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Nonlinear Wave Dynamics of Materials and Structures

Part of the Advanced Structured Materials Book Series (volume 122)

Editors: Altenbach, Holm; Eremeyev, Victor A.; Pavlov, Igor S.; Porubov, Alexey V.

DOI: 10.1007/978-3-030-38708-2

ISBN: 978-3-030-38707-5

Publisher: Springer International Publishing - Springer Journals

Apr 23, 2020

1 - 10 of 27 Chapters

LitStream

Chapter 1Elimination of the Flutter Phenomenon in a Forced and Self-excited Nonlinear Beam Using an Improved Saturation Controller Algorithm

Abdelhafez, Hassan M.; Nasedkin, Andrey V.; Nassar, Mohamed E.

Pages: 1 –23

[Flutter is a dynamic instability of an elastic structure subjected to fluid flow. Flutter phenomenon of the beam cannot occur unless bending and twisting vibrations occur simultaneously. This paper intends to eliminate the flutter phenomenon by suppressing the bending mode vibrations. The...
LitStream

Chapter 2Use of the Modified Method of Parameter Continuation in Nonlinear Dynamics

Andrianov, Igor V.; Olevskyi, Viktor I.; Olevska, Yuliia B.

Pages: 25 –55

[The modified method of parameter continuation (MMPC) is an asymptotic technique for estimating the eigenfrequencies and eigenmodes of nonlinear oscillations of beams, plates and shells with complicated boundary conditions. Unlike the Bolotin method, which is usually used for such estimations,...
LitStream

Chapter 3A Mathematically Consistent Vector-Matrix Representation of Generalized Hooke’s Law for Shear-Rigid Plates

Aßmus, Marcus; Altenbach, Holm

Pages: 57 –67

[The present contribution is dedicated to the mathematical consistent expression of constitutive relations needed for efficient computational treatment of thin-walled structural elements within a geometrically and physically linear framework, as usually used by engineers. Hereby, the direct...
LitStream

Chapter 4Mathematical Simulation of the Plate–Beam Interaction Affected by Colored Noise

Bazhenov, Valentin G.; Yakovleva, Tatyana V.; Krysko, Vadim A.

Pages: 69 –76

[The article presents a mathematical simulation of interaction between a plate and a beam locally supporting the plate in its center. The system is exposed to an external transverse load and external additive colored noise (pink, red, white). The structure is located in a steady temperature...
LitStream

Chapter 5Dynamic Homogenization of a Chain with Bistable Springs. Statistical Approach

Blake, Charlotte; Cherkaev, Andrej

Pages: 77 –96

[We study the problem of dynamic homogenization, replacing a high-frequency vibrating mass-spring chain with a single nonlinear spring and determine its time-averaged elastic characteristics. A mass-spring chain of n equal non-monotonic bistable springs that join equal small masses is considered....
LitStream

Chapter 6Analysis of Resistance to Penetration of a Cone into Frozen Sand Based on Data from Inverted Experiments

Bragov, Anatoliy; Balandin, Vladimir V.; Balandin, Vladimir Vl.; Igumnov, Leonid; Kotov, Vasiliy

Pages: 97 –105

[The laws of contact interaction between rigid and deformable strikers with dry and water-saturated soils in a wide range of temperatures were studied experimentally. Studies of the processes of impact and penetration of a steel conical striker into frozen sandy soil were carried out on the basis...
LitStream

Chapter 7Some Solutions of Dynamic and Static Nonlinear Nonautonomous Klein-Fock-Gordon Equation

Bulygin, Anatolii N.; Pavlov, Yuri V.

Pages: 107 –120

[Methods of constructing exact analytical solutions of dynamic and static nonlinear nonautonomous Klein-Fock-Gordon (NKFG) equations are developed. Solutions are given in the form of a composite function \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym}...
LitStream

Chapter 8A Comparison Between Heterogeneous and Homogeneous Layers for Nonlinear Bright Solitary SH Waves in Terms of Heterogeneous Effect

Demirkuş, Dilek

Pages: 121 –143

[In this chapter, we compare the nonlinear bright solitary shear horizontal (SH) waves in heterogeneous and homogeneous layers in terms of the heterogeneous effect. Each layer has finite thickness overlying a rigid substratum. We assume that the layers are made up of isotropic, hyper-elastic and...
LitStream

Chapter 9On Surface Kinetic Constitutive Relations

Eremeyev, Victor A.; Lebedev, Leonid P.

Pages: 145 –152

[In the framework of the strain gradient surface elasticity we discuss a consistent form of surface kinetic energy. This kinetic constitutive equation completes the statement of initial–boundary value problems. The proposed surface kinetic energy density is the most general function consistent...
LitStream

Chapter 10Reduced Linear Viscoelastic Isotropic Cosserat Medium with Translational Viscosity: A Double Negative Acoustic Metamaterial

Grekova, Elena F.; Piatysheva, Aleksandra P.

Pages: 153 –167

[We investigate here the influence of translational viscosity on the plane shear-rotational wave propagation in the linear isotropic reduced Cosserat medium. In such a medium, body points possess independent rotational and translational degrees of freedom, but the medium does not resist to the...

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