Identification of Nonlinear Vibrating Structures: Part I—Formulation

Abstract

A self-starting multistage, time-domain procedure is presented for the identification of nonlinear, multi-degree-of-freedom systems undergoing free oscillations or subjected to arbitrary direct force excitations and/or nonuniform support motions. Recursive least-squares parameter estimation methods combined with non-parametric identification techniques are used to represent, with sufficient accuracy, the identified system in a form that allows the convenient prediction of its transient response under excitations that differ from the test signals. The utility of this procedure is demonstrated in a companion paper.

On‐line identification of non‐linear hysteretic structural systems using a variable trace approach

“…It is noteworthy that the fast convergence to the steady-state parameters, as shown in Figure 2, is strongly dependent not only on the 'richness' of the excitation at the beginning of the time history, but also on the large value of the initial adaptation gains used in Equation (18). In the phase-plane plots, this leads to almost no discrepancies between the simulated and predicted restoring forces even at the beginning of the time history.…”

“…Another classiÿcation of such algorithms can be considered on the basis of their search space. The ÿrst group is deÿned as 'parametric methods', indicating that they search the solution directly in the parameter space [13][14][15][16], while the second group, called 'non-parametric', represents algorithms that search in a function space [17][18][19]. It should be pointed out that non-parametric methods are particularly well suited for the case of no a priori knowledge of the type and order of the model non-linearities.…”

A Review of Nonlinear Dynamics of Mechanical Systems in Year 2008

“…In a series of efforts, best represented by the foundational work of Masri and co-workers (223) - (226) , nonparametric identification schemes have been presented for single-degree-offreedom and multi-degree-of-freedom systems. Masri, Miller, Saud, and Caughey (225), (226) first used a recursive time-domain technique to identify the linear properties of the system, and subsequently, building on this step, they used a nonparametric identification scheme that needs accurate measurements of system accelerations in response to a random, an impulse, or a deterministic excitation. In another effort, Natke and Zamirowski (227) , proposed a scheme to identify the functional forms (polynomial representations) of damping and stiffness terms in nonlinear multi-degree-of-freedom mechanical systems.…”

A Decrement Method for Quantifying Nonlinear and Linear Damping in Multi-Degree of Freedom Systems

“…Granger [3] developed an estimation technique essentially based on a nonlinear optimisation of a data model composed of damped sinusoidal basis functions (and so the scheme was nonlinear in the identification parameters) and applied the method specifically to fluidelastic systems. In the time domain, the force surface mapping technique [4][5][6][7] has been successfully applied to lightly damped fluidelastic systems [8]. A recent survey of identification methods [9] cites mainly systems exhibiting relatively strong nonlinearities.…”