Non-parametric simultaneous identification of both the nonlinear damping and restoring characteristics of nonlinear systems whose dampings depend on velocity alone

A numerical scheme for recovering the nonlinear characteristics of a single degree of freedom structure: non-parametric system identification

“…The system is governed by the nonlinear ordinary differential equation ( ) ( ) my ky f y r y      (1) with the following initial conditions [20],…”

“…The values of  and  are assumed to have the following magnitude in this paper [7,18,20]: It is then possible to construct an integral equation for u, given by…”

“…with the kernel K defined as The relationship in eqn (10) is classified as a Volterra-type integral equation of the first kind [20], which defines an inverse problem for the simultaneous identification of the velocity-dependent nonlinear damping and restoring force together with the nonlinear function defined by eqn (9). Eqn (10) and eqn (9) constitute the required equations of the present nonlinear inverse problem for the two unknown functions, f and r.…”

“…For this purpose, a non-parametric procedure according to Jang's method [20] is applied; this involves a non-parametric, simultaneous identification of the nonlinear characteristics of both damping and restoring force for systems whose damping depends on velocity alone. The nonlinear damping and restoring force parameters of a system with time dependent damping are numerically obtained.…”

Simultaneous detection of the nonlinear restoring and excitation of a forced nonlinear oscillation: an integral approach

“…The nonlinear oscillators are well studied by many researchers for instant see [8][9][10][11][12][13][14][15][16] and references therein. A valuable investigation has been conducted to detect the parameters from noisy data for forced nonlinear oscillators [17][18][19][20][21][22][23][24] and provides base for the new exploration in area of inverse problems.…”