Dynamics of Solid Structures : Methods Using Integrodifferential Relations

This monograph covers new variational and projection methods to study the dynamics within solid structures. To cope with the underlying initial-boundary value problems, the method of integrodifferential relations is employed. Applications and examples in physics, mechanics and control engineering range from natural vibrations or forced motions of elastic and viscoelastic bodies to heat and mass transfer processes. **Contents**Generalized formulations of parabolic and hyperbolic problems Variational principles in linear elasticity Variational statements in structural mechanics Ritz method for initial-boundary value problems Variational and projection techniques with semi-discretization Integrodifferential approach to eigenvalue problems Spatial vibrations of elastic beams with convex cross-sections Double minimization in optimal control problems Semi-discrete approximations in inverse dynamic problems Modeling and control in mechatronics This monograph covers new variational and projection methods to study the dynamics within solid structures. To cope with the underlying initial-boundary value problems, the method of integrodifferential relations is employed. Applications and examples in physics, mechanics and control engineering range from natural vibrations or forced motions of elastic and viscoelastic bodies to heat and mass transfer processes. Contents Generalized formulations of parabolic and hyperbolic problems Variational principles in linear elasticity Variational statements in structural mechanics Ritz method for initial-boundary value problems Variational and projection techniques with semi-discretization Integrodifferential approach to eigenvalue problems Spatial vibrations of elastic beams with convex cross-sections Double minimization in optimal control problems Semi-discrete approximations in inverse dynamic problems Modeling and control in mechatronics Preface Basic notation Contents 1. Introduction 2. Generalized formulations of parabolic and hyperbolic problems 3. Variational principles in linear elasticity 4. Variational statements in structural mechanics 5. Ritz method for initial-boundary value problems 6. Variational and projection techniques with semi-discretization 7. Integrodifferential approach to eigenvalue problems 8. Spatial vibrations of elastic beams with convex cross-sections 9. Double minimization in optimal control problems 10. Semi-discrete approximations in inverse dynamic problems 11. Modeling and control in mechatronics A. Vectors and tensors B. Sobolev spaces Bibliography Index