Modal Techniques for Remote Identification of Nonlinear Reactions at Gap-Supported Tubes Under Turbulent Excitation

Abstract

Predictive computation of the nonlinear dynamical responses of gap-supported tubes subjected to flow excitation has been the subject of very active research. Nevertheless, experimental results are still very important, for validation of the theoretical predictions as well as for asserting the integrity of field components. Because carefully instrumented test tubes and tube-supports are seldom possible, due to space limitations and to the severe environment conditions, there is a need for robust techniques capable of extracting, from the actual vibratory response data, information that is relevant for asserting the components integrity. The dynamical contact/impact (vibro-impact) forces are of paramount significance, as are the tube/support gaps. Following our previous studies in this area using wave-propagation techniques (, , and , 1998, “Remote Identification of Impact Forces on Loosely Supported Tubes: Part 1—Basic Theory and Experiments,” J. Sound Vib., 215, pp. 1015–1041; , , and , 1998, “Remote Identification of Impact Forces on Loosely Supported Tubes: Part 2—Complex Vibro-Impact Motions,” J. Sound Vib., 215, pp. 1043–1064; , , and , 1999, “Remote Identification of Impact Forces on Loosely Supported Tubes: Analysis of Multi-Supported Systems,” ASME J. Pressure Vessel Technol., 121, pp. 61–70), we apply modal methods in the present paper for extracting such information. The dynamical support forces, as well as the vibratory responses at the support locations, are identified from one or several vibratory response measurements at remote transducers, from which the support gaps can be inferred. As for most inverse problems, the identification results may prove quite sensitive to noise and modeling errors. Therefore, topics discussed in the paper include regularization techniques to mitigate the effects of nonmeasured noise perturbations. In particular, a method is proposed to improve the identification of contact forces at the supports when the system is excited by an unknown distributed turbulence force field. The extensive identification results presented are based on realistic numerical simulations of gap-supported tubes subjected to flow turbulence excitation. We can thus confront the identified dynamical support contact forces and vibratory motions at the gap-support with the actual values stemming from the original nonlinear computations. The important topic of dealing with the imperfect knowledge of the modal parameters used to build the inverted transfer functions is thoroughly addressed elsewhere (, , and , 2009, “Identification of Nonlinear Interaction Forces Acting on Continuous Systems Using Remote Measurements of the Vibratory Responses,” Proceedings of the Seventh EUROMECH Solids Mechanics Conference (ESMC2009) , Lisbon, Portugal, Sept. 7–11). Nevertheless, identifications are performed in this paper based on both the exact modes and also on randomly perturbed modal parameters. Our results show that, for the system addressed here, deterioration of the identifications is moderate when realistic errors are introduced in the modal parameters. In all cases, the identified results compare reasonably well with the real contact forces and motions at the gap-supports.