... at the contact points of rolling elements and races, whose stiffnesses are obtained by using Hertzian elastic contact deformation theory. The numerical integration technique Newmark-β with the Newton–Raphson method is used to solve the nonlinear differential equations, iteratively. The effect of bearing running...

... understanding of the causes of accidents and derailments. longitudinal train forces coupler geometric nonlinearities noninertial coordinates railroad vehicle dynamics multibody systems couplings differential algebraic equations kinematics Newton-Raphson method railways vehicle dynamics...

... , dotted line: t 0 = 4   s , and dashed-dotted line: t 0 = 0.5   s . ( a ) Linear displacement and ( b ) nonlinear displacement. 05 06 2008 13 03 2009 02 09 2009 elasticity fibre reinforced composites laminates Newton-Raphson method plates...