Michał K. Kalkowski

Active control of parametrically excited systems

This article discusses active control of parametrically excited systems. Parametric resonance is observed in a wide range of applications and can lead to high levels of unwanted motion. For example, in cable-stayed bridges, the vibration of the deck excites the cables axially, inducing a periodically time-varying tension. If the frequency of deck vibration is about twice the natural frequency of the cable, a parametric resonance occurs and leads to a large-amplitude swinging motion of the cable. To tackle the consequences of parametric instability, active vibration control employing a piezoelectric actuator is proposed in this article. We consider a beam subjected to an axial harmonic load that represents a parametrically excited system with a periodically varying stiffness. Using both analytical and experimental methods, we assess the stability of the beam and propose active control aimed at relocating the transition curves and hence stabilising the system via velocity feedback and pole placement. Analytical relationship between the transition curves and the poles of the system is derived. Transition curves can be assigned to a prescribed location using appropriate velocity and displacement control gains. Finally, we demonstrate the proposed approach with experiments on a beam equipped with a macro fibre composite patch.

Delamination of surface accretions with structural waves: Piezo-actuation and power requirements:

Unwanted accretions on structures, such as aircraft and wind turbine icing or deposits in pipes, are a common problem, which can pose a serious safety threat if not treated effectively and punctually. In this article we investigate the capability of piezo-excited structural waves to delaminate accreted material. The core of the concept is to utilise the stress distribution associated with waves propagating through the structure to detach unwanted build-up. We apply a wave-based technique for modelling piezoelectric excitation based on semi-analytical finite elements to calculate the shear stress at the interface between the host structure and the accretion generated by piezo-actuated waves. Our analyses include the effects of the actuator’s dynamics and allow for comparing different types of actuators, identifying the most effective frequency of excitation and formulating realistic power requirements. For the dual purposes of proof of concept and validation of the model, we present a demonstration experiment in which patches of accreted material are removed from a beam-like waveguide with emulated anechoic terminations using ultrasonic excitation.

Removing surface accretions with piezo-excited high-frequency structural waves

Unwanted accretions on structures are a common machinery maintenance problem, which can pose a serious safety threat if not treated effectively and punctually. In this paper we investigate the capability of piezo-excited structural waves for invoking delamination of accreted material from waveguides. We apply a wave-based technique for modelling piezoelectric excitation based on semi-analytical finite elements to model the interface shear stress associated with piezo-actuated structural waves. As a proof of concept, we present a demonstration experiment in which patches of material are removed from a beam-like waveguide with emulated anechoic terminations using ultrasonic excitation.

Wave propagation in rods with an exponentially varying cross-section - modelling and experiments

In this paper we analyse longitudinal wave propagation in exponentially tapered rods from both a theoretical and an experimental perspective. The tapering introduces significant changes to the behaviour of the rod. The longitudinal wave does not propagate from zero frequency, its cut-off frequency depending on the coefficient in the exponent. The analytical description of this phenomenon is well established, however little experimental work has been published to date. After a brief review of the classical solution of the exponential rod equation, we derive a methodology allowing the wavenumbers to be estimated from a set of equally spaced dynamic responses. Our approach is verified numerically against a finite element simulation and validated experimentally, both showing very good agreement. To further explain the results and provide an outlook for future work, we present a finite element model of the tapered rod embedded in an infinite solid medium. We conclude with a discussion on the effects of the surrounding medium on the behaviour of the structure and resulting characteristic features of the wavenumber.

Semi-analytical modelling of piezoelectric excitation of guided waves

Piezoelectric elements are a key component of modern non-destructive testing (NDT) and structural health monitoring (SHM) systems and play a significant role in many other areas involving dynamic interaction with the structure such as energy harvesting, active control, power ultrasonics or removal of surface accretions using structural waves. In this paper we present a wave-based technique for modelling waveguides equipped with piezoelectric actuators in which there is no need for common simplifications regarding their dynamic behaviour or mutual interaction with the structure. The proposed approach is based on the semi-analytical finite element (SAFE) method. We developed a new piezoelectric semi-analytical element and employed the analytical wave approach to model the distributed electric excitation and scattering of the waves at discontinuities. The model is successfully validated against an experiment on a beam-like waveguide with emulated anechoic terminations.