%0 Conference Paper
%A Koh, K.J.
%A Yasreen, A.Y.M.
%D 2017
%F scholars:8593
%I EDP Sciences
%K Drag; Iterative methods; Kinematics; Stiffness; Stiffness matrix; Structural dynamics; Vibration analysis, Convergence characteristics; Displacement-Based; Equivalent algorithm; Euler Bernoulli beams; Iterative algorithm; Primitive variables; Slender structures; Tangent stiffness matrix, Damping
%R 10.1051/matecconf/201711101004
%T On Newton-Raphson formulation and algorithm for displacement based structural dynamics problem with quadratic damping nonlinearity
%U https://khub.utp.edu.my/scholars/8593/
%V 111
%X 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.
%Z cited By 1; Conference of 2nd International Conference on Fluids and Chemical Engineering, FluidsChE 2017 ; Conference Date: 4 April 2017 Through 6 April 2017; Conference Code:128326