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.

Table of Contents:
Part 1: general overview; on the contents of the book. Part 2 Modelling of networks of elastic strings: modelling of nonlinear elastic strings; networks of nonlinear elastic strings; linearization; wellposedness of the network equations; controllability of networks of elastic strings - exact controllability of tree networks, lack of controllability for networks with closed circuits; stabilizability of string networks; string networks with masses at the nodes. Part 3 Networks of thermoelastic beams; modelling of a thin thermoelastic curved beam; the equations of motion - some remarks on warping and torsion; rotating beams - dynamic stiffening; nonlinear nonshearable 3-d beams - approximation-generalizations; linear shearable 3-d beams; nonlinear shearable 2-d beams - approximation-generalizations; a list of beam models - damping; networks of beams - geometric joint conditions, rigid joints pinned joints, dynamic joint conditions, rigid joints, pinned joints; rotating two-link nonlinear shearable beams. Part 4 A general hyperbolic model for networks: the general model; some special cases - string networks, networks of planar Timoshenko beams, networks of linear shearable beams, networks of initially curved bresse beams, beams and strings; existence and regularity of solutions; energy estimates for hyperbolic systems; exact controllability of the network model; stabilizability of the network model. Part 5 Spectral analysis and numerical simulation: eigenvalue problems for networks - notation; networks of strings; setworks of Timoshenko beams; Euler-Bernoulli beams; the eigenvalue problem for mechanical networks - the string case, homogeneous network of strings, examples, the homogenous Timoshenko network; numerical simulations of controlled networks, introductory remarks, absorbing controls, cirecting controls; finite element approximations of networks - dry friction at joints. Part 6 Interconnected membranes: modelling of dynamic nonlinear elastic membranes - equations of motion, edge conditions, Hamilton's Principle; systems of interconnected elastic membranes - geometric junction conditions, dynamic conditions, linearization, well-posedness of the linear model; controllability of linked isotropic membranes - observability estimates for the homogeneous problem, a priori estimates for serially connected membranes, a priori estimates for single jointed membrane systems, the reachable states, serially connected membranes, membrane transmission problems. Part 7 Systems of linked plates: modelling of dynamic nonlinear elastic plates (Part contents)