Proceedings of IMEC’01 2001 ASME International Mechanical Engineering Congress November 11-16, 2001, New York, New York, USA DETC98/DAC-1234 TRANSIENT SIMULATION OF ADAPTIVE STRUCTURES Sven Herold Department of Adaptronics Institute of Mechanics University of Magdeburg Universit ¨ atsplatz 2 Magdeburg, 39106 Germany sven.herold@mb.uni-magdeburg.de Dirk Mayer Department of Adaptronics Institute of Mechanics University of Magdeburg Universit ¨ atsplatz 2 Magdeburg, 39106 Germany dirk.mayer@mb.uni-magdeburg.de Holger Hanselka Department of Adaptronics Institute of Mechanics University of Magdeburg Universit ¨ atsplatz 2 Magdeburg, 39106 Germany holger.hanselka@mb.uni-magdeburg.de ABSTRACT An approach is utilised to design an adaptronic system by means of Rapid-Prototyping on the basis of a simulation. The modelling of the vibration behaviour of mechanical systems with actuators and sensors and additionally an adaptive controller in time domain is presented. The method includes the calculation of the dynamic behaviour of the mechanical structure with the help of FEM. The FE-model of the mechanical structure is trans- formed into modal space, then reduced and embedded as state- space-model in the MATLAB/Simulink-environment. A com- parison of an analytical solution with the solution of reduced FE-model shows good agreement (a simple mechanical struc- ture is used). Actuators and sensors are appliqued to the me- chanical structure. Based on the resulting dynamical behaviour of the mechanical structure an adaptive control algorithm for the reduction of structural vibrations is developed. Experimen- tal tests are performed to confirm and to update the simula- tions. The hardware-in-the-loop-simulations are realized with a Dspace-system. Some aspects (e.g. speed-up, precision) of this simulation method in comparison with other methods are indi- cated. This procedure allows the development and the evaluation of more complex adaptive mechanical structures. Address all correspondence to this author. NOMENCLATURE C stiffness matrix C f parameter of the charge amplifier D damping matrix G PPF-control matrix G i PPF modal control gain E Young’s modulus E p Young’s modulus of the piezo ceramic M mass matrix U voltage A B C D state space matrices b p width of the piezo ceramic d 31 piezoelectric constant u vector of input (state space) w vector of physical displacements x vector of physical coordinates y vector of output (state space) z vector of modal displacements Φ matrix of mode shapes Φ el matrix of electrical mode shapes δ i modal damping coefficients ϖ 0i eigenfrequencies ζ vector of states 1 Copyright  2001 by ASME