Natural Frequencies of a Cracked Beam Coupled with a Compressible Sloshing Fluid

This article describes studies into the flexural vibration of a cracked cantilevered beam in contact with a non-viscous fluid. The crack has been represented by a mass-less rotational spring, the flexibility of which has been calculated using linear fracture mechanics. The coupled system is subject to undisturbed boundary condition at infinity in the fluid domain. A range of different boundary conditions have been analysed such as both incompressible and compressible fluid, with and without sloshing. Various crack sizes and positions have been considered in order to assess the effect of damage in the fluid-structure interaction problem

Detecting mode-shape discontinuities without differentiation - Examining a Gaussian process approach

Detecting damage by inspection of mode-shape curvature is an enticing approach which is hindered by the requirement to differentiate the inferred mode-shape. Inaccuracies in the inferred mode-shapes are compounded by the numerical differentiation process; since these small inaccuracies are caused by noise in the data, the method is untenable for most real situations. This publication proposes a new method for detecting discontinuities in the smoothness of the function, without directly calculating the curvature i.e. without differentiation. We present this methodology and examine its performance on a finite element simulation of a cracked beam under random excitation. In order to demonstrate the advantages of the approach, increasing amounts of noise are added to the simulation data, and the benefits of the method with respect to simple curvature calculation is demonstrated. The method is based upon Gaussian Process Regression, a technique usually used for pattern recognition and closely related to neural network approaches. We develop a unique covariance function, which allows for a non-smooth point. Simple optimisation of this point (by complete enumeration) is effective in detecting the damage location. We discuss extensions of the technique (to e.g. multiple damage locations) as well as pointing out some potential pitfall

Non-destructive testing on aramid fibres for the long-term assessment of interventions on heritage structures

High strength fibre reinforced polymers (FRPs) are composite materials made of fibres such as carbon, aramid and/or glass, and a resin matrix. FRPs are commonly used for structural repair and strengthening interventions and exhibit high potential for applications to existing constructions, including heritage buildings. In regard to aramid fibres, uncertainties about the long-term behaviour of these materials have often made the designers reluctant to use them in structural engineering. The present study describes simple and non-destructive nonlinearity tests for assessing damage or degradation of structural properties in Kevlar fibres. This was obtained by using high precision measurements to detect small deviations in the dynamic response measured on fibres and ropes. The change in dynamic properties was then related to a damage produced by exposure of the sample to UV rays for a defined time period, which simulated long-term sun exposure. In order to investigate the sensitivity of such an approach to damage detection, non-linearity characterisation tests were conducted on aramid fibres in both damaged and undamaged states. With the purpose of carrying out dynamic tests on small fibre specimens, a dedicated instrumentation was designed and built in cooperation with the Metrology Laboratory of the Department of Electronics at the Politecnico di Torino

uncertainty bounds on higher order frfs from gaussian process narx models

One of the most versatile and powerful algorithms for the identification of nonlinear dynamical systems is the NARMAX (Nonlinear Auto-regressive Moving Average with eXogenous inputs) approach. The model represents the current output of a system by a nonlinear regression on past inputs and outputs and can also incorporate a nonlinear noise model in the most general case. In recent papers, one of the authors introduced a NARX (no noise model) formulation based on Gaussian Process (GP) regression and derived the corresponding expressions for Higher-order Frequency Response Functions (HFRFs). This paper extends the theory for the GP-NARX framework by providing a means of converting the GP prediction bounds in the time domain into bounds on the HFRFs. The approach is demonstrated on the Duffing oscillator

Influence of the patellar button thickness on the knee flexion after total knee arthroplasty

Purpose: One of the main problems of knee replacement is the limit of knee flexion. This study focuses on the knee implant and the patellar component currently in use in total knee arthroplasty, analyzing the influence of patellar thickness on the degree of knee flexion following surgery. Methods: A kinematics study was performed to evaluate whether an optimal patellar thickness can be identified, which enables the maximum flexion angle to be achieved. Using TC images, a healthy model was built. On this basis, a model of a knee joint which had undergone total knee arthroplasty using a Legion PS prosthesis was constructed. Initially, the standard thickness of patellar implant (9 mm) was used to build the model; then several different patellar implant thicknesses (in the range of 5–15 mm) were analyzed. Results: The results show a non-linear trend: a button thickness of less than 9 mm does not change the flexion angle, whereas a button thickness of over 9 mm results in a loss of flexion. The flexion loss is significant in the first two additions of thicknesses but negligible in the last ones. Conclusions: In the case studied, flexion reduction is not linearly proportional to the patellar thickness. The outcome of total knee arthroplasty is considered to be satisfactory with the standard patellar button. The results of this study could be used to compare the kinematics with other total prosthesis and patellar implants, and should enable the optimization of the patellar residue bone thickness to obtain deep flexion

Video processing techniques for the contactless investigation of large oscillations

The experimental acquisition of large vibrations presents various technical difficulties. Especially in the case of geometric nonlinearities, dealing with very flexible, very light structures causes minimal variations in mass or stiffness to affect severely the dynamical response. Thus, sensors' added masses change the behaviour of the structure with respect to the unloaded condition. Moreover, the most common tools regularly employed for acquisition in vibration analysis - that is to say, laser vibrometers and accelerometers - are often designed with small amplitudes in mind. Their recordings are known to lack accuracy when the investigated structure undergoes large or very large motions, due to geometrical reasons. Image-based measurement techniques offer a valid solution to this problem. Here, an ensemble of three video processing techniques are benchmarked against each other and tested as viable options for the non-contact dynamic characterisation of slender beam-like structures. The methods have been applied to the case study of an aluminium spar for a highly-flexible airwing prototype and compared to the measurements recorded by a laser velocimeter and several Raspberry PI Inertial Measurement Units (IMUs), which also proved to be minimally invasive

Using video processing for the full-field identification of backbone curves in case of large vibrations

Nonlinear modal analysis is a demanding yet imperative task to rigorously address real-life situations where the dynamics involved clearly exceed the limits of linear approximation. The specific case of geometric nonlinearities, where the effects induced by the second and higher-order terms in the strain–displacement relationship cannot be neglected, is of great significance for structural engineering in most of its fields of application—aerospace, civil construction, mechanical systems, and so on. However, this nonlinear behaviour is strongly affected by even small changes in stiffness or mass, e.g., by applying physically-attached sensors to the structure of interest. Indeed, the sensors placement introduces a certain amount of geometric hardening and mass variation, which becomes relevant for very flexible structures. The effects of mass loading, while highly recognised to be much larger in the nonlinear domain than in its linear counterpart, have seldom been explored experimentally. In this context, the aim of this paper is to perform a noncontact, full-field nonlinear investigation of the very light and very flexible XB-1 air wing prototype aluminum spar, applying the well-known resonance decay method. Video processing in general, and a high-speed, optical target tracking technique in particular, are proposed for this purpose; the methodology can be easily extended to any slender beam-like or plate-like element. Obtained results have been used to describe the first nonlinear normal mode of the spar in both unloaded and sensors-loaded conditions by means of their respective backbone curves. Noticeable changes were encountered between the two conditions when the structure undergoes large-amplitude flexural vibrations