A method for detection and characterisation of structural non-linearities using the Hilbert transform and neural networks

This paper presents a method for detection and characterization of structural non-linearities from a single frequency response function using the Hilbert transform in the frequency domain and arti cial neural networks. A frequency response function is described based on its Hilbert transform using several common and newly introduced scalar parameters, termed non-linearity indexes, to create training data of the artificial neural network. This network is subsequently used to detect the existence of non-linearity and classify its type. The theoretical background of the method is given and its usage is demonstrated on di erent numerical test cases created by single degree of freedom non-linear systems and a lumped parameter multi degree of freedom system with a geometric non-linearity. The method is also applied to several experimentally measured frequency response functions obtained from a cantilever beam with a clearance non-linearity and an under-platform damper experimental rig with a complex friction contact interface. It is shown that the method is a fast and noise-robust means of detecting and characterizing non-linear behaviour from a single frequency response function

On the effects of roughness on the nonlinear dynamics of a bolted joint: a multiscale analysis

Accurate prediction of the vibration response of friction joints is of great importance when estimating both the performance and the life of build-up structures. The contact conditions at the joint interface, including local normal load distribution and contact stiffness, play a critical role in the nonlinear dynamic response. These parameters strongly depend on the mating surfaces, where the surface roughness is well known to have a significant impact on the contact conditions in the static case. In contrast, its effects on the global and local nonlinear dynamic response of a build-up structure is not as well understood due to the complexity of the involved mechanisms. To obtain a better understanding of the dependence of the nonlinear dynamic response on surface roughness, a newly proposed multiscale approach has been developed. It links the surface roughness to the contact pressure and contact stiffness, and in combination with a multiharmonic balance solver, allows to compute the nonlinear dynamic response for different interface roughness. An application of the technique to a single bolted lap joint highlighted a strong impact of larger roughness values on the pressure distribution and local contact stiffness and in turn on the nonlinear dynamic response

Identification of complex non-linear modes of mechanical systems using the Hilbert-Huang transform from free decay responses

Modal analysis is a well-established method for analysis of linear systems, but its extension to non-linear structures has proven to be much more problematic. Several competitive definitions of non-linear modes and a variety of experimental methods have been introduced. In this paper, the definition of complex non-linear modes (CNMs) of mechanical systems is adopted and the possibility of their identification from experimental free decay responses using the Hilbert-Huang transform (HHT) is explored. It is firstly discussed that since there are similarities in the definition of intrinsic mode functions obtained using the HHT and reduced order model of slow-flow dynamics based on the CNMs, there is a reason to believe that the HHT can indeed extract the CNMs. This paper, however, presents a new insight into the use of the Hilbert-Huang transform by showing that the amplitude-dependent frequency and damping extracted from a free decay response are only suitable for detection and characterisation of non-linearities, but they cannot be used to quantify the non-linear behaviour by fitting the CNMs even if a model of the system is known. The analytical proof of the HHT cannot be currently formulated due to a limited understanding of its empirical nature. Instead, this unconventional conclusion is supported by a series of numerical studies of conservative and non-conservative non-linear systems with a wide range of parameters. In all cases, a special care is taken to apply the basic HHT only on such signals for which mode separation is possible (no mode-mixing occurs). This eliminates the need for more sophisticated HHT versions and clearly demonstrates the inability of the HHT to extract CNMs even for the simplest cases. In addition to numerical studies, the identification of several non-linear modes is demonstrated experimentally using the free decay responses obtained from the ECL benchmark. It is shown that the HHT is able to successfully extract several non-linear modes whose character correspond to the numerical reference, but which cannot be used to quantify the system parameters due to conclusions made in this paper. The findings highlight that the ability of the HHT to quantify non-linear behaviour using non-linear modes extracted from free decay responses is severely limited, while detection and characterisation of non-linear behaviour in a non-parametric manner is feasible

Output-Only Modal Analysis Using Continuous-Scan Laser Doppler Vibrometry and Application to a 20kW Wind Turbine

Continuous-scan laser Doppler vibrometry (CSLDV) is a method whereby one continuously sweeps the laser measurement point over a structure while measuring, in contrast to the conventional scanning LDV approach where the laser spot remains stationary while the response is collected at each point. The continuous-scan approach can greatly accelerate measurements, allowing one to capture spatially detailed mode shapes along a scan path in the same amount of time that is typically required to measure the response at a single point. The method is especially beneficial when testing large structures, such as wind turbines, whose natural frequencies are very low and hence require very long time records. Several CSLDV methods have been presented that employ harmonic excitation or impulse excitation, but no prior work has performed CSLDV with an unmeasured, broadband random input. This work extends CSLDV to that class of input, developing an output-only CSLDV method (OMA-CSLDV). This is accomplished by adapting a recently developed algorithm for linear time-periodic systems to the CSLDV measurements, which makes use of harmonic power spectra and the harmonic transfer function concept developed by Wereley. 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 natural frequencies and mode shapes are extracted from the harmonic power spectrum of the vibrometer signal and show good agreement with the first seven analytically-derived modes of the beam. The method is then applied to identify the shapes of several modes of a 20kW wind turbine using a ground based laser and with only a light breeze providing excitation.

Cross-disc coupling in a flexible shaft–disc assembly in presence of asymmetric axial–radial bearing supports

In a flexible shaft–disc assembly supported by linear bearings, the disc 1 Nodal Diameter (ND) modes are known to couple with the shaft lateral (bending) modes, whilst the 0ND modes can couple with the shaft axial modes. In addition to these well known coupling phenomena, a previous work by the authors has shown that, in presence of an asymmetric axial–radial bearing supporting structure, shaft axial and lateral modes can interact and lead to a coupling with a single flexible disc 0 and 1 ND modes simultaneously. Given that in most circumstances a shaft carries more than one disc, this work extends the previous findings to a shaft carrying two flexible discs and particularly investigates the mechanisms of cross disc coupling due to an asymmetric supporting structure. A full 3D FEM model of the assembly has been developed to model its dynamic behaviour. New classes of coupled modes involving the shaft and the two discs have been identified and a physical explanation will be provided, considering forces/moments applied at the interface amongst subcomponents and following the hypothesis that each disc acts like an independent dynamic absorber. A parametric study of the dual discs arrangement varying stiffness, thickness and position of one disc further highlighted the dynamic interaction of the subcomponents. Specific arrangements will allow an Engine Order forcing pattern applied to one disc to excite a different mode on the other disc, with the shaft and the supports acting as the vibration energy transmitter between the two discs. The industrial implications of such phenomena are also discussed throughout this work

Honeycomb elastic material properties: A review of some existing theories and a new dynamic approach

The influence of the nine orthotropic material properties of honeycomb on the dynamic response of a finite element model of a simple supported sandwich plate are examined. Fifteen available theories from the literature for the material properties of honeycomb are reviewed and their values calculated for a Hex Web 5.2-1/4-25(3003) Aluminium core. The agreement between the theoretical material properties and the major ASTM (American Society for Testing and Materials) standard test methods is investigated. A new and simple technique is described for measuring the dynamic shear moduli of honeycomb materials and its values are compared with those presented in the literature

A method for non-parametric identification of non-linear vibration systems with asymmetric restoring forces from a resonant decay response

© 2018 Elsevier Ltd A method for non-parametric identification of systems with asymmetric non-linear restoring forces is proposed in this paper. The method, named the zero-crossing method for systems with asymmetric restoring forces (ZCA), is an extension of zero-crossing methods and allows identification of backbones, damping curves and restoring elastic and dissipative forces from a resonant decay response. The validity of the proposed method is firstly demonstrated on three simulated resonant decay responses of the systems with off-centre clearance, bilinear and quadratic stiffness. Then, the method is applied to experimental data from a micro-electro-mechanical resonator in order to quantify its non-linear damping and stiffness effects. Throughout the paper the proposed method is also compared with the Hilbert vibration decomposition to demonstrate that the ZCA yields more accurate results with much less effort

The dynamic behaviour of mulifunctional power strucutres

New design approaches will be required to increase the payload to mass fraction for future satellite generations. The multifunctional design concept, where spacecraft subsystems are integrated into the load bearing structure of the satellite, is one considered technology. This paper describes the design, analysis and manufacture of a particular multifunctional power structure with a special focus on its dynamic response. An analytical and a finite element analysis of ten proposed multifunctional power structures, based on a sandwich panel configuration, are presented. The theoretical out-of-plane material properties for the investigated designs are derived with the help of the virtual displacement method. These theoretical properties are compared to finite element models and subsequently used in a parameter optimisation of the dynamic response of the ten introduced sandwich panels. The optimisation allows the identification of the most favourable multifunctional power structure. The experimental dynamic response of a manufactured multifunctional power panel is presented and compared to a conventional honeycomb panel for a successful evaluation of the introduced multifunctional approach. The results of this work show the ability of the presented multifunctional design to successfully combine the structural and power storage functions which makes the multifunctional power structure an excellent design approach for future space missions

The dynamic behaviour of mulifunctional power strucutres

New design approaches will be required to increase the payload to mass fraction for future satellite generations. The multifunctional design concept, where spacecraft subsystems are integrated into the load bearing structure of the satellite, is one considered technology. This paper describes the design, analysis and manufacture of a particular multifunctional power structure with a special focus on its dynamic response. An analytical and a finite element analysis of ten proposed multifunctional power structures, based on a sandwich panel configuration, are presented. The theoretical out-of-plane material properties for the investigated designs are derived with the help of the virtual displacement method. These theoretical properties are compared to finite element models and subsequently used in a parameter optimisation of the dynamic response of the ten introduced sandwich panels. The optimisation allows the identification of the most favourable multifunctional power structure. The experimental dynamic response of a manufactured multifunctional power panel is presented and compared to a conventional honeycomb panel for a successful evaluation of the introduced multifunctional approach. The results of this work show the ability of the presented multifunctional design to successfully combine the structural and power storage functions which makes the multifunctional power structure an excellent design approach for future space missions