Alexander D. Shaw

Asynchronous partial contact motion due to internal resonance in multiple degree-of-freedom rotordynamics

Sudden onset of violent chattering or whirling rotor–stator contact motion in rotational machines can cause significant damage in many industrial applications. It is shown that internal resonance can lead to the onset of bouncing-type partial contact motion away from primary resonances. These partial contact limit cycles can involve any two modes of an arbitrarily high degree-of-freedom system, and can be seen as an extension of a synchronization condition previously reported for a single disc system. The synchronization formula predicts multiple drivespeeds, corresponding to different forms of mode-locked bouncing orbits. These results are backed up by a brute-force bifurcation analysis which reveals numerical existence of the corresponding family of bouncing orbits at supercritical drivespeeds, provided the damping is sufficiently low. The numerics reveal many overlapping families of solutions, which leads to significant multi-stability of the response at given drive speeds. Further, secondary bifurcations can also occur within each family, altering the nature of the response and ultimately leading to chaos. It is illustrated how stiffness and damping of the stator have a large effect on the number and nature of the partial contact solutions, illustrating the extreme sensitivity that would be observed in practice.

Dynamics of an MDOF Rotor Stator Contact System

The vibrations of rotating machinery are an important issue in many engineered systems, from aircraft engines to drilling platforms. In many cases there is a possibility of rotor stator contact, which leads to non-smooth nonlinearities; this leads to complex multi period responses in a single rotor system, and poses a challenging problem when more degrees of freedom are considered. In this work we examine how interaction of the underlying modes of a two disc rotor, can lead to complex multi-period responses with intermittent contact. These motions can be excited at driving speeds that are well removed from the linear critical speeds of the rotor. However, it is demonstrated that the driving frequencies can be predicted and explained by synchronisation between two modal responses and the driving frequency.

Experimental Identification of a Structure with Internal Resonance

Engineered structures are becoming increasingly lightweight and flexible, and as such more likely to achieve large amplitude and nonlinear vibratory responses. This leads to a demand for new methods and experimental test structures to see how in practice nonlinearity can be handled. In previous work, the authors studied a continuous modal structure with a local nonlinearity. The structure has been designed to have transparent underlying physics, and easily adjustable natural frequencies, and this leads to the ability to investigate an approximately 3:1 internal resonance between the 1st and 2nd modal frequencies. Therefore the structure exhibits complex responses to harmonic excitation, including isolated regions of the frequency response and quasiperiodic behaviour. In the present work we discuss a rapid means of identifying the structure with the minimum requirements of test data and time. A particular aim is to characterise the underlying linear system using data that is strongly influenced by nonlinearity. A harmonic balance procedure is used to identify a nonlinear discrete spring-mass system, that is modally equivalent to the structure under test. It is found that the inclusion of harmonic components in the test data and the presence of internal resonance leads to surprising amounts of information about modes that are not directly excited by the fundamental stepped-sine excitation.

Development of a morphing wingtip based on compliant structures

Compliant structures, such as flexible corrugated panels and honeycomb structures, are promising structural solutions for morphing aircraft. The compliant structure can be tailored to carry aerodynamic loads and achieve the geometry change simultaneously, while the reliability of the morphing aircraft can be guaranteed if conventional components and materials are used in the fabrication of the morphing structure. In this article, a compliant structure is proposed to change the dihedral angle of a morphing wingtip. Unsymmetrical stiffness is introduced in the compliant structure to induce the rotation of the structure. Trapezoidal corrugated panels are used, whose geometry parameters can be tailored to provide the stiffness asymmetry. An equivalent model of the corrugated panel is employed to calculate the deformation of the compliant structure. To provide the airfoil shape, a flexible honeycomb structure is used in the leading and trailing edges. An optimisation is performed to determine the geometry variables, while also considering the actuator requirements and the available space to instal the compliant structure. An experimental prototype has been manufactured to demonstrate the deformation of the morphing wingtip and conduct basic wind tunnel tests.