On Newton-Raphson formulation and algorithm for displacement based structural dynamics problem with quadratic damping nonlinearity

Quadratic damping nonlinearity is challenging for displacement based structural dynamics problem as the problem is nonlinear in time derivative of the primitive variable. For such nonlinearity, the formulation of tangent stiffness matrix is not lucid in the literature. Consequently, ambiguity relate...

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Main Authors: Koh, K.J., Yasreen, A.Y.M.
Format: Article
Institution: Universiti Teknologi Petronas
Record Id / ISBN-0: utp-eprints.20062 /
Published: EDP Sciences 2017
Online Access: https://www.scopus.com/inward/record.uri?eid=2-s2.0-85021332417&doi=10.1051%2fmatecconf%2f201711101004&partnerID=40&md5=680a475913a79a0cba9e1e6d69c63ba4
http://eprints.utp.edu.my/20062/
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spelling utp-eprints.200622018-04-22T14:39:24Z On Newton-Raphson formulation and algorithm for displacement based structural dynamics problem with quadratic damping nonlinearity Koh, K.J. Yasreen, A.Y.M. Quadratic damping nonlinearity is challenging for displacement based structural dynamics problem as the problem is nonlinear in time derivative of the primitive variable. For such nonlinearity, the formulation of tangent stiffness matrix is not lucid in the literature. Consequently, ambiguity related to kinematics update arises when implementing the time integration-iterative algorithm. In present work, an Euler-Bernoulli beam vibration problem with quadratic damping nonlinearity is addressed as the main source of quadratic damping nonlinearity arises from drag force estimation, which is generally valid only for slender structures. Employing Newton-Raphson formulation, tangent stiffness components associated with quadratic damping nonlinearity requires velocity input for evaluation purpose. For this reason, two mathematically equivalent algorithm structures with different kinematics arrangement are tested. Both algorithm structures result in the same accuracy and convergence characteristic of solution. © The Authors, published by EDP Sciences, 2017. EDP Sciences 2017 Article PeerReviewed https://www.scopus.com/inward/record.uri?eid=2-s2.0-85021332417&doi=10.1051%2fmatecconf%2f201711101004&partnerID=40&md5=680a475913a79a0cba9e1e6d69c63ba4 Koh, K.J. and Yasreen, A.Y.M. (2017) On Newton-Raphson formulation and algorithm for displacement based structural dynamics problem with quadratic damping nonlinearity. MATEC Web of Conferences, 111 . http://eprints.utp.edu.my/20062/
institution Universiti Teknologi Petronas
collection UTP Institutional Repository
description Quadratic damping nonlinearity is challenging for displacement based structural dynamics problem as the problem is nonlinear in time derivative of the primitive variable. For such nonlinearity, the formulation of tangent stiffness matrix is not lucid in the literature. Consequently, ambiguity related to kinematics update arises when implementing the time integration-iterative algorithm. In present work, an Euler-Bernoulli beam vibration problem with quadratic damping nonlinearity is addressed as the main source of quadratic damping nonlinearity arises from drag force estimation, which is generally valid only for slender structures. Employing Newton-Raphson formulation, tangent stiffness components associated with quadratic damping nonlinearity requires velocity input for evaluation purpose. For this reason, two mathematically equivalent algorithm structures with different kinematics arrangement are tested. Both algorithm structures result in the same accuracy and convergence characteristic of solution. © The Authors, published by EDP Sciences, 2017.
format Article
author Koh, K.J.
Yasreen, A.Y.M.
spellingShingle Koh, K.J.
Yasreen, A.Y.M.
On Newton-Raphson formulation and algorithm for displacement based structural dynamics problem with quadratic damping nonlinearity
author_sort Koh, K.J.
title On Newton-Raphson formulation and algorithm for displacement based structural dynamics problem with quadratic damping nonlinearity
title_short On Newton-Raphson formulation and algorithm for displacement based structural dynamics problem with quadratic damping nonlinearity
title_full On Newton-Raphson formulation and algorithm for displacement based structural dynamics problem with quadratic damping nonlinearity
title_fullStr On Newton-Raphson formulation and algorithm for displacement based structural dynamics problem with quadratic damping nonlinearity
title_full_unstemmed On Newton-Raphson formulation and algorithm for displacement based structural dynamics problem with quadratic damping nonlinearity
title_sort on newton-raphson formulation and algorithm for displacement based structural dynamics problem with quadratic damping nonlinearity
publisher EDP Sciences
publishDate 2017
url https://www.scopus.com/inward/record.uri?eid=2-s2.0-85021332417&doi=10.1051%2fmatecconf%2f201711101004&partnerID=40&md5=680a475913a79a0cba9e1e6d69c63ba4
http://eprints.utp.edu.my/20062/
_version_ 1741196310540713984
score 11.62408

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