Dynamic analysis of piecewise linear oscillators with time periodic coefficients

Non-Linear Dynamics of Gear-Pair Systems With Periodic Stiffness and Backlash

“…Similar methods, suitable for piecewise linear systems with time-periodic coe$cients, were originally presented in reference [10]. Here, this analysis is "rst extended by considering more general external forcing conditions and more solution types of a gear-pair system.…”

Effect of non-linearities in the identification and fault detection of gear-pair systems

“…where n are prespecified mean angular velocity components of the gear shafts and n represent small variations caused by vibration of the mating gear teeth [11,13,14]. In such cases, both the gear mesh stiffness and the static transmission error can be considered as time-periodic functions.…”

“…is time-periodic and includes contributions from the external torques as well as from the geometric irregularities of the mating gear teeth [14].…”

“…An example class of mechanical systems with typical non-linearities in the restoring forces is the class of geared rotor-bearing systems [11][12][13][14][15]. Among all the factors affecting the response of such a system in a significant way, it was shown that the presence of gear backlash plays a dominant role and has to be included in the theoretical formulations [11,15].…”

Modelling localized nonlinearities in continuous systems via the method of augmentation by non-smooth basis functions

“…Systems with localized, non-smooth nonlinearities include joints in large structures [1], gears with backlash [2,3], steam generator tubes in nuclear power plants [4], rotating shafts with cracks [5], rotors and other rotating systems with finite clearances [6,7] and fluid conveying pipes with supports [8] among many other applications [9][10][11]. Typically, these nonlinearities are approximated by piecewise-linear models; however, the simplification of the non-smooth nonlinearity as a piecewise-linear model can significantly affect the dynamics of the system.…”