Vibration-based damage detection in an aircraft wing scaled model using principal component analysis and pattern recognition

This study deals with vibration-based fault detection in structures and suggests a viable methodology based on principal component analysis (PCA) and a simple pattern recognition (PR) method. The frequency response functions (FRFs) of the healthy and the damaged structure are used as initial data. A PR procedure based on the nearest neighbour principle is applied to recognise between the categories of the damaged and the healthy wing data. A modified PCA method is suggested here, which not only reduces the dimensionality of the FRFs but in addition makes the PCA transformed data from the two categories more differentiable. It is applied to selected frequency bands of FRFs which permits the reduction of the PCA transformed FRFs to two new variables, which are used as damage features. In this study, the methodology is developed and demonstrated using the vibration response of a scaled aircraft wing simulated by a finite element (FE) model. The suggested damage detection methodology is based purely on the analysis of the vibration response of the structure. This makes it quite generic and permits its potential development and application for measured vibration data from real aircraft wings as well as for other real and complex structures

Nonlinear modal analysis of an L-shape beam structure

In this work it is derived the nonlinear equations of motion of L-shaped beam structure considering rotary inertia terms for out-of-plane motion in order to be used for nonlinear modal analysis of the structure. The dynamics has been projected in the infinite mode shapes space and it is derived the equations of motion in generalized coordinates. The nonlinear equations of motion indicates that there is coupling between in-plane and out-of-plane motions which in linear case is not the case

Lense-Thirring Precession - Theoretical Narrative

We start with the premise that an inertial frame is defined as one that isn’t accelerating in the usual detectable sense. General Relativity states that inertial frames are 'influenced and dragged by the distribution and flow of mass–energy in the universe', noting the relativistic equivalence of mass and energy [1]. This dragging of inertial frames is simply called frame dragging and is shown conceptually in Figure 1. Frame dragging also influences the flow of time around a spinning body

Contact model for elastoplastic analysis of half-space indentation by a spherical impactor

This paper presents a new contact model for analysis of post-yield indentation of a half-space target by a spherical indenter. Unlike other existing models, the elastoplastic regime of the present model was modelled using two distinct force–indentation relationships based on experimentally and theoretically established indentation characteristics of the elastoplastic regime. The constants in the model were derived from continuity conditions and indention theory. Simulations of the present model show good prediction of experimental data. Also, an approach for determining the maximum contact force and indentation of an elastoplastic half-space from the impact conditions has been proposed

Linear modal analysis of L-shaped beam structures

In this article a theoretical linear modal analysis of Euler-Bernoulli L-shaped beam structures is performed by solving two sets of coupled partial differential equations of motion. The first set, with two equations, corresponds to in-plane bending motions whilst the second set with four equations corresponds to out-of-plane motions with bending and torsion. The case is also shown of a single cantilever beam taking into account rotary inertia terms. At first for the case of examination of the results for the L-shaped beam structure, an individual modal analysis is presented for four selected beams which will be used for modelling an L-shaped beam structure; in order to investigate the influence of rotary inertia terms and shear effects. Then, a theoretical and numerical modal analysis is performed for four models of the L-shaped beam structure consisting of two sets of beams, in order to examine the effect of the orientation of the secondary beam (oriented in two ways) and also shear effects. The comparison of theoretical and finite element simulations shows a good agreement for both in-plane and out-of-plane motions, which validates the theoretical analysis. This work is essential to make progress with new investigations into the nonlinear equations for the L-shaped beam structures within Nonlinear Normal Mode theory

Towards linear modal analysis for an L-shaped beam: equations of motion

We consider an L-shaped beam structure and derive all the equations of motion considering also the rotary inertia terms. We show that the equations are decoupled in two motions, namely the in-plane bending and out-of-plane bending with torsion. In neglecting the rotary inertia terms the torsional equation for the secondary beam is fully decoupled from the other equations for out-of-plane motion. A numerical modal analysis was undertaken for two models of the L-shaped beam, considering two different orientations of the secondary beam, and it was shown that the mode shapes can be grouped into these two motions: in-plane bending and out-of-plane motion. We compared the theoretical natural frequencies of the secondary beam in torsion with finite element results which showed some disagreement, and also it was shown that the torsional mode shapes of the secondary beam are coupled with the other out-of-plane motions. These findings confirm that it is necessary to take rotary inertia terms into account for out-of-plane bending. This work is essential in order to perform accurate linear modal analysis on the L-shaped beam structure

Review of: "Speed of gravity: a simple experiment to test the general relativity theory"

Gravitational wave experiments are based firmly in classical physics, which in turn is based on Einstein’s premise for general relativity whereby the speed of light is a universal constant. There have been several attempts to create theoretical models in which the speed of light is not necessarily constant, notably and firstly by Dicke in 1957. As far as I know predictions from the various variable speed of light models have not actually undermined the underlying principles behind the various tests of GR that have been devised, however that in itself doesn’t disprove or rule out the validity of variable speed of light models, nor does it imply any possible future invalidation of the various tests of GR that have been undertaken. It’s also important to distinguish between theoretical modelling assumptions and the actual physical propagation speed of photons when questioning experimental techniques for measurement such as LIGO. Variable speed of light modelling may predict the actual propagation speed of photons correctly, or not, but the actual propagation speed of photons in different physical contexts also needs to be demonstrated in a categorical experiment to support any variable speed of light model. The argument of the paper appears to be that because there have been, and are, theoretical models which propose variable speed of light effects in some circumstances, then there is a basis for not believing the results from the LIGO experiments for the measurement of gravitational waves, despite those experiments being based on classical physics (which has not been disproved in this context). A response to that could be that it would be better to expand in more detail on a plausible theoretical basis for an experiment (for example the experiment proposed in this paper) that moves us closer to confirming the ultimate truth of variable speed of light models and their applicability, and importantly that this is the case within the ‘stretched and contracted spaces’ referred to. The paper introduces a thought experiment that might be developed but doesn’t elaborate on it in any detail. So, it seems to me that the stronger argument is one based on an experimental proof that variable speed of light can be the case in some circumstances, and then to do that specifically for the circumstance of the ‘stretched and contracted spaces’, rather than saying that because variable speed of light may be a physical fact in some circumstances that this possibility then invalidates LIGO

Stabilising high energy orbit oscillations by the utilisation of centrifugal effects for rotating-tyre-induced energy harvesting

Nonlinear energy harvesters are frequently considered in preference to linear devices because they can potentially overcome the narrow frequency bandwidth limitations inherent to linear variants however, the possibility of variable harvesting efficiency is raised for the nonlinear case. This paper proposes a rotational energy harvester which may be fitted into an automobile tyre, with the advantage that it may broaden the rotating frequency bandwidth and simultaneously stabilise high-energy orbit oscillations. By consideration of the centrifugal effects due to rotation, the overall restoring force will potentially be increased for a cantilever implemented within the harvester, and this manifests as an increase in its equivalent elastic stiffness. In addition, this study reveals that the initial potential well barriers become as shallow as those for a bistable system. When the rotational frequency increases beyond an identifiable boundary frequency, the system transforms into one with a potential barrier of a typical monostable system. On this basis, the inter-well motion of the bistable system can provide sufficient kinetic energy so that the cantilever maintains its high-energy orbit oscillation for monostable hardening behaviour. Furthermore, in a vehicle drive experiment, it has been shown that the effective rotating frequency bandwidth can be widened from 15 km/h-25 km/h to 10 km/h-40 km/h. In addition, it is confirmed that the centrifugal effects can improve the harvester performance, producing a mean power of 61 μW at a driving speed of 40 km/h, and this is achieved by stabilising the high-energy orbit oscillations of the rotational harvester

Stabilisation of the high energy orbit for a nonlinear energy harvester with variable damping

The non-linearity of a hardening-type oscillator provides a wider bandwidth and a higher energy harvesting capability under harmonic excitations. Also, both low- and high-energy responses can coexist for the same parameter combinations at relatively high excitation levels. However, if the oscillator’s response happens to coincide with the low-energy orbit then the improved performance achieved by the non-linear oscillator over that of its linear counterpart, could be impaired. This is therefore the main motivation for stabilisation of the high-energy orbit. In the present work, a schematic harvester design is considered consisting of a mass supported by two linear springs connected in series, each with a parallel damper, and a third-order non-linear spring. The equivalent linear stiffness and damping coefficients of the oscillator are derived through variation of the damper element. From this adjustment the variation of the equivalent stiffness generates a corresponding shift in the frequency–amplitude response curve, and this triggers a jump from the low-energy orbit to stabilise the high-energy orbit. This approach has been seen to require little additional energy supply for the adjustment and stabilisation, compared with that needed for direct stiffness tuning by mechanical means. Overall energy saving is of particular importance for energy harvesting applications. Subsequent results from simulation and experimentation confirm that the proposed method can be used to trigger a jump to the desirable state, thereby introducing a beneficial addition to the performance of the non-linear hardening-type energy harvester that improves overall efficiency and broadens the bandwidth

Dynamics of an omnidirectional pendulum energy harvester : a comparative analysis between numerical and experimental results

The spherical pendulum is a mathematically interesting model that has been studied extensively in the past. In the field of energy harvesting however, the pendulum energy harvesters are generally confined to planar motions. This minimisation of the available degrees of freedom potentially limits the areas of application of the energy harvester, and certainly its overall capability. In this work an omnidirectional pendulum energy harvester is proposed in the form of a two degree of freedom system which has the potential to harvest energy from motions along the three axes of translation and from the three corresponding rotations about those axes. The dynamics of such an energy harvester are examined experimentally for different power take-off modes and are subsequently compared to numerical predictions from an analytical model. An optimal operational point is proposed for the harvester and it is shown how an up-sweep and down-sweep of the excitation frequency can significantly broaden the operational range of the energy harvester by up to 130%