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

Abstract

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)