Elastic and thermoelastic problems in nonlinear dynamics of structural members applications of the Bubnov-Galerkin and finite difference methods /: applications of the Bubnov-Galerkin and finite difference methods. (2020)

• Record Type: Book
• Further Information: Note: Jan Awrejcewicz, Vadim A. Krysko, editors.
• Other Names: Awrejcewicz, J (Jan); Krysʹko, V. A (Vadim Anatolʹevich), 1937-
• 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
• Edition: 2nd ed
• Publisher Details: Cham : Springer
• Publication Date: 2020
• Extent: 1 online resource (615 p.)
• Subjects: 624.1/71; Structural dynamics -- Mathematics; Maths for scientists; Dynamics & vibration; Mathematical physics; Computers -- Computer Science; Technology & Engineering -- Mechanical; Science -- Mathematical Physics; Structural dynamics -- Mathematics; Electronic books; Electronic books; Textbooks
• Languages: English
• ISBNs: 9783030376635; 3030376621; 9783030376628; 9783030376642; 3030376648; 9783030376659; 3030376656
• Related ISBNs: 303037663X; 9783030376628
• Notes: Note: Includes bibliographical references.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.