Vadim Anatol evich Krys ko's Books

This monograph is devoted to nonlinear dynamics of thin plates and shells with thermosensitive excitation. Because of the variety of sizes and types of mathematical models in current use, there is no prospect of solving them analytically. However, the book emphasizes a rigorous mathematical treatment of the obtained differential equations, since it helps efficiently in further developing of various suitable numerical algorithms to solve the stated problems.

This volume introduces new approaches to modeling strongly nonlinear behaviour of structural mechanical units: beams, plates and shells or composite systems. The text draws on bifurcation theory and chaos, emphasizing control and stability of objects and systems.

This monograph is devoted to recent advances in nonlinear dynamics of continuous elastic systems. A major part of the book is dedicated to the analysis of non-homogeneous continua, e.g. plates and shells characterized by sudden changes in their thickness, possessing holes in their bodies or/and edges, made from different materials with diverse dynamical characteristics and complicated boundary conditions. New theoretical and numerical approaches for analyzing the dynamics of such continua are presented, such as the method of added masses and the method of proper orthogonal decomposition. The presented hybrid approach leads to results that cannot be obtained by other standard theories in the field. The demonstrated methods are illustrated by numerous examples of application.

From the reviews: "A unique feature of this book is the nice blend of engineering vividness and mathematical rigour. [...] The authors are to be congratulated for their valuable contribution to the literature in the area of theoretical thermoelasticity and vibration of plates." Journal of Sound and Vibration

Among the theoretical methods for solving many problems of applied mathematics, physics, and technology, asymptotic methods often provide results that lead to obtaining more effective algorithms of numerical evaluation. Presenting the mathematical methods of perturbation theory, Introduction to Asymptotic Methods reviews the most important m

Book's by Vadim Anatol evich Krys ko

Thermo-Dynamics of Plates and Shells

Thermo-Dynamics of Plates and Shells

Chaos in Structural Mechanics

Chaos in Structural Mechanics

Nonlinear Dynamics of Continuous Elastic Systems

Nonlinear Dynamics of Continuous Elastic Systems

Nonclassical Thermoelastic Problems in Nonlinear Dynamics of Shells

Nonclassical Thermoelastic Problems in Nonlinear Dynamics of Shells

Introduction to Asymptotic Methods

Introduction to Asymptotic Methods

Nonlinear Dynamics of Continuous Elastic Systems

Nonlinear Dynamics of Continuous Elastic Systems

Thermo-Dynamics of Plates and Shells

Thermo-Dynamics of Plates and Shells

Chaos in Structural Mechanics

Chaos in Structural Mechanics

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