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

Linear modal analysis of L-shaped beam structures: parametric studies

Linear modal analysis of L-shaped beam structures indicates that there are two independent motions, these are in-plane bending and out of plane motions including bending and torsion. Natural frequencies of the structure can be determined by finding the roots of two transcendental equations which correspond to in-plane and out-of-plane motions. Due to the complexity of the equations of motion the natural frequencies cannot be determined explicitly. In this article we nondimensionalise the equations of motion in the space and time domains, and then we solve the transcendental equations for selected values of the L-shaped beam parameters in order to determine their natural frequencies. We use a numerical continuation scheme to perform the parametric solutions of the considered transcendental equations. Using plots of the solutions we can determine the natural frequencies for a specific L-shape beam configuration

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

On the design of external excitations in order to make nonlinear oscillators respond as free oscillators of the same or different type

This study deals with nonlinear oscillators whose restoring force has a polynomial nonlinearity of the cubic or quadratic type. Conservative unforced oscillators with such a restoring force have closed-form exact solutions in terms of Jacobi elliptic functions. This fact can be used to design the form of the external elliptic-type excitation so that the resulting forced oscillators also have closed-form exact steady-state solutions in terms of these functions. It is shown how one can use the amplitude of such excitations to change the way in which oscillators behave, making them respond as free oscillators of the same or different type. Thus, in cubic oscillators, a supercritical or subcritical pitchfork bifurcation can appear, whilst in quadratic oscillators, a transcritical bifurcation can take place

Motorised momentum exchange space tethers : the dynamics of asymmetrical tethers and some recent new applications

This paper reports on a first attempt to model the dynamics of an asymmetrical motorised momentum exchange tether for spacecraft payload propulsion, and it also provides some interesting summary results for two novel applications for motorised momentum exchange tethers. The asymmetrical tether analysis is very important because it represents the problematic scenario when payload mass unbalance intrudes, due to unexpected payload loss or failure to retrieve. Mass symmetry is highly desirable both dynamically and logistically, but it is shown in this paper that there is still realistic potential for mission rescue should an asymmetry condition arise. Conceptual designs for tethered payload release from LEO and lunar tether delivery and retrieval are also presented as options for future development