Multiparameter spectral analysis for aeroelastic instability problems

This paper presents a novel application of multiparameter spectral theory to the study of structural stability, with particular emphasis on aeroelastic flutter. Methods of multiparameter analysis allow the development of new solution algorithms for aeroelastic flutter problems; most significantly, a direct solver for polynomial problems of arbitrary order and size, something which has not before been achieved. Two major variants of this direct solver are presented, and their computational characteristics are compared. Both are effective for smaller problems arising in reduced-order modelling and preliminary design optimization. Extensions and improvements to this new conceptual framework and solution method are then discussed.Comment: 20 pages, 8 figure

The self-oscillation paradox in the flight motor of D. melanogaster

Tiny flying insects, such as Drosophila melanogaster, fly by flapping their wings at frequencies faster than their brains are able to process. To do so, they rely on self-oscillation: dynamic instability, leading to emergent oscillation, arising from muscle stretch-activation. Many questions concerning this vital natural instability remain open. Does flight motor self-oscillation necessarily lead to resonance - a state optimal in efficiency and/or performance? If so, what state? And is self-oscillation even guaranteed in a motor driven by stretch-activated muscle, or are there limiting conditions? In this work, using state-of-the-art muscular and wingbeat data, we provide answers to these questions. Across a range of motor models, we establish a fundamental condition for motor self-oscillation: a relationship between relative elasticities across the motor. Remarkably, D. melanogaster hovering flight apparently defies this condition: a paradox of motor operation. We explore potential resolutions to this paradox, and, within its confines, establish that the D. melanogaster flight motor is likely not resonant with respect to exoskeletal elasticity: instead, the muscular elasticity plays a dominant role. Contrary to common supposition, the stiffness of stretch-activated muscle is an obstacle to, rather than an enabler of, the operation of the D. melanogaster flight motor

Supermanoeuvrability in a biomimetic morphing-wing aircraft

In this work we study the supermanoeuvrability of a biomimetic morphing-wing case study aircraft system. Analytical and computational models of biomimetic flight dynamics are developed, utilising multibody dynamics, computational fluid dynamics, and reduced-order aerodynamic models; and validated with respect to experimentally-derived flight dynamics of a Pioneer RQ-2 UAV. These models are used to explore the capability of this system for a wide range of biological and other supermanoeuvres: multi-axis quasistatic nose-pointing-and-shooting (NPAS) / direct force capability; multi-axis rapid-nose-pointing-and-shooting (RaNPAS) including Pugachev’s cobra; ballistic transition; and anchor turning. Novel contributions include the development of transient aerodynamic models for a three-dimensional flight-simulation context; the development of novel methods for assessing transient model validity; the development of improved methods of quaternion variational integration; the development of quasi-trim and continuation-based methods for the design, exploration, analysis and control of manoeuvres in biomimetic morphing-wing systems; an assessment of the complex spiral mode stability effects present in asymmetrically-morphed system trim states; and a demonstration of the wide-ranging potential for advanced supermanoeuvrability in biomimetic morphing-wing systems. Industrial applications include the design of high-precision guided missiles for use in complex, e.g. urban, environments.Cambridge Commonwealth Prince of Wales Scholarship (Cambridge Trust

Solving the thoracic inverse problem in the fruit fly

In many insect species, the thoracic exoskeletal structure plays a crucial role in enabling flight. In the dipteran indirect flight mechanism, thoracic cuticle acts as a transmission link between the flight muscles and the wings, and it is often thought to act as an elastic modulator: improving flight motor efficiency thorough linear or nonlinear resonance. But peering closely into the drivetrain of tiny insects is experimentally difficult, and the nature of this elastic modulation is unclear. Here, we present a new inverse-problem methodology to surmount this difficulty. In a data synthesis process, we integrate experimentally-observableliterature-reported rigid-wing aerodynamic and musculoskeletal data into a planar oscillator model for the fruit fly Drosophila melanogaster, and use this integrated dataset data to identify several surprising properties of the fly\u27s thorax. We find that fruit flies likely have an energetic need for flight motor resonance: absolute power savings due to flight motor elasticity range from 0-30% across literature-reported datasets, averaging \ua0average 16%. However, in all cases, the intrinsic high effective stiffness of the active asynchronous flight muscles accounts for all the elasticity elastic energy storage required by the wingbeat. The D. melanogaster flight motor should be considered as a system in which the wings are resonant with the elastic effects of the motor’s asynchronous musculature, and not with the elastic effects of the thoracic exoskeleton. We discover also a fundamental link betweenthat the D. melanogaster wingbeat kinematics and musculature dynamics: wingbeat kinematics areshow subtle adaptions adapted to that ensure that wingbeat load requirements match musculature load outputmuscular forcing capability. Together, these newly-identified properties lead suggestto a novel conceptual model of the fruit fly\u27s flight motor: a structure that is resonant due to muscular elasticity, and is thereby intensely concerned with ensuring that the primary flight muscles are operating efficiently. Our inverse-problem methodology sheds new light on the complex behaviour of these tiny flight motors, and provides avenues for further studies in a range of other insect species

Pseudospectral continuation for aeroelastic stability analysis

This technical note is concerned with aeroelastic flutter problems: the analysis of aeroelastic systems undergoing airspeed-dependent dynamic instability. Existing continuation methods for parametric stability analysis are based on marching along an airspeed parameter until the flutter point is found - an approach which may waste computational effort on low-airspeed system behavior, before a flutter point is located and characterized. Here, we describe a pseudospectral continuation approach which instead marches outwards from the system's flutter points, from points of instability to points of increasing damping, allowing efficient characterization of the subcritical and supercritical behavior of the system. This approach ties together aeroelastic stability analysis and abstract linear algebra, and provides efficient methods for computing practical aeroelastic stability properties - for instance, flight envelopes based on maximum modal damping, and the location of borderline-stable zones.Comment: Technical not

Aeroelastic flutter as a multiparameter eigenvalue problem

In this thesis we explore the relationship between aeroelastic flutter and multiparameter spectral theory. We first introduce the basic concept of the relationship between these two fields in abstract terms. Then we expand on this initial concept, using it to devise visualisation methods and a wide variety of solvers for flutter problems. We assess these solvers, applying them to real-life aeroelastic systems and measuring their performance. We then discuss and devise methods for improving these solvers. All our conclusions are supported by a variety of evidence from numerical experiments. Finally, we assess all of our methods, providing recommendations as to their use and future development. We do achieve several things in this thesis which have not been achieved before. Firstly, we solved a non-trivial flutter problem with a direct solver. The only direct solvers that have previously been presented are those that arise from classical flutter analysis, which applies only to very simple systems. Secondly, and as an extension of this first point, we solved a system with Theodorsen aerodynamics (approximated by a highly accurately) with a direct solver. This was achieved in an industrially competitive time (0.2s). This has never before been achieved. Thirdly, we solved an unstructured multiparameter eigenvalue problem. Unstructured problems have not been considered before, even in theoretical literature. This result is thus of significance both for multiparameter spectral theory and aeroelasticity. However, the single most important contribution of this thesis is the opening of a whole new field of study which stretches beyond aeroelasticity and into other industries: the treatment of instability problems using multiparameter methods. This field of research is wide and untrodden, and has the potential to change the way we analyse instability across many industries

Quaternion Variational Integration for Inertial Maneuvering in a Biomimetic Unmanned Aerial Vehicle

Biological flying, gliding, and falling creatures are capable of extraordinary forms of inertial maneuvering: free-space maneuvering based on fine control of their multibody dynamics, as typified by the self-righting reflexes of cats. However, designing inertial maneuvering capability into biomimetic robots, such as biomimetic unmanned aerial vehicles (UAVs), is challenging. Accurately simulating this maneuvering requires numerical integrators that can ensure both singularity-free integration, and momentum and energy conservation, in a strongly coupled system—properties unavailable in existing conventional integrators. In this work, we develop a pair of novel quaternion variational integrators (QVIs) showing these properties, and demonstrate their capability for simulating inertial maneuvering in a biomimetic UAV showing complex multibody dynamics coupling. Being quaternion-valued, these QVIs are innately singularity-free; and being variational, they can show excellent energy and momentum conservation properties. We explore the effect of variational integration order (left-rectangle versus midpoint) on the conservation properties of integrator, and conclude that in complex coupled systems in which canonical momenta may be time-varying, the midpoint integrator is required. The resulting midpoint QVI is well suited to the analysis of inertial maneuvering in a biomimetic UAV—a feature that we demonstrate in simulation—and of other complex dynamical systems

Multi-Axis Nose-Pointing-and-Shooting in a Biomimetic Morphing-Wing Aircraft

Modern high-performance combat aircraft exceed conventional flight-envelope limits on maneuverability through the use of thrust vectoring, and so achieve supermaneuverability. With ongoing development of biomimetic unmanned aerial vehicles (UAVs), the potential for supermaneuverability through biomimetic mechanisms becomes apparent. So far, this potential has not been well studied: biomimetic UAVs have not yet been shown to be capable of any forms of classical supermaneuverability, as are available to thrust-vectored aircraft. Here we show this capability, by demonstrating how biomimetic morphing-wing UAVs can perform sophisticated slow-timescale nose-pointing-and-shooting (NPAS). Nonlinear flight-dynamics analysis is used to characterize the extent and stability of the multidimensional space of aircraft trim states that arises from biomimetic morphing. Navigating this trim space provides an effective model-based guidance strategy for generating open-loop NPAS maneuvers in simulation. Our results demonstrate the capability of biomimetic aircraft for air combat-relevant supermaneuverability, and provide strategies for the exploration, characterization, and guidance of further forms of classical and nonclassical supermaneuverability in such aircraft