With its roots in kinetic theory and the cellular automaton concept, the lattice-Boltzmann (LB) equation can be used to obtain continuum flow quantities from simple and local update rules based on particle interactions. The simplicity of formulation and its versatility explain the rapid expansion of the LB method to applications in complex and multiscale flows. We review many significant developments over the past decade with specific examples. Some of the most active developments include the entropic LB method and the application of the LB method to turbulent flow, multiphase flow, and deformable particle and fiber suspensions. Hybrid methods based on the combination of the Eulerian lattice with a Lagrangian grid system for the simulation of moving deformable boundaries show promise for more efficient applications to a broader class of problems. We also discuss higherorder boundary conditions and the simulation of microchannel flow with finite Knudsen number. Additionally, the remarkable scalability of the LB method for parallel processing is shown with examples. Teraflop simulations with the LB method are routine, and there is no doubt that this method will be one of the first candidates for petaflop computational fluid dynamics in the near future.

Lattice-Boltzmann Method for Complex Flows

The investigation of the conversion of vibrational energy into electrical power has become a major field of research. In recent years, bistable energy harvesting devices have attracted significant attention due to some of their unique features. Through a snap-through action, bistable systems transition from one stable state to the other, which could cause large amplitude motion and dramatically increase power generation. Due to their nonlinear characteristics, such devices may be effective across a broad-frequency bandwidth. Consequently, a rapid engagement of research has been undertaken to understand bistable electromechanical dynamics and to utilize the insight for the development of improved designs. This paper reviews, consolidates, and reports on the major efforts and findings documented in the literature. A common analytical framework for bistable electromechanical dynamics is presented, the principal results are provided, the wide variety of bistable energy harvesters are described, and some remaining challenges and proposed solutions are summarized.

https://iopscience.iop.org/article/10.1088/0964-1726/22/2/023001/pdf

A review of the recent research on vibration energy harvesting via bistable systems

This paper gives a systematic introduction to HMM, the heterogeneous multiscale methods, including the fundamental design principles behind the HMM philosophy and the main obstacles that have to be ...

Heterogeneous multiscale methods: A review

Molecular Dynamics

The last two decades have witnessed several advances in microfabrication technologies and electronics, leading to the development of small, low-power devices for wireless sensing, data transmission, actuation, and medical implants. Unfortunately, the actual implementation of such devices in their respective environment has been hindered by the lack of scalable energy sources that are necessary to power and maintain them. Batteries, which remain the most commonly used power sources, have not kept pace with the demands of these devices, especially in terms of energy density. In light of this challenge, the concept of vibratory energy harvesting has flourished in recent years as a possible alternative to provide a continuous power supply. While linear vibratory energy harvesters have received the majority of the literature’s attention, a significant body of the current research activity is focused on the concept of purposeful inclusion of nonlinearities for broadband transduction. When compared to their linear resonant counterparts, nonlinear energy harvesters have a wider steady-state frequency bandwidth, leading to a common belief that they can be utilized to improve performance in ambient environments. Through a review of the open literature, this paper highlights the role of nonlinearities in the transduction of energy harvesters under different types of excitations and investigates the conditions, in terms of excitation nature and potential shape, under which such nonlinearities can be beneficial for energy harvesting. [DOI: 10.1115/1.4026278]

On the Role of Nonlinearities in Vibratory Energy Harvesting: A Critical Review and Discussion

A method is developed to investigate the behaviour of a liquid under the action of a very high shearing force using computer simulated molecular dynamics. Values for the viscosity are calculated but these require more extensive computation for statistical accuracy. A short calculation is, however, sufficient to establish the nature of the processes involved, and to plot the velocity distribution curve; these graphs are presented. The method abandons the usual homogeneous isotropic cyclic conditions used so far in calculation of transport coefficients and can be applied to arbitrarily large shear.

https://iopscience.iop.org/article/10.1088/0022-3719/5/15/006/pdf

The computer study of transport processes under extreme conditions

This book equips the reader to understand every important aspect of the dynamics of rotating machines. Will the vibration be large? What influences machine stability? How can the vibration be reduced? Which sorts of rotor vibration are the worst? The book develops this understanding initially using extremely simple models for each phenomenon, in which (at most) four equations capture the behavior. More detailed models are then developed based on finite element analysis, to enable the accurate simulation of the relevant phenomena for real machines. Analysis software (in MATLAB) is associated with this book, and novices to rotordynamics can expect to make good predictions of critical speeds and rotating mode shapes within days. The book is structured more as a learning guide than as a reference tome and provides readers with more than 100 worked examples and more than 100 problems and solutions.

/pdf/dynamics-of-rotating-machines-499re2kizd.pdf

Dynamics of rotating machines

A common energy harvesting device uses a piezoelectric patch on a cantilever beam with a tip mass. The usual configuration exploits the linear resonance of the system; this works well for harmonic excitation and when the natural frequency is accurately tuned to the excitation frequency. A new configuration is proposed, consisting of a cantilever beam with a tip mass that is mounted vertically and excited in the transverse direction at its base. This device is highly non-linear with two potential wells for large tip masses, when the beam is buckled. The system dynamics may include multiple solutions and jumps between the potential wells, and these are exploited in the harvesting device. The electromechanical equations of motion for this system are developed, and its response for a range of parameters is investigated using phase portraits and bifurcation diagrams. The model is validated using an experimental device with three different tip masses, representing three interesting cases: a linear system; a low...

Non-linear piezoelectric vibration energy harvesting from a vertical cantilever beam with tip mass

https://hal.archives-ouvertes.fr/hal-00207691/document

The influence of cracks in rotating shafts

This paper aims to provide a broad review of the state of the art in fault diagnosis techniques, with particular regard to rotating machinery. Fault diagnosis is a subject too wide ranging to allow a comprehensive coverage of all of the areas associated with this field to be undertaken, and it is not the authors' intention to do so. However, a general overview of the broader issues of fault diagnosis is provided, and several of the various methodologies are discussed. A detailed review of the subject of fault diagnosis in rotating machinery is then presented. Special treatment is given to the areas of mass unbalance, bowed shafts, and cracked shafts, these being among the most common rotor-dynamic faults. Vibration response measurements yield a great deal of information concerning any faults within a rotating machine, and many of the methods using this technique are reviewed.

Arthur W. Lees

Papers

The computer study of transport processes under extreme conditions

Dynamics of rotating machines

Non-linear piezoelectric vibration energy harvesting from a vertical cantilever beam with tip mass

The influence of cracks in rotating shafts

Fault diagnosis of rotating machinery