Normal oscillations of a string with concentrated masses on non-linearly elastic supports

Nonsmooth Modal Analysis of Piecewise-Linear Impact Oscillators

“…A majority of such works consists either in i) regularizing the impact condition(s) with the addition of springs [4,7,15,19,27,28,36,41] or ii) investigating the dynamics of a forced vibro-impact oscillator [12,34,35,43,44]. Regularizing is known to introduce numerical stiffness [1,2] and is not considered in this work (the relationship between regularized and infinitely rigid impact was studied using a two-degree-of-freedom system with an elastic stop with one impact per period in ref.…”

Periodic Motions of Coupled Impact Oscillators

“…Nonsmooth modes in two degrees-of-freedom impacting systems have been studied in a number of works, see e.g. [30,40] in the case of symmetric constraints and [22] for more references. In what follows we discuss the case when I 1 and I 2 consist of the sets of odd and even integers respectively.…”

Normal vibrations of a general class of conservative oscillators

“…Before proceeding to construct the solution it is worth noting that the singular points of equations (6) are roots of the equation: h = x x 2 : : : x n : (11) As the order of approximation varies so does the estimate of the energy h, since the solution x i x, i = 2 : : : n , becomes more accurate through the inclusion of higher order terms.…”

“…Different results and new ideas concerning NNMs of conservative systems were performed by Vito [9], Mikhlin [10], Vedenova et al [11], Vakakis [12], Vakakis and Rand [13], Shaw and Pierre [14,15], Nayfeh and Nayfeh [16], etc.…”

“…In [10] Padé approximations are used for an analysis of the NNMs with large amplitudes. In [11] nonlinear mode localization is studied in discrete nonlinear systems with impact nonlinearities. In [12] asymptotic methodology is used; for an oscillator with weak coupling stiffness in both localized and non-localized modes are detected.…”