| Description |
1 online resource (615 pages) |
| Series |
Scientific Computation |
|
Scientific computation.
|
| Contents |
Intro -- Preface -- Contents -- 1 Introduction -- 2 Coupled Thermoelasticity and Transonic Gas Flow -- 2.1 Coupled Linear Thermoelasticity of Shallow Shells -- 2.1.1 Fundamental Assumptions -- 2.1.2 Differential Equations -- 2.1.3 Boundary and Initial Conditions -- 2.1.4 An Abstract Coupled Problem -- 2.1.5 Existence and Uniqueness of Solutions of Thermoelasticity Problems -- 2.2 Cylindrical Panel Within Transonic Gas Flow -- 2.2.1 Statement and Solution of the Problem -- 2.2.1.1 Equations of Motion and Boundary Conditions of a Panel -- 2.2.1.2 Equations of Transonic Ideal-Gas Motion |
|
2.2.1.3 Equations and Boundary Conditions of Panel-Flow Interaction -- 2.2.1.4 Analysis of Panel Oscillations -- 2.2.1.5 Method of Solution of the Problem -- 2.2.1.6 Interaction Between a Flow and a Panel -- 2.2.2 Stable Vibrating Panel Within a Transonic Flow -- 2.2.2.1 Shock Wave Motion -- 2.2.2.2 Interaction of a Flow and a Panel -- 2.2.3 Stability Loss of Panel Within Transonic Flow -- 2.2.3.1 Stability Criteria -- 2.2.3.2 Analysis of Stress-Strain State -- 3 Estimation of the Errors of the Bubnov-Galerkin Method -- 3.1 An Abstract Coupled Problem |
|
3.2 Coupled Thermoelastic Problem Within the Kirchhoff-Love Model -- 3.3 Case of a Simply Supported Plate Within the Kirchhoff Model -- 3.4 Coupled Problem of Thermoelasticity Within a Timoshenko-Type Model -- 4 Numerical Investigations of the Errors of the Bubnov-Galerkin Method -- 4.1 Vibration of a Transversely Loaded Plate -- 4.2 Vibration of a Plate with an Imperfection in the Form of a Deflection -- 4.3 Vibration of a Plate with a Given Variable Deflection Change -- 5 Coupled Nonlinear Thermoelastic Problems -- 5.1 Fundamental Relations and Assumptions -- 5.2 Differential Equations |
|
5.3 Boundary and Initial Conditions -- 5.4 On the Existence and Uniqueness of a Solution and on the Convergence of the Bubnov-Galerkin Method -- 6 Theory with Physical Nonlinearities and Coupling -- 6.1 Fundamental Assumptions and Relations -- 6.2 Variational Equations of Physically Nonlinear Coupled Problems -- 6.3 Equations in Terms of Displacements -- 7 Nonlinear Problems of Hybrid-Form Equations -- 7.1 Method of Solution for Nonlinear Coupled Problems -- 7.2 Relaxation Method -- 7.3 Numerical Investigations and Reliability of the Results Obtained |
|
7.4 Vibration of Isolated Shell Subjected to Impulse -- 7.5 Dynamic Stability of Shells Under Thermal Shock -- 7.6 Influence of Coupling and Rotational Inertia on Stability -- 7.7 Numerical Tests -- 7.8 Influence of Damping and Excitation Amplitude A -- 7.9 Spatial-Temporal Symmetric Chaos -- 7.10 Dissipative Nonsymmetric Oscillations -- 7.11 Solitary Waves -- 8 Dynamics of Thin Elasto-Plastic Shells -- 8.1 Fundamental Relations -- 8.2 Method of Solution -- 8.3 Oscillations and Stability of Elasto-Plastic Shells -- 9 Mathematical Model of Cylindrical/Spherical Shell Vibrations |
| Summary |
Adding seven new chapters integrating modern approaches to dynamical systems theory, this revised second edition describes numerical approaches to the nonlinear theory of beams, plates and shells, with an emphasis to the elastic and thermoelastic features. The added chapters discuss in particular how to understand, model, and obtain reliable results while detecting and analysing chaotic dynamics exhibited by thin structural members. The authors attempt to address the large impact of new directions of nonlinear dynamical phenomena in the context of the overall state-of-the art presented in the first book edition. They also present new perspectives of the unsolved problems of thin structural members. The authors made every effort to keep the text intelligible for both practitioners and graduate students, although they offer a rigorous treatment of both purely mathematical and numerical approaches presented so that the reader can understand, analyse and track the nonlinear dynamics of spatial systems (shells) with thermomechanical behaviours |
| Bibliography |
Includes bibliographical references |
| Notes |
9.1 Fundamental Relations and Assumptions |
|
Print version record |
| Subject |
Structural dynamics -- Mathematics
|
|
Maths for scientists.
|
|
Dynamics & vibration.
|
|
Mathematical physics.
|
|
Computers -- Computer Science.
|
|
Technology & Engineering -- Mechanical.
|
|
Science -- Mathematical Physics.
|
|
Structural dynamics -- Mathematics
|
| Genre/Form |
Electronic books
|
|
Textbooks
|
| Form |
Electronic book
|
| Author |
Krysʹko, V. A. (Vadim Anatolʹevich), 1937-
|
| ISBN |
9783030376635 |
|
303037663X |
|
3030376621 |
|
9783030376628 |
|
9783030376642 |
|
3030376648 |
|
9783030376659 |
|
3030376656 |
|
