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Full Description
The purpose of this monograph is threefold. First, mathematical models of the transient behavior of some or all of the state variables describing the motion of multiple-link flexible structures will be developed. The structures which we have in mind consist of finitely many interconnected flexible ele ments such as strings, beams, plates and shells or combinations thereof and are representative of trusses, frames, robot arms, solar panels, antennae, deformable mirrors, etc. , currently in use. For example, a typical subsys tem found in almost all aircraft and space vehicles consists of beam, plate and/or shell elements attached to each other in a rigid or flexible manner. Due to limitations on their weights, the elements themselves must be highly flexible, and due to limitations on their initial configuration (i. e. , before de ployment), those aggregates often have to contain several links so that the substructure may be unfolded or telescoped once it is deployed. The point of view we wish to adopt is that in order to understand completely the dynamic response of a complex elastic structure it is not sufficient to con to take into account the sider only its global motion but also necessary flexibility of individual elements and the interaction and transmission of elastic effects such as bending, torsion and axial deformations at junctions where members are connected to each other. The second object of this book is to provide rigorous mathematical analyses of the resulting models.
Contents
I. Introduction.- 1. General Overview.- 2. On the Contents of the Book.- II. Modeling of Networks of Elastic Strings.- 1. Modeling of Nonlinear Elastic Strings.- 2. Networks of Nonlinear Elastic Strings.- 3. Linearization.- 4. Well-posedness of the Network Equations.- 5. Controllability of Networks of Elastic Strings.- 6. Stabilizability of String Networks.- 7. String Networks with Masses at the Nodes.- III. Networks of Thermoelastic Beams.- 1. Modeling of a Thin Thermoelastic Curved Beam.- 2. The Equations of Motion.- 3. Rotating Beams.- 4. Straight, Untwisted, Nonshearable Nonlinear 3—d Beams.- 5. Straight, Untwisted Shearable Linear 3—d Beams.- 6. Shearable Nonlinear 2—d Beams with Curvature.- 7. A List of Beam Models.- 8. Networks of Beams.- 9. Rotating Two-link Flexible Nonlinear Shearable Beams.- IV. A General Hyperbolic Model for Networks.- 1. The General Model.- 2. Some Special Cases.- 3. Existence and Regularity of Solutions.- 4. Energy Estimates for Hyperbolic Systems.- 5. Exact Controllability of the Network Model.- 6. Stabilizability of the Network Model.- V. Spectral Analysis and Numerical Simulations.- 1. Preliminaries.- 2. Eigenvalue Problems for Networks of 1—d Elements.- 3. Numerical Simulations of Controlled 1—d Networks.- 4. Finite Element Approximations of Timoshenko Networks.- 5. Implicit Runge-Kutta Method: Dry Friction at Joints.- VI. Interconnected Membranes.- 1. Modeling of Dynamic Nonlinear Elastic Membranes.- 2. Systems of Interconnected Elastic Membranes.- 3. Controllability of Linked Isotropic Membranes.- VII. Systems of Linked Plates.- 1. Modeling of Dynamic Nonlinear Elastic Plates.- 2. Linearization.- 3. Systems of Linked Reissner Plates.- 4. Well-posedness of Systems of Linked Reissner Plates.- 5. Controllability of LinkedReissner Plates.- 6. Systems of Linked Kirchhoff Plates.- VIII. Plate-Beam Systems.- 1. Introduction.- 2. Modeling of the Plate-Beam Junction: I.- 3. Function Spaces and Well-Posedness.- 4. The Reachable Set.- 5. Limit Model as the Shear Moduli Approach Infinity.- 6. Modeling of a Plate-Beam Junction: II.
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