calculation of steady-state processes in AC/AC three-phase converters that are described by nonstationary periodical differential equations. The method is based on the extension of nonstationary differential equations and the use of Galerkin's method. The results of calculations are presented in the form of a double Fourier series. As an example, a three-phase matrix-reactance frequency converter (MRFC) with boost topology is considered and the results of computation are compared with a numerical method.

scholarly journals Slice holomorphic solutions of some directional differential equations with bounded L-index in the same direction

2019 ◽  
Vol 52 (1) ◽  
pp. 482-489 ◽  
Author(s):  
Andriy Bandura ◽  
Oleh Skaskiv ◽  
Liana Smolovyk
Keyword(s):  
Partial Differential Equations ◽  
Continuous Function ◽  
Differential Equations ◽  
Sufficient Conditions ◽  
Holomorphic Functions ◽  
Positive Continuous Function ◽  
Partial Differential ◽  
Partial Derivatives ◽  
Fixed Direction

AbstractIn the paper we investigate slice holomorphic functions F : ℂn → ℂ having bounded L-index in a direction, i.e. these functions are entire on every slice {z0 + tb : t ∈ℂ} for an arbitrary z0 ∈ℂn and for the fixed direction b ∈ℂn \ {0}, and (∃m0 ∈ ℤ+) (∀m ∈ ℤ+) (∀z ∈ ℂn) the following inequality holds{{\left| {\partial _{\bf{b}}^mF(z)} \right|} \over {m!{L^m}(z)}} \le \mathop {\max }\limits_{0 \le k \le {m_0}} {{\left| {\partial _{\bf{b}}^kF(z)} \right|} \over {k!{L^k}(z)}},where L : ℂn → ℝ+ is a positive continuous function, {\partial _{\bf{b}}}F(z) = {d \over {dt}}F\left( {z + t{\bf{b}}} \right){|_{t = 0}},\partial _{\bf{b}}^pF = {\partial _{\bf{b}}}\left( {\partial _{\bf{b}}^{p - 1}F} \right)for p ≥ 2. Also, we consider index boundedness in the direction of slice holomorphic solutions of some partial differential equations with partial derivatives in the same direction. There are established sufficient conditions providing the boundedness of L-index in the same direction for every slie holomorphic solutions of these equations.

An implicit multistep numerical method for real-time simulation of stiff systems

SIMULATION ◽  
2021 ◽  
pp. 003754972110216
Author(s):  
Zhang Lei ◽  
Li Jie ◽  
Wang Menglu ◽  
Liu Mengya
Keyword(s):  
Differential Equations ◽  
Numerical Method ◽  
Real Time ◽  
Physical System ◽  
Physical Models ◽  
Stiff Systems ◽  
Real Time Simulation ◽  
Stiff Ordinary Differential Equations ◽  
Root Finding ◽  
Time Simulation

Simulating a physical system in real-time is widely used in equipment design, test, and validation. Though an implicit multistep numerical method excels at solving physical models that are usually composed of stiff ordinary differential equations, it is not suitable for real-time simulation because of state discontinuity and massive iterations for root finding. Thus, a method based on the backward differential formula is presented. It divides the main fixed step of real-time simulation into limited minor steps according to computing cost and accuracy demand. By analyzing and testing its capability, this method shows advantage and efficiency in real-time simulation, especially when the system contains stiff equations. A simulation application will have more flexibility while using this method.

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