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Dynamics of a cantilever beam with piezoelectric sensor: Parameter identification
Cimrman, Robert ; Kolman, Radek ; Musil, Ladislav ; Kotek, Vojtěch ; Kylar, Jaromír
The piezoelectric materials are electroactive materials often applied for real-time sensing or structural health monitoring, both important research topics in dynamics. Mathematical models of such structures have to allow also for the external electrical circuits and contain several material parameters that need to be identified from experiments. We present a model of a simple experiment involving dynamics of a cantilever beam with an attached piezoelectric sensor excited by a suddenly removed weight. The external circuit can be taken into account as having either a finite or infinite resistance. We also outline the parameter identification procedure based on automatic differentiation and present the experimental and numerical results.
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Direct construction of reciprocal mass matrix and higher order fininite element method
Cimrman, Robert ; Kolman, Radek ; González, J. A. ; Park, K. C.
When solving dynamical problems of computational mechanics, such as contact-impact problems or cases involving complex structures under fast loading conditions, explicit time-stepping algorithms are usually preferred over implicit ones. The explicit schemes are normally combined with the lumped (diagonal) mass matrix so that the calculations are efficient and moreover dispersion errors in wave propagation are partially eliminated. As an alternative to lumping with advantageous properties, the reciprocal mass matrix is an inverse mass matrix that has the same sparsity structure as the original consistent mass matrix, preserves the total mass, captures well the desired frequency spectrum and leads thus to efficient and accurate calculations. In the contribution we comment on the usability of the reciprocal mass matrix in connection with higher order FEM.
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