Atanas A. Popov

Parametric resonance in cylindrical shells: A case study in the nonlinear vibration of structural shells

The aim of this work is to demonstrate in a tutorial fashion how recent ideas and methods of bifurcation theory and nonlinear dynamics have improved the understanding of structural buckling under dynamic loads and vibration of shells under parametric excitation. The paper focuses on geometrically nonlinear forced vibrations of circular cylindrical shells. The emphasis is on fundamental issues and differences between results obtained by linear and nonlinear analysis. Analytical and numerical results for shell models are presented and discussed in the light of nonlinear mode interaction and parametric resonance. The main conclusion from the case studied is that linear theory provides only incomplete and in some cases inaccurate results, when the vibration amplitude becomes comparable to the shell thickness.

A geometric parameter study of piezoelectric coverage on a rectangular cantilever energy harvester

This paper proposes a versatile model for optimizing the performance of a rectangular cantilever beam piezoelectric energy harvester used to convert ambient vibrations into electrical energy. The developed model accounts for geometric changes to the natural frequencies, mode shapes and damping in the structure. This is achieved through the combination of finite element modelling and a distributed parameter electromechanical model, including load resistor and charging capacitor models. The model has the potential for use in investigating the influence of numerous geometric changes on harvester performance, and incorporates a model for accounting for changes in damping as the geometry changes. The model is used to investigate the effects of substrate and piezoelectric layer length, and piezoelectric layer thickness on the performance of a microscale device. Findings from a parameter study indicate the existence of an optimum sample length due to increased mechanical damping for longer beams and improved power output using thicker piezoelectric layers. In practice, harvester design is normally based around a fixed operating frequency for a particular application, and improved performance is often achieved by operating at or near resonance. To achieve unbiased comparisons between different harvester designs, parameter studies are performed by changing multiple parameters simultaneously with the natural frequency held fixed. Performance enhancements were observed using shorter piezoelectric layers as compared to the conventional design, in which the piezoelectric layer and substrate are of equal length.

Bifurcation Analyses in the Parametrically Excited Vibrations of Cylindrical Panels

We consider parametrically excited vibrations of shallow cylindrical panels. The governing system of two coupled nonlinear partial differential equations is discretized by using the Bubnov–Galerkin method. The computations are simplified significantly by the application of computer algebra, and as a result low dimensional models of shell vibrations are readily obtained. After applying numerical continuation techniques and ideas from dynamical systems theory, complete bifurcation diagrams are constructed. Our principal aim is to investigate the interaction between different modes of shell vibrations under parametric excitation. Results for system models with four of the lowest modes are reported. We essentially investigate periodic solutions, their stability and bifurcations within the range of excitation frequency that corresponds to the parametric resonances at the lowest mode of vibration.

Laboratory measurement of rolling resistance in truck tyres under dynamic vertical load

Abstract This paper deals with the rolling resistance of heavy vehicle tyres measured on a large drum under dynamically varying vertical load. The aim is to simulate in the laboratory the dynamic loading conditions arising from interaction of the vehicle with a randomly rough road. A dynamically varying vertical force is generated using a hydraulic actuator. A comprehensive set of experimental data for two different truck tyres is presented, and the influence of dynamic load on the mean rolling resistance is quantified and discussed. The measurements indicate that there is no significant effect of dynamic vertical load on the mean rolling resistance of the two tyres tested.

Active fixturing: literature review and future research directions

Fixtures are used to fixate, position and support workpieces and represent a crucial tool in manufacturing. Their performance determines the result of the whole manufacturing process of a product. There is a vast amount of research done on automatic fixture layout synthesis and optimisation and fixture design verification. Most of this work considers fixture mechanics to be static and the fixture elements to be passive. However, a new generation of fixtures has emerged that has actuated fixture elements for active control of the part–fixture system during manufacturing operations to increase the end product quality. This paper analyses the latest studies in the field of active fixture design and its relationship with flexible and reconfigurable fixturing systems. First, a brief introduction is given on the importance of research of fixturing systems. Secondly, the basics of workholding and fixture design are visited, after which the state-of-the-art in active fixturing and related concepts is presented. Fourthly, part–fixture dynamics and design strategies which take these into account are discussed. Fifthly, the control strategies used in active fixturing systems are examined. Finally, some final conclusions and prospective future research directions are presented.

A review on motorcycle and rider modelling for steering control

The paper is a review of the state of knowledge and understanding of steering control in motorcycles and of the existing rider models. Motorcycles are well known to have specific instability characteristics, which can detrimentally affect the riders control, and as such a suitable review of these characteristics is covered in the first instance. Next, early models which mostly treat riding as a regulatory task are considered. A rider applies control based on sensory information available to him/her, predominantly from visual perception of a target path. The review therefore extends to cover also the knowledge and research findings into aspects of road preview control. Here, some more emphasis is placed on recent applications of optimal control and model predictive control to the riding task and the motorcycle–rider interaction. The review concludes with some open questions which naturally present a scope for further study.

Optimization of piezoelectric cantilever energy harvesters including non-linear effects

This paper proposes a versatile non-linear model for predicting piezoelectric energy harvester performance. The presented model includes (i) material non-linearity, for both substrate and piezoelectric layers, and (ii) geometric non-linearity incorporated by assuming inextensibility and accurately representing beam curvature. The addition of a sub-model, which utilizes the transfer matrix method to predict eigenfrequencies and eigenvectors for segmented beams, allows for accurate optimization of piezoelectric layer coverage. A validation of the overall theoretical model is performed through experimental testing on both uniform and non-uniform samples manufactured in-house. For the harvester composition used in this work, the magnitude of material non-linearity exhibited by the piezoelectric layer is 35 times greater than that of the substrate layer. It is also observed that material non-linearity, responsible for reductions in resonant frequency with increases in base acceleration, is dominant over geometric non-linearity for standard piezoelectric harvesting devices. Finally, over the tested range, energy loss due to damping is found to increase in a quasi-linear fashion with base acceleration. During an optimization study on piezoelectric layer coverage, results from the developed model were compared with those from a linear model. Unbiased comparisons between harvesters were realized by using devices with identical natural frequencies—created by adjusting the device substrate thickness. Results from three studies, each with a different assumption on mechanical damping variations, are presented. Findings showed that, depending on damping variation, a non-linear model is essential for such optimization studies with each model predicting vastly differing optimum configurations.

Review and comparison of different support loss models for micro-electro-mechanical systems resonators undergoing in-plane vibration

Several approaches for calculating support loss in micro-electro-mechanical system resonators undergoing in-plane vibration are reviewed. In each of them, the support is approximated as a semi-infinite domain. The first approach is analytical and models the support as a semi-infinite thin plate. This is compared with two different finite element approaches that introduce artificial boundaries to their finite domain. In order to absorb outgoing waves and model the infinite support, a perfectly matched layer method and the use of infinite elements are considered. Simple test cases are studied and the results for the support losses predicted by the different methods are compared. It is shown that each of the methods yields similar trends. Using the developed analytical model, a parametric study is performed on the support losses of a ring-based resonator. General strategies for improving the quality factor by reducing support losses are provided.

Application of predictive control strategies to the motorcycle riding task

Model predictive control (MPC) techniques have been applied to the modelling of a motorcycle rider, believed to offer more realistic representation of the riding strategy compared with previous methods, notably optimal control. The results from the MPC model have been compared with the optimal control results, showing good similarities and also some notable differences. The results of the application of MPC techniques to the simulation of a motorcycle rider suggest that the approach has wider applicability to rider modelling, and allows greater scope for the definition of the riders control approach. Notably, for limited rider preview, shortcomings using the optimal control approach are overcome using the MPC method. Furthermore, the approach is believed to more accurately reflect the control actions taken by a human motorcycle rider.

Final Undergraduate Project in Engineering: Towards More Efficient and Effective Tutorials.

The paper presents strategies for improving the quality of student learning in the context of the final undergraduate project in mechanical engineering. Special attention is paid to particular situations where the lecturer is faced with the problem of supervising a number of individual projects at a time. An action research project has been conducted for a period of one academic year, and the outcomes of change in practice have been assessed on a batch of seven student projects. The results obtained show that a deep approach to learning can be fostered in students by a careful selection of project topics, together with a good balance of group and individual tutorials which can stimulate significant peer interaction. One additional positive aspect of the implemented approach is the more efficient way of managing the time of academic staff without interfering with effective learning.