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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

Elastic and Thermoelastic Problems in Nonlinear Dynamics of Structural Members: Applications of the Bubnov-Galerkin and Finite Difference Methods

Second/New Edition (in bold the new material): 1 Introduction (to be updated).- 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.- 2.2.2 Stable Vibrating Panel Within a Transonic Flow.- 2.2.3 Stability Loss of Panel Within Transonic Flow.- 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.- 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 e 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.- 9.1. Fundamental Relations and Assumptions. - 9.2. The Bubnov-Galerkin Method.- 9.2.1. Closed Cylindrical Shell.- 9.2.2. Cylindrical Panel.- 9.3. Reliability of the Obtained Results.- 9.4. On the Set up Method in the Theory of Flexible Shallow Shells.- 9.5. Dynamic Stability Loss of the Shells Under the Step-Type Function.- 10 Chaotic Vibrations of Cylindrical and Spherical Shells.- 10.1. Novel Models of Scenarios of Transition from Periodic to Chaotic Orbits.- 10.2. Sharkovskiy's Periodicity Exhibited by PDEs Governing Dynamics of Flexible Shells.- 10.3. On the Space-Temporal Chaos.- 11 Mathematical Models of Chaotic Vibrations of Closed Cylindrical Shells with Circular Cross Section.- 11.1. On the Convergence of the Bubnov-Galerkin (BG) Method in the Case of Chaotic Vibrations of Closed Cylindrical Shells.- 11.2. Chaotic Vibrations of Closed Cylindrical Shells Versus Their Geometric Parameters and the Area of the External Load Action.- 12 Chaotic Dynamics of Flexible Closed Cylindrical Nanoshells under Local Load.- 12.1. Statement of the Problem.- 12.2. Algorithm of the Bubnov-Galerkin Method.- 12.3. Numerical Experiment.- 13 Contact Interaction of Two Rectangular Plates Made From Different Materials Taking into Account Physical Nonlinearity.- 13.1. Statement of the Problem.- 13.2. Reduction of PDEs to ODEs.- 13.2.1. Method of Kantorovich-Vlasov (MKV).- 13.2.3. Method of Variational Iteration (MVI).- 13.2.4. Method of Arganovskiy-Baglay-Smirnov (MABS).- 13.2.5. Combined Method (MC).- 13.2.6. Matching of the Methods of Kantorovich-Vlasov and Arganovskiy-Baglay-Smirnov (MKV+MABS).- 13.2.7. Matching of the Method