Span morphing using the compliant spar

This paper develops and models the Compliant Spar concept that allows the wing span to be varied to provide roll control and enhance the operational performance for a medium altitude long endurance (MALE) UAV. The wing semi-span is split into morphing partitions and the concept maybe incorporated in each partition; however only the tip partition is considered here. The Compliant Spar is made of compliant joints arrange in series to allow the partition to be flexible under axial (spanwise) loads but at the same time stiff enough to resist bending loads. Each compliant joint consists of two concentric overlapping AL 2024-T3 tubes joined together using elastomeric material. Under axial (spanwise) loading, the elastomeric material deforms in shear allowing the overlapping distance between the tubes to vary and hence the length (in the spanwise direction) of the joint/spar to vary. High fidelity modelling of the concept is performed. Then, structural optimisation studies are performed to minimise the axial stiffness and the structural mass of the concept for various design constraints. The flexible skin and actuation system to be used are also addressed

The mechanics of composite corrugated structures: A review with applications in morphing aircraft

Corrugation has long been seen as a simple and effective means of forming lightweight structures with high anisotropic behaviour, stability under buckling load and energy absorption capability. This has been exploited in diverse industrial applications and academic research. In recent years, there have been numerous innovative developments to corrugated structures, involving more elaborate and ingenious corrugation geometries and combination of corrugations with advanced materials. This development has been largely led by the research interest in morphing structures, which seek to exploit the extreme anisotropy of a corrugated panel, using the flexible degrees of freedom to allow a structure’s shape to change, whilst bearing load in other degrees of freedom. This paper presents a comprehensive review of the literature on corrugated structures, with applications ranging from traditional engineering structures such as corrugated steel beams through to morphing aircraft wing structures. As such it provides an important reference for researchers to have a broad but succinct perception of the mechanical behaviour of these structures. Such a perception is highly required in the multidisciplinary design of corrugated structures for the application in morphing aircraft

An adaptive markov chain monte carlo method for bayesian finite element model updating

Abstract: In this paper, an adaptive Markov Chain Monte Carlo (MCMC) approach for Bayesian finite element model updating is presented. This approach is known as the Adaptive Hamiltonian Monte Carlo (AHMC) approach. The convergence rate of the Hamiltonian/Hybrid Monte Carlo (HMC) algorithm is high due to its trajectory which is guided by the derivative of the posterior probability distribution function. This can lead towards high probability areas in a reasonable period of time. However, the HMC performance decreases when sampling from posterior functions of high dimension and when there are strong correlations between the uncertain parameters. The AHMC approach, a locally adaptive version of the HMC approach, allows efficient sampling from complex posterior distribution functions and in high dimensions. The efficiency and accuracy of the AHMC method are investigated by updating a real structure

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

Probabilistic optimization of engineering system with prescribed target design in a reduced parameter space

A novel probabilistic robust design optimization framework is presented here using a Bayesian inference framework. The objective of the proposed study is to obtain probabilistic descriptors of the system parameters conditioned on the user-prescribed target probability distributions of the output quantities of interest or figures of merit of a system. A criterion-based identification of a reduced important parameter space is performed from the typically high number of parameters modelling the stochastically parametrized physical system. The criterion can be based on sensitivity indices, design constraints or expert opinion or a combination of these. The posterior probabilities on the reduced or important parameters conditioned on prescribed target distributions of the output quantities of interest is derived using the Bayesian inference framework. The probabilistic optimal design proposed here offers the distinct advantage of prescribing probability bounds of the system performance functions around the optimal design points such that robust operation is ensured. The proposed method has been demonstrated with two numerical examples including the optimal design of a structural dynamic system based on user-prescribed target distribution for the resonance frequency of the system

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

Analysis of Harvesting Energy from Mistuned Multiple Harvesters with and without Coupling

AbstractEnergy harvesting has received a lot of attention in the recent past. At present a single device does not harvested energy enough to power up an electronic sensors. In order to increase the power output multiple identical harvesters are used. When multiple harvesters are used, they bring in non-uniformity in their physical parameters due to variability during manufacturing or even during deployment. Therefore, ‘n’ numbers of harvesters do not necessary produce ‘n’ times the harvested power of a single device. The variability in parameters is less enough to be coined as mistuning. In this paper, an analysis of multiple energy harvesters is studied. The harvesters are assumed to show mistuning. The study is further extended to understand the effect of mechanical coupling between the harvesters. For simplification, pendulums are considered as the harvesters, with magnetic tip masses for the electromagnetic energy harvesting. Mistuning is achieved by varying the length of the pendulums. A generalized mathematical model for n coupled harvesters with mistuning is developed. Simulations are performed with the number of harvesters varying from 2 to 6 with ±1% non-repetitive mistuning in the lengths of the harvesters, and a comparison of the power harvested between mechanically coupled and uncoupled harvesters is presented

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 a nonlinear energy sink on the gust response of a wing

In this paper, the potential effectiveness of a nonlinear energy sink (NES) to absorb the energy from a wing that is vibrating as a result of flying in a gusty environment is investigated. The structural dynamics of the wing is simulated using a rigid airfoil mounted on two linear/nonlinear springs to represent the bending and torsional stiffness of the wing. The wing is subjected to a combination of gust and aerodynamic loads. The unsteady aerodynamic lift and moment are modelled using Wagner's theory. Furthermore, the gust loads are obtained by assuming two different gust profiles, e.g. sharp-edged and 1-cosine gust profiles. A nonlinear energy sink, which comprises of a concentrated mass, damper and a nonlinear spring, is attached to the wing, and its effectiveness to absorb the gust energy is investigated. The coupled nonlinear aeroelastic equations are integrated numerically to determine the response of the wing. To verify the developed aeroelastic model, the obtained results are compared with the available results in the literature and an excellent agreement is observed. The results highlight that adding the NES to the wing is capable of reducing the gust oscillation amplitude of the wing significantly when the NES parameters are chosen accordingly

Multiple solutions and corresponding power output of a nonlinear bistable piezoelectric energy harvester

We examine multiple responses of a vibrational energy harvester composed of a vertical beam and a tip mass. The beam is excited horizontally by a harmonic inertial force while mechanical vibrational energy is converted to electrical power through a piezoelectric patch. The mechanical resonator can be described by single or double well potentials depending on the gravity force from the tip mass. By changing the tip mass we examine the appearance of various solutions and their basins of attraction. Identification of particular solutions of the energy harvester is important as each solution may provide a different level of power output