Identifying space-time dependent force on the vibrating Euler–Bernoulli beam by a boundary functional method

Identifying space-time dependent force on the vibrating Euler–Bernoulli beam by a boundary... AbstractIn this paper we estimate an unknown space-time dependent force being exerted on the vibrating Euler–Bernoulli beam under different boundary supports, which is obtained with the help of measured boundary forces as additional conditions.A sequence of spatial boundary functions is derived, and all the boundary functions and the zero element constitute a linear space.A work boundary functional is coined in the linear space, of which the work is approximately preserved for each work boundary function.The linear system used to recover the unknown force with the work boundary functions as the bases is derived and the iterative algorithm is developed, which converges very fast at each time step.The accuracy and robustness of the boundary functional method (BFM) are confirmed by comparing the estimated forces under large noise with the exact forces.We also recover the unknown force on the damped vibrating Euler–Bernoulli beam equation. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Inverse and III-posed Problems de Gruyter

Identifying space-time dependent force on the vibrating Euler–Bernoulli beam by a boundary functional method

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Publisher
de Gruyter
Copyright
© 2020 Walter de Gruyter GmbH, Berlin/Boston
ISSN
1569-3945
eISSN
1569-3945
DOI
10.1515/jiip-2019-0013
Publisher site
See Article on Publisher Site

Abstract

AbstractIn this paper we estimate an unknown space-time dependent force being exerted on the vibrating Euler–Bernoulli beam under different boundary supports, which is obtained with the help of measured boundary forces as additional conditions.A sequence of spatial boundary functions is derived, and all the boundary functions and the zero element constitute a linear space.A work boundary functional is coined in the linear space, of which the work is approximately preserved for each work boundary function.The linear system used to recover the unknown force with the work boundary functions as the bases is derived and the iterative algorithm is developed, which converges very fast at each time step.The accuracy and robustness of the boundary functional method (BFM) are confirmed by comparing the estimated forces under large noise with the exact forces.We also recover the unknown force on the damped vibrating Euler–Bernoulli beam equation.

Journal

Journal of Inverse and III-posed Problemsde Gruyter

Published: Jun 1, 2020

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