An efficient method to solve the strongly coupled nonlinear differential equations of impact dampers

In this paper, ongoing studies to solve nonlinear differential equations are extended by combining the Newmark-beta integration method and the piecewise linearization approach. The discussed method is illustrated with a practical example. In doing so, the coupled nonlinear differential equations of an impact oscillator, which incorporates the Hertzian contact, are derived. To investigate this problem, an object-oriented computer code, based on the presented method, is written in MATLAB. Furthermore, the discussed problem is solved numerically using the Runge–Kutta commercial code. To verify the calculated results, the contact durations, which are obtained using the discussed methods, are compared with the previous analytical results. In this study, accuracy of solution and the process time (cost) are selected as two main parameters of the solution method. The so-called adequacy factor is presented to combine the two main parameters of solution. Finally, it is shown that in the case of Hertzian contact, the presented method can be more adequate than the Runge–Kutta method.