Stochastic modelling and updating of a joint contact interface

Dynamic properties of the contact interfaces in joints and mechanical connections have a great influence on the overall dynamic properties of assembled structures. Uncertainty and nonlinearity are two major effects of contact interfaces which introduce challenges in accurate modeling. Randomness in surface roughness quality, surface finish and contact preload are the main sources of variability in the contact interfaces. On the other side, slip and slap are two mechanisms responsible for nonlinear behavior of joints. Stochastic linear/nonlinear models need to be developed for such uncertain structures to be used in dynamic response analysis or system parameter identification. In this paper, variability in linear behavior of an assembled structure containing a bolted lap-joint is investigated by using experimental results. A stochastic model is then constructed for the structure by employing a stochastic generic joint model and the uncertainty in the joint model parameters is identified by using a Bayesian identification approach

Rotational and ply-level uncertainty in response of composite shallow conical shells

This paper presents the quantification of rotational and ply level uncertainty of random natural frequency for laminated composite conical shells by using surrogate modeling approach. The stochastic eigenvalue problem is solved by using QR iteration algorithm. Sensitivity analysis is carried out to address the influence of different input parameters on the output natural frequencies. The sampling size and computational cost is reduced by employing the present approach compared to direct Monte Carlo simulation. The stochastic mode shapes are also depicted for a typical laminate configuration. Statistical analysis is presented to illustrate the results and its performance

Aircraft turbulence and gust identification using simulated in-flight data

Gust and turbulence events are of primary importance for the analysis of flight incidents, for the design of gust load alleviation systems and for the calculation of loads in the airframe. Gust and turbulence events cannot be measured directly but they can be obtained through direct or optimisation-based methods. In the direct method the discretisation of the Fredholm Integral equation is associated with an ill conditioned matrix. In this work the effects of regularisation methods including Tikhonov regularisation, Truncated Single Value Decomposition (TSVD), Damped Single Value Decomposition (DSVD) and a recently proposed method using cubic B-spline functions are evaluated for aeroelastic gust identification using in flight measured data. The gust identification methods are tested in the detailed aeroelastic model of FFAST and an equivalent low-fidelity aeroelastic model developed by the authors. In addition, the accuracy required in the model for a reliable identification is discussed. Finally, the identification method based on B-spline functions is tested by simultaneously using both low-fidelity and FFAST aeroelastic models so that the response from the FFAST model is used as measurement data and the equivalent low-fidelity model is used in the identification process

Conceptual-level evaluation of a variable stiffness skin for a morphing wing leading edge

A morphing leading edge produces a continuous aerodynamic surface that has no gaps between the moving and fixed parts. The continuous seamless shape has the potential to reduce drag, compared to conventional devices, such as slats that produce a discrete aerofoil shape change. However, the morphing leading edge has to achieve the required target shape by deforming from the baseline shape under the aerodynamic loads. In this paper, a conceptual-level method is proposed to evaluate the morphing leading edge structure. The feasibility of the skin design is validated by checking the failure index of the composite when the morphing leading edge undergoes the shape change. The stiffness of the morphing leading edge skin is spatially varied using variable lamina angles, and comparisons to the skin with constant stiffness are made to highlight its potential to reduce the actuation forces. The structural analysis is performed using a two-level structural optimisation scheme. The first level optimisation is applied to find the optimised structural proper- ties of the leading edge skin and the associated actuation forces. The structural properties of the skin are given as a stiffness distribution, which is controlled by a B spline interpolation function. In the second level, the design solution of the skin is investigated. The skin is assumed to be made of variable stiffness composite. The stack sequence of the composite is optimised element-by-element to match the target stiffness. A failure criterion is employed to obtain the failure index when the leading edge is actuated from the baseline shape to the target shape. Test cases are given to demonstrate that the optimisation scheme is able to provide the stiffness distribution of the leading edge skin and the actuation forces can be reduced by using a spatially variable stiffness skin

Design and Analysis of Vibration Energy Harvesters Based on Peak Response Statistics

Abstract. Energy harvesting using cantilever piezoelectric vibration energy harvesters excited by Gaussian broadband random base excitation is considered. The optimal design and analysis of energy harvesters under random excitation is normally performed using the mean and standard deviation of a response quantity of interest, such as the voltage. An alternative approach based on the statistics of the peak voltage is developed in this paper. Three extreme response characteristics, namely (a) level crossing, (b) response peaks above certain level, and (c) fractional time spend above a certain level, have been employed. Two cases, namely the harvesting circuit with and without an inductor, have been considered. Exact closed-form expressions have been derived for number of level crossings, statistics of response peaks and fractional time spend above a certain level for the output voltage. It is shown that these quantities can be related to the standard deviation of the voltage and its derivative with respect to time. Direct numerical simulation has been used to validate the analytical expressions. Based on the analytical results, closed-form expressions for optimal system parameters have been proposed. Numerical examples are given to illustrate the applicability of the analytical results

Design and Analysis of Vibration Energy Harvesters Based on Peak Response Statistics

Abstract. Energy harvesting using cantilever piezoelectric vibration energy harvesters excited by Gaussian broadband random base excitation is considered. The optimal design and analysis of energy harvesters under random excitation is normally performed using the mean and standard deviation of a response quantity of interest, such as the voltage. An alternative approach based on the statistics of the peak voltage is developed in this paper. Three extreme response characteristics, namely (a) level crossing, (b) response peaks above certain level, and (c) fractional time spend above a certain level, have been employed. Two cases, namely the harvesting circuit with and without an inductor, have been considered. Exact closed-form expressions have been derived for number of level crossings, statistics of response peaks and fractional time spend above a certain level for the output voltage. It is shown that these quantities can be related to the standard deviation of the voltage and its derivative with respect to time. Direct numerical simulation has been used to validate the analytical expressions. Based on the analytical results, closed-form expressions for optimal system parameters have been proposed. Numerical examples are given to illustrate the applicability of the analytical results

Nonlinear MEMS Piezoelectric Harvesters in the presence of geometric and structural variabilities

This paper investigates the use of an electrostatic device to improve the performance of MEMS piezoelectric harvesters in the presence of geometric and structural variabilities due to the manufacturing process. Different types of uncertain parameters including material and geometric uncertainties have been considered. The variability of these parameters are estimated based on available existing experimental data in the literature. Monte Carlo simulation (MCS) is used for uncertainty propagation and it is shown that the resonance frequencies of the majority of the samples are far away from the excitation frequency and consequently this results in less harvested power. This paper identifies these samples and uses electrostatic devices to improve the performance of the harvester. The proposed device is composed of an unsymmetric arrangement of two electrodes to decrease the resonance frequency of samples through a softening nonlinearity. The unsymmetric arrangement of two electrodes is inevitable and due to geometric variability of the harvester. There are also two arch shape electrodes which can be used to create a hardening effect to increase the resonance frequency of samples which have resonance frequencies smaller than the nominal value

An equivalent model of a nonlinear bolted flange joint

The dynamic response of individual components in an assembled structure shows high accuracy compared to experimental measurements of the system response. However, when it comes to assemblies, the conventional linear approaches fail to deliver good accuracy, due to the uncertain linear and nonlinear mechanisms in the contact interface of the joints. Therefore, the inherent dynamics of the contact interfaces needs to be considered in modeling assembled structures. In this paper the prediction of the nonlinear dynamic response in a bolted flange joint was obtained in two ways. First, a 3D detailed finite element model capable of representing the micro-slip mechanism was made using a quasi-static time stepping analysis. The linear characteristics and nonlinear mechanisms developing in the contact interface of a bolted joint are investigated by using the 3D detailed model. Moreover, the natural frequencies of the assembled structure (representing the linear response) and the micro-slip behavior in terms of hysteresis loops (representing the nonlinear response) are obtained using the detailed model. Second, an equivalent model composed of beam elements and an appropriate joint model is then constructed for the assembled structure. An identification approach is proposed, and the parameters of the joint model are identified using both linear and nonlinear characteristics, i.e. natural frequencies and hysteresis loops. Comparing the hysteresis loops obtained from the detailed and equivalent models verifies the accuracy of the joint model used to represent the contact interface and the identification approach proposed for parameter quantification

The effect of folding wingtips on the worst-case gust loads of a simplified aircraft model

In recent years, the development of lighter and more efficient transport aircraft has led to an increased focus on gust load alleviation. A recent strategy is based on the use of folding wingtip devices that increase the aspect ratio and therefore improve the aircraft performance. Moreover, numerical studies have suggested such a folding wingtip solution may incorporate spring devices in order to provide additional gust load alleviation ability in flight. It has been shown that wingtip mass, stiffness connection and hinge orientation are key parameters to avoid flutter and achieve load alleviation during gusts. The objective of this work is to show the effects of aeroelastic hinged wingtip on the problem of worst-case gust prediction and the parameterization and optimization of such a model for this particular problem, that is, worst-case gust load prediction. In this article, a simplified aeroelastic model of full symmetric aircraft with rigid movable wingtips is developed. The effects of hinge position, orientation and spring stiffness are considered in order to evaluate the performance of this technique for gust load alleviation. In addition, the longitudinal flight dynamics of a rigid aircraft with an elastic wing and folding wingtips is studied. Multi-objective optimizations are performed using a genetic algorithm to exploit the optimal combinations of the wingtip parameters that minimize the gust response for the whole flight envelope while keeping flutter speed within the safety margin. Two strategies to increase flutter speed based on the modification of the wingtip parameters are presented

Porous piezoelectric materials for energy harvesting

In this paper, we assess the energy harvesting capabilities of porous piezoelectric material under harmonic excitation and investigate the advantages of functionally grading the air inclusions. A cantilever beam energy harvester with base excitation is used to demonstrate the effects of porosity on the power generated. A homogenization step using the analytical Mori-Tanaka approach is performed initially to reduce the computational requirements. This homogenization will estimate the material properties for different levels of porosity. An Euler-Bernoulli beam model is used to efficiently estimate the power generated for a piezoelectric sensor with uniform properties. A 2D finite element model is then developed to verify the beam model; this detailed model may be used to analyze harvesters where the porosity varies through the thickness or along the length of the beams. An optimization is performed, focusing on the impact of the percentage of inclusions on the energy harvesting efficienc