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The objective of this publication is to propose a novel technique for black-box identification of structures with geometric nonlinearity. The technique is based on a recently introduced frequency-domain system identification method called Nonlinear Identification through eXtended Outputs (NIXO). The proposed algorithm first expresses the nonlinear part of modal equation of motion (EOM) as a general polynomial of high order, and then removes the terms which are determined to be irrelevant to the mechanical system's response. This division into dominant and irrelevant nonlinear terms relies on the values of two novel indicators that are particular to NIXO. The heuristic presented here was observed to work well only when the tested structure is excited with various swept-sine input signals of different magnitudes (so that the system oscillates at sufficiently distinctive amplitudes in different experimental tests). The technique is first demonstrated on a noise-free numerical case study employing a reduced model of a curved beam. The results obtained are verified via comparing the true Nonlinear Normal Mode (NNM) to the one computed using the modal EOM pointed out by NIXO. Then the method is demonstrated on experimental measurements collected on a 3D-printed flat beam exhibiting significant natural frequency shifts, and the outcomes are verified by overlaying the identified NNMs on the swept-sine responses. [ABSTRACT FROM AUTHOR]

This work presents a novel technique for nonlinear system identification that operates in the frequency domain and fits a model to measured spectra to estimate the parameters in a modal domain nonlinear equation of motion (EOM). Nonlinear terms are added to the linear EOM in the form of polynomials, and the proposed algorithm estimates the polynomial coefficients as well as the underlying linear Frequency Response Function (FRF). This method is an extension to a popular nonlinear system identification algorithm called NIFO, from Nonlinear Identification through Feedback of the Outputs. However, NIFO identifies the nonlinear parameters as complex numbers that may be different at each frequency line, even though the mechanical system is expected to be governed by an EOM in which the nonlinear parameters are real and constant with frequency. This might be problematic, because any variation in the identified nonlinear parameters will distort the linear FRFs estimated by NIFO, and those linear FRFs are important to tell the user whether all of the significant nonlinearity has been extracted from the system. The proposed algorithm, here dubbed Nonlinear Identification through eXtended Outputs (NIXO), estimates the nonlinear parameters as frequency-independent and real. Additionally, it is demonstrated that for the systems studied here that the algorithm works when random and swept-sine inputs are used to excite the tested structure, while NIFO only worked well when random inputs were used. The method is first evaluated numerically using benchmark case studies, starting with the SDOF equation and then reduced models of a clamped-clamped flat beam, and the results are compared to those obtained with NIFO. Then the algorithm is applied to swept-sine measurements from a 3D-printed flat beam and the results are validated by computing the primary nonlinear normal mode of the identified model and comparing it with measurements. [ABSTRACT FROM AUTHOR]

Abstract: Continuous-Scan Laser Doppler Vibrometry (CSLDV) is a technique where the measurement point continuously sweeps over a structure while measuring, capturing both spatial and temporal information. The continuous-scan approach can greatly accelerate measurements, allowing one to capture spatially detailed mode shapes in the same amount of time that conventional methods require to measure the response at a single point. The method is especially beneficial when testing large structures, such as wind turbines, that have low natural frequencies and hence may require very long time records at each measurement point. Several CSLDV methods have been presented that use sinusoidal excitation or impulse excitation, but CSLDV has not previously been employed with an unmeasured, broadband random input. This work extends CSLDV to that class of input, developing an Output-only Modal Analysis method (OMA-CSLDV). A recently developed algorithm for linear time-periodic system identification, which makes use of harmonic power spectra and the harmonic transfer function concept developed by Wereley [17], is used in conjunction with CSLDV measurements. One key consideration, the choice of the scan frequency, is explored. The proposed method is validated on a randomly excited free-free beam, where one-dimensional mode shapes are captured by scanning the laser along the length of the beam. The first seven natural frequencies and mode shapes are extracted from the harmonic power spectrum of the vibrometer signal and show good agreement with the analytically-derived modes of the beam. The method is then applied to identify the mode shapes of a parked 20kW wind turbine using a ground based laser and with only a light breeze providing excitation. [Copyright &y& Elsevier]

This work presents a new technique for nonlinear system identification that utilizes near-resonant steady-state harmonically excited vibration measurements to estimate the Nonlinear Normal Mode backbones. The algorithm is based on the previously proposed Single Nonlinear Resonant Mode formula and uses it in a new and more effective way to estimate one point on the nonlinear mode from only one steady-state measurement collected near the resonance. A by-product of this work is a derivation of a novel formula expressing how the damping ratio changes with the motion amplitude. Several measurements at various forcing amplitudes can be combined to estimate the nonlinear mode and damping as a function of amplitude, which can be further used to predict the forced steady-state response of the structure in the vicinity of the mode of interest. Compared to existing phase resonance methods, the proposed technique can reduce the time required to obtain measurements and avoids difficulties due to e.g. the premature jump phenomenon. The algorithm assumes that the modes are well-separated and no internal resonances are present in the system. Additionally, it requires the accurate identification of linear modes in the low-amplitude vibration tests and it assumes that the nonlinear normal mode shape does not change significantly with response amplitude The method is first evaluated numerically using reduced models of clamped–clamped flat and curved beams that exhibit both stiffening and softening–stiffening responses, respectively. Then the method is employed experimentally to measure the NNM backbones of beams that were manufactured from polylactide using a 3D printer and experience significant eigen-frequency shifts when the motion amplitude increases. The results are validated against measurements collected using the traditional phase resonance testing approach. • A new technique to utilize the Single Nonlinear Resonant Mode formula is presented. • The method uses near-resonant steady-state measurements to estimate the Nonlinear Normal Modes of a structure. • A novel formula expressing how the damping ratio changes with the motion amplitude is derived. • The experimental data is collected with a phase resonance method. • The method is applied to identify the NNMs of 3D printed flat and curved beams. [ABSTRACT FROM AUTHOR]

Abstract: An extension of the inverse structural filter (ISF) force reconstruction algorithm is presented that utilizes data from multiple time steps simultaneously to improve the accuracy and robustness of the ISF. The ISF algorithm uses a discrete-time system model of a structure and the measured response to estimate the forces causing the response. The proposed algorithm, dubbed the delayed, multi-step ISF (DMISF), is compared with the original ISF and with the sum of weighted accelerations technique (SWAT) and the classical frequency domain (FD) inverse method in terms of both accuracy and sensitivity to errors in the forward system model. The SWAT and ISF algorithms are capable of estimating the forces acting on a structure in real time, or when time data is available over such a short duration that FD methods cannot be applied effectively. The new DMISF can be created from a forward system model identified by any standard modal analysis algorithm, so one can leverage expertise with a particular system identification methodology. In contrast, the previously presented ISF was derived directly from experimental data using a proscribed technique. The theory behind the algorithms is presented, after which their performance is demonstrated using laboratory test data. The results of a Monte Carlo simulation are also presented, illustrating the nature of the sensitivity of the methods to errors in the modal parameters of the forward system. The DMISF algorithm is shown to yield a stable inverse system for the structure of interest whereas the traditional ISF is unstable, and hence gives erroneous estimates of the input forces. [Copyright &y& Elsevier]

Although flip chips have received wide acceptance as an integrated circuit package, significant manufacturing problems exist with the integrity of the connection between the package and the printed circuit board (PCB). Conventional X-ray, ultrasonic and electronic testing systems have been used to assess the integrity of this connection, however, none of these have proven suitable for detecting open solder bumps between the chip and the board. The inability to detect open solder bumps with traditional methods merits the investigation of new, nondestructive methods for detecting defects in a manufacturing environment. This work assesses the feasibility of monitoring the vibration characteristics of flip chips to detect open solder joints. Test vehicles with open solder joints were created, and a nondestructive laser ultrasonic system was used to measure the free vibration response of the chips attached to the printed circuit board. The algorithm of mode isolation (AMI) was applied to the vibration response data in order to extract the modal parameters of the chip. The statistical differences between the modal parameters of sets of damaged and undamaged chips were assessed, revealing the ability of the method to determine the location and severity of these defects in the presence of experimental scatter and manufacturing variation. The parameters of the first mode of vibration, especially its mode shape, were found to be much more sensitive to damage than those of a higher frequency mode. [ABSTRACT FROM AUTHOR]

• Two different nonlinear models are identified for two experimental test rigs. • The models are used to predict dynamic behavior under sine (-sweep) excitations. • The modal model is accurate for sine excitation close to resonance. • The modal model is sensitive for uncontrolled sweeps if the excitation force drops. • Polynomial nonlinear state-space models highly depend on the used training data. In the present paper, two existing nonlinear system identification methodologies are used to identify data-driven models. The first methodology focuses on identifying the system using steady-state excitations. To accomplish this, a phase-locked loop controller is implemented to acquire periodic oscillations near resonance and construct a nonlinear-mode model. This model is based on amplitude-dependent modal properties, i.e. does not require nonlinear basis functions. The second methodology exploits uncontrolled experiments with broadband random inputs to build polynomial nonlinear state-space models using advanced system identification tools. The methods are applied to two experimental test rigs, a magnetic cantilever beam and a free-free beam with a lap joint. The respective models obtained by either method for both specimens are then challenged to predict dynamic, near-resonant behavior observed under different sine and sine-sweep excitations. The vibration prediction of the nonlinear-mode and state-space models clearly highlight capabilities and limitations. The nonlinear-mode model, by design, yields a perfect match at resonance peaks and high accuracy in close vicinity. However, it is limited to well-spaced modes and sinusoidal excitation. The state-space model covers a wider dynamic range, including transient excitations. However, the real-life nonlinearities considered in this study can only be approximated by polynomial basis functions. Consequently, the identified state-space models are found to be highly input-dependent, in particular for sinusoidal excitations where they are found to lead to a low predictive capability. [ABSTRACT FROM AUTHOR]