1 Division of Water and Soil, The Faculty of Engineering and Science, Aalborg University, VBN2 Geotechnical Engineering Research Group, The Faculty of Engineering and Science, Aalborg University, VBN3 Department of Civil Engineering, The Faculty of Engineering and Science, Aalborg University, VBN4 The Faculty of Engineering and Science (ENG), Aalborg University, VBN5 unknown
We consider periodic solutions for nonlinear free vibration of conservative, coupled mass-spring systems with linear and nonlinear stiffnesses. Two practical cases of these systems are explained and introduced. An analytical technique called energy balance method (EBM) was applied to calculate approximations to the achieved nonlinear differential oscillation equations where the displacement of the two-mass system can be obtained directly from the linear second-order differential equation using the first order of the current approach. Compared with exact solutions, just one iteration leads us to high accuracy which is valid for a wide range of vibration amplitudes as indicated in the presented examples.
Zeitschrift Fuer Naturforschung. Section A: a Journal of Physical Sciences, 2011, Vol 66a, Issue 1, p. 16-25
Coupled Nonlinear Oscillators; Nonlinear Stiffness; Duffing Equation; Energy Balance Method