High frequency homogenisation for elastic lattices

A complete methodology, based on a two-scale asymptotic approach, that enables the homogenisation of elastic lattices at non-zero frequencies is developed. Elastic lattices are distinguished from scalar lattices in that two or more types of coupled waves exist, even at low frequencies. Such a theory enables the determination of effective material properties at both low and high frequencies. The theoretical framework is developed for the propagation of waves through lattices of arbitrary geometry and dimension. The asymptotic approach provides a method through which the dispersive properties of lattices at frequencies near standing waves can be described; the theory accurately describes both the dispersion curves and the response of the lattice near the edges of the Brillouin zone. The leading order solution is expressed as a product between the standing wave solution and long-scale envelope functions that are eigensolutions of the homogenised partial differential equation. The general theory is supplemented by a pair of illustrative examples for two archetypal classes of two-dimensional elastic lattices. The efficiency of the asymptotic approach in accurately describing several interesting phenomena is demonstrated, including dynamic anisotropy and Dirac cones.Comment: 24 pages, 7 figure

Fluid-loaded metasurfaces

We consider wave propagation along fluid-loaded structures which take the form of an elastic plate augmented by an array of resonators forming a metasurface, that is, a surface structured with sub-wavelength resonators. Such surfaces have had considerable recent success for the control of wave propagation in electromagnetism and acoustics, by combining the vision of sub-wavelength wave manipulation, with the design, fabrication and size advantages associated with surface excitation. We explore one aspect of recent interest in this field: graded metasurfaces, but within the context of fluid-loaded structures. Graded metasurfaces allow for selective spatial frequency separation and are often referred to as exhibiting rainbow trapping. Experiments, and theory, have been developed for acoustic, electromagnetic, and even elastic, rainbow devices but this has not been approached for fluid-loaded structures that support surface waves coupled with the acoustic field in a bulk fluid. This surface wave, coupled with the fluid, can be used to create an additional effect by designing a metasurface to mode convert from surface to bulk waves. We demonstrate that sub-wavelength control is possible and that one can create both rainbow trapping and mode conversion phenomena for a fluid-loaded elastic plate model.Comment: 13 pages, 10 figure

Localisation for a line defect in an infinite square lattice

Localised defect modes generated by a finite line defect composed of several masses, embedded an infinite square cell lattice, are analysed using the linear superposition of Green's function for a single mass defect. Several representations of the lattice Green's function are presented and discussed. The problem is reduced to an eigenvalue system and the properties of the corresponding matrix are examined in detail to yield information regarding the number of symmetric and skew-symmetric modes. Asymptotic expansions in the far field, associated with long wavelength homogenisation are presented. Asymptotic expressions for Green's function in the vicinity of the band edge are also discussed. Several examples are presented where eigenfrequencies linked to this system and the corresponding eigenmodes are computed for various defects and compared with the asymptotic expansions. The case of an infinite defect is also considered and an explicit dispersion relation is obtained. For the case when the number of masses within the line defect is large, it is shown that the range of the eigenfrequencies can be predicted using the dispersion diagram for the infinite chain

Tilted resonators in a triangular elastic lattice: chirality, Bloch waves and negative refraction

We consider a vibrating triangular mass-truss lattice whose unit cell contains a resonator of a triangular shape. The resonators are connected to the triangular lattice by trusses. Each resonator is tilted, i.e. it is rotated with respect to the triangular lattice's unit cell through an angle $\vartheta_0$. This geometrical parameter is responsible for the emergence of a resonant mode in the Bloch spectrum for elastic waves and strongly affects the dispersive properties of the lattice. Additionally, the tilting angle $\vartheta_0$ triggers the opening of a band gap at a Dirac-like point. We provide a physical interpretation of these phenomena and discuss the dynamical implications on elastic Bloch waves. The dispersion properties are used to design a structured interface containing tilted resonators which exhibit negative refraction and focussing, as in a "flat elastic lens"

Cymatics for the cloaking of flexural vibrations in a structured plate

Based on rigorous theoretical findings, we present a proof-of-concept design for a structured square cloak enclosing a void in an elastic lattice. We implement high-precision fabrication and experimental testing of an elastic invisibility cloak for flexural waves in a mechanical lattice. This is accompanied by verifications and numerical modelling performed through finite element simulations. The primary advantage of our square lattice cloak, over other designs, is the straightforward implementation and the ease of construction. The elastic lattice cloak, implemented experimentally, shows high efficiency

Willing and able: action-state orientation and the relation between procedural justice and employee cooperation

Existing justice theory explains why fair procedures motivate employees to adopt cooperative goals, but it fails to explain how employees strive towards these goals. We study self-regulatory abilities that underlie goal striving; abilities that should thus affect employees’ display of cooperative behavior in response to procedural justice. Building on action control theory, we argue that employees who display effective self-regulatory strategies (action oriented employees) display relatively strong cooperative behavioral responses to fair procedures. A multisource field study and a laboratory experiment support this prediction. A subsequent experiment addresses the process underlying this effect by explicitly showing that action orientation facilitates attainment of the cooperative goals that people adopt in response to fair procedures, thus facilitating the display of actual cooperative behavior. This goal striving approach better integrates research on the relationship between procedural justice and employee cooperation in the self-regulation and the work motivation literature. It also offers organizations a new perspective on making procedural justice effective in stimulating employee cooperation by suggesting factors that help employees reach their adopted goals

Using self-definition to predict the influence of procedural justice on organizational, interpersonal, and job/task-oriented citizenship behaviors

An integrative self-definition model is proposed to improve our understanding of how procedural justice affects different outcome modalities in organizational behavior. Specifically, it is examined whether the strength of different levels of self-definition (collective, relational, and individual) each uniquely interact with procedural justice to predict organizational, interpersonal, and job/task-oriented citizenship behaviors, respectively. Results from experimental and (both single and multisource) field data consistently revealed stronger procedural justice effects (1) on organizational-oriented citizenship behavior among those who define themselves strongly in terms of organizational characteristics, (2) on interpersonal-oriented citizenship behavior among those who define themselves strongly in terms of their interpersonal relationships, and (3) on job/task-oriented citizenship behavior among those who define themselves weakly in terms of their distinctiveness or uniqueness. We discuss the relevance of these results with respect to how employees can be motivated most effectively in organizational settings

What’s past (and present) is prologue : interactions between justice levels and trajectories predicting behavioral reciprocity

Much of organizational justice research has tended to take a static approach, linking employees’ contemporaneous justice levels to outcomes of interest. In the present study, we tested a dynamic model emphasizing the interactive influences of both justice levels and trajectories for predicting behavioral social exchange outcomes. Specifically, our model posited both main effects and interactions between present justice levels and past justice changes over time in predicting helping behavior and voluntary turnover behavior. Data over four yearly measurement periods from 4,348 employees of a banking organization generally supported the notion that justice trajectories interact with absolute levels to predict both outcomes. Together, the findings highlight how employees invoke present fairness evaluations within the context of past fairness trends—rather than either in isolation—to inform decisions about behaviorally reciprocating at work

The Precursors and Products of Justice Climates: Group Leader Antecedents and Employee Attitudinal Consequences

Drawing on the organizational justice, organizational climate, leadership and personality, and social comparison theory literatures, we develop hypotheses about the effects of leader personality on the development of three types of justice climates (e.g., procedural, interpersonal, and informational), and the moderating effects of these climates on individual level justice- attitude relationships. Largely consistent with the theoretically-derived hypotheses, the results showed that leader (a) agreeableness was positively related to procedural, interpersonal and informational justice climates, (b) conscientiousness was positively related to a procedural justice climate, and (c) neuroticism was negatively related to all three types of justice climates. Further, consistent with social comparison theory, multilevel data analyses revealed that the relationship between individual justice perceptions and job attitudes (e.g., job satisfaction, commitment) was moderated by justice climate such that the relationships were stronger when justice climate was high