Finite element discretization and direct integration of equations of motion are powerful and wide applied tools for solving a large number of engineering problems. Despite the large applicability of such approach the computational eort may result in long lasting analysis as the problem dimension increases and non-linearities take place. Analytical solutions, on the other side, often do not require large computational eorts and provide elegant and powerful representation of the problem. In this work a non-linear nite element model and an equivalent linear analytical model are used to simulate the behavior of a non-resonant taut cable with a linear active control device to dampen in-plane vibrations. The aim of the investigation is to examine the eectiveness of the linear model in describing the cable response when non-linearities are negligible. Such model is based on the transfer functions denition of the system composed by the cable and the active device. Analytical product between the Laplace transforms of the modal load components and the modal transfer functions of the system, provide the cable responses in the frequency domain. The inverse transition to the time domain is then analytically performed. The external excitations are composed by Dirac delta nodal loads so as to assess a general load condition. The analysis first explore the uncontrolled cable in-plane free vibrations in order to validate the basic assumption of linearizable problem. An active control device based on the use of a linear quadratic regulator is then introduced and the procedure is extended to general load conditions.

Analytic and numeric approach to controlled cables

UBERTINI, Filippo;
2006

Abstract

Finite element discretization and direct integration of equations of motion are powerful and wide applied tools for solving a large number of engineering problems. Despite the large applicability of such approach the computational eort may result in long lasting analysis as the problem dimension increases and non-linearities take place. Analytical solutions, on the other side, often do not require large computational eorts and provide elegant and powerful representation of the problem. In this work a non-linear nite element model and an equivalent linear analytical model are used to simulate the behavior of a non-resonant taut cable with a linear active control device to dampen in-plane vibrations. The aim of the investigation is to examine the eectiveness of the linear model in describing the cable response when non-linearities are negligible. Such model is based on the transfer functions denition of the system composed by the cable and the active device. Analytical product between the Laplace transforms of the modal load components and the modal transfer functions of the system, provide the cable responses in the frequency domain. The inverse transition to the time domain is then analytically performed. The external excitations are composed by Dirac delta nodal loads so as to assess a general load condition. The analysis first explore the uncontrolled cable in-plane free vibrations in order to validate the basic assumption of linearizable problem. An active control device based on the use of a linear quadratic regulator is then introduced and the procedure is extended to general load conditions.
2006
8837116217
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11391/161535
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