Identification of Nonlinear Vibrating Structures: Part II—Applications

Abstract

It is worth noting from Fig. 8 that the spread of the results (i.e., dimensionless ordinate scales of the two plots) pertaining to the damping and stiffness influence coefficients differ by more than an order of magnitude (a factor of about 50). This behavior is consistent with the fact that, in the example under discussion, the relative contribution of damping-related forces and stiffens-related forces is nearly inversely proportional to the above-mentioned spread.4.4 Determination of Nonlinear Forces. Using the available measurements and the previously identified system matrices, the nonlinear system forces can now be computed from With that, the time history of the nonlinear force vector f, ( t ) components can be determined and are shown in Fig. 9. For convenience, identical scales are used for the three plots.At this stage of the identification procedure, the "best" (in least-squares sense) equivalent linear model has been determined in the form of the identified matrices. Thus, if for the purposes of a particular application the norm of the residual error, Ilf, (t) II, as computed from equation (6) is sufficiently small, then the identification task can be terminated. For more demanding situations, additional processing is required to more accurately identify the residual forces that have been determined.As pointed out earlier, if there is a need to augment the parametric identification results with additional results from the nonparametric phase of the data processing, one can proceed directly to develop approximating analytical representations, for as many of the components of fN(t) as warranted, in terms of a series expansion involving suitable generalized coordinates. However, when the order of the dynamic system is relatively large, dealing with a transformed set of nonlinear forces may lead to a faster rate of convergence of the applicable series.A convenient and natural transformation to use with realistic dynamic systems is the one expressed by equation (A33): where and @ is the modal matrix associated with MjjlKl,. Although the linear modal transformation of equation (8)

A Review of Nonlinear Dynamics of Mechanical Systems in Year 2008

“…The parameters of the polynomials that best fit the data are determined by making use of the orthogonality of the polynomials. 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 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.…”

Data-based Identification of nonlinear restoring force under spatially incomplete excitations with power series polynomial model

“…The method was extremely appealing in its simplicity because its starting point was Newton's second law. Masri et al [11,12] developed a self-starting, multi-stage, time-domain approach for the nonparametric identification of nonlinear MDOF systems undergoing free oscillations or subjected to arbitrary direct force excitations and/or non-uniform support motions. Worden and Tomlinson [28] described numerous approaches for the detection, identification, and modeling of nonlinear systems in their textbook.…”

A Decrement Method for Quantifying Nonlinear and Linear Damping in Multidegree 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.…”