Modeling, Analysis and Control of Dynamic Elastic Multi-Link Structures (Systems & Control: Foundations and Applications) - Hardcover

Lagnese, J.E.; Leugering, Günter; Schmidt, E.J.P.G.

Hardcover

ISBN 10: 0817637052 ISBN 13: 9780817637057

Verlag: Birkhäuser, 1994

Inhaltsangabe

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.- 5.1. Exact Controllability of Tree Networks.- 5.2. Lack of Controllability for Networks with Closed Circuits.- 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.- 2.1. Some Remarks on Warping and Torsion.- 3. Rotating Beams.- 3.1. Dynamic Stiffening.- 4. Straight, Untwisted, Nonshearable Nonlinear 3-d Beams.- 4.1. Approximation-Generalizations.- 5. Straight, Untwisted Shearable Linear 3-d Beams.- 6. Shearable Nonlinear 2-d Beams with Curvature.- 6.1. Approximation-Generalizations.- 7. A List of Beam Models.- Damping.- 8. Networks of Beams.- 8.1. Geometric Joint Conditions.- 8.1.1. Rigid Joints.- 8.1.2. Pinned Joints.- 8.2. Dynamic Joint Conditions.- 8.2.1. Rigid Joints.- 8.2.2. Pinned Joints.- 9. Rotating Two-link Flexible Nonlinear Shearable Beams.- IV. A General Hyperbolic Model for Networks.- 1. The General Model.- 2. Some Special Cases.- 2.1. String Networks.- 2.2. Networks of Planar Timoshenko Beams.- 2.4. Networks of Initially Curved Bresse Beams.- 2.5. Beams and Strings.- 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.- 1.1. Notation.- 1.2. Networks of Strings.- 1.3. Networks of Timoshenko Beams.- 1.4. Networks of Euler-Bernoulli Beams.- 2. Eigenvalue Problems for Networks of 1-d Elements.- 2.1. Introduction.- 2.2. General String Networks.- 2.3. Homogeneous String Networks.- 2.3.1. Examples.- 2.4. Networks of Timoshenko Beams.- 2.4.1. The Case Where ? =0.- 2.4.2. The Case Where ? Belongs to an Individual Beam.- 2.4.3. Eigenvalues for the Entire Graph.- 2.5. Homogeneous Timoshenko Networks.- 3. Numerical Simulations of Controlled 1-d Networks.- 3.1. Introductory Remarks.- 3.2. Networks of Strings.- 3.2.1. Absorbing Controls.- 3.2.2. Directing Controls.- 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.- 1.1. Equations of Motion.- 1.2. Edge Conditions.- 1.3. Hamilton's Principle.- 2. Systems of Interconnected Elastic Membranes.- 2.1. Geometric Junction Conditions.- 2.2. Dynamic Conditions.- 2.3. Linearization.- 2.4. Well-Posedness of the Linear Model.- 3. Controllability of Linked Isotropic Membranes.- 3.1. Observability Estimates for the Homogeneous Problem.- 3.2. A Priori Estimates for Serially Connected Membranes.- 3.3. A Priori Estimates for Single Jointed Membrane Systems.- 3.4. The Reachable States.- 3.4.1. Serially Connected Membranes.- 3.4.2. Membrane Transmission Problems.- VII. Systems of Linked Plates.- 1. Modeling of Dynamic Nonlinear Elastic Plates.- 1.1. Equations of Motion.- 1.2. Edge Conditions.- 1.3. Hamilton's Principle.- 1.4. Additional Kinematic and Material Assumptions.- 1.5. Rotations Associated with Plate Deformation.- 2. Linearization.- 2.1. Linearization of Equations of Motion.- 2.2. Linearization of Edge Conditions.- 2.3. Hamilton's Principle for the Reissner Model.- 2.4. Linearization of the Vector Rotation Angle.- 2.5. The Kirchhoff Plate Model.- 3. Systems of Linked Reissner Plates.- 3.1. Geometric Junction Conditions.- 3.2. Linearization of the Geometric Joint Conditions.- 3.3. Dynamic Joint Conditions.- 3.3.1. Dynamic conditions at a connected joint.- 3.3.2. Dynamic conditions at a hinged joint.- 3.3.3. Dynamic conditions at a semi-rigid joint.- 3.3.4. Dynamic conditions at a rigid join...

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Críticas

"The book is carefully written and is a welcome addition to the growing literature on multibody systems. Purchase by libraries, students, researchers, and professionals in the field is recommended." --Zentralblatt Math

Reseña del editor

A typical subsystem 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 deployment), those aggregates often have to contain several links so that the substructure may be unfolded or telescoped once it is deployed. The defining philosophy of this monograph is that in order to understand completely the dynamic response of such a complex elastic structure, it is not sufficient to consider only its global motion but also necessary to take into account the 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. Therefore, the purposes of this monograph are: to derive distributed parameter models of the transient behavior of some or all of the state and interval variables which describe the dynamic response of multiple-link flexible structures such as trusses, frames, robot arms, solar panels, antennae and deformable mirrors, based on the principles of continuum mechanics and under reasonable constraints on the geometry of the admissible deformations; to provide rigorous mathematical analyses of the resulting models; and to develop control theoretic properties of multiple-link flexible structures based on the control theoretic properties of the models. The modelling and analysis of these complicated and realistic structural configurations should be of interest to a diverse group of applied mathematicians, structural, aeronautical, aerospace, and mechanical engineers and to advanced graduate students working on such problems.

Details zur Ausgabe

• Verlag: Birkhäuser
• Erscheinungsdatum: 1994
• Sprache: Englisch
• ISBN 10: 0817637052
• ISBN 13: 9780817637057
• Einband: Tapa dura
• Anzahl der Seiten: 408
• Kontakt zum Hersteller: Nicht verfügbar