Modeling, Analysis and Control of Dynamic Elastic Multi-Link Structures

Inhalt

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)