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An Elastic Membrane With an Attached Non-Linear Thermoelastic Rod

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Horn W. , Sokołowski J.

International Journal of Applied Mathematics and Computer Science

2002

tom Vol. 12, no 4

479-486

We study a thermo-mechanical system consisting of an elastic membrane to which a shape-memory rod is glued. The slow movements of the membrane are controlled by the motions of the attached rods. A quasi-static model is used. We include the elastic feedback of the membrane on the rods. This results in investigating an elliptic boundary value problem in a domain W is subset R2 with a cut, coupled with non-linear equations for the vertical motions of the rod and the temperature on the rod. We prove the existence of a unique global weak solution to this problem using a fixed point argument.

A model for passive damping of a membrane

100%

Horn W. , Sokołowski J.

Control and Cybernetics

2005

tom Vol. 34, no 1

325-337

We introduce a model in which a wire made of shape memory alloy is used to passively damp the vibrations of a membrane. The mechanical energy of the membrane is transformed into heat via the thermo-elastic properties of the shape memory alloy. We describe the model and prove existence and uniqueness of solutions. Finally we will show that for suitable initial and boundary conditions, the energy of the entire system is a decreasing function.