Flexoelectric effect on thickness-shear vibration of a rectangular piezoelectric crystal plate

Thickness-shear (TSh) vibration of a rectangular piezoelectric crystal plate is studied with the consideration of flexoelectric effect in this paper. The developed theoretical model is based on the assumed displacement function which includes the anti-symmetric mode through thickness and symmetric mode in length. The constitutive equation with flexoelectricity, governing equations and boundary conditions are derived from the Gibbs energy density function and variational principle. For the effect of flexoelectricity, we only consider the shear strain gradient in the thickness direction so as to simply the mathematical model. Thus, two flexoelectric coefficients are used in the present model. The electric potential functions are also obtained for different electric boundary conditions. The present results clearly show that the flexoelectric effect has significant effect on vibration frequencies of thickness-shear modes of thin piezoelectric crystal plate. It is also found that the flexoelectric coefficients and length to thickness ratio have influence on the thickness-shear modes. The results tell that flexoelectricity cannot be neglected for design of small size piezoelectric resonators.

Effective field theory for hydrodynamics without boosts

We formulate the Schwinger-Keldysh effective field theory of hydrodynamics without boost symmetry. This includes a spacetime covariant formulation of classical hydrodynamics without boosts with an additional conserved particle/charge current coupled to Aristotelian background sources. We find that, up to first order in derivatives, the theory is characterised by the thermodynamic equation of state and a total of 29 independent transport coefficients, in particular, 3 hydrostatic, 9 non-hydrostatic non-dissipative, and 17 dissipative. Furthermore, we study the spectrum of linearised fluctuations around anisotropic equilibrium states with non-vanishing fluid velocity. This analysis reveals a pair of sound modes that propagate at different speeds along and opposite to the fluid flow, one charge diffusion mode, and two distinct shear modes along and perpendicular to the fluid velocity. We present these results in a new hydrodynamic frame that is linearly stable irrespective of the boost symmetry in place. This provides a unified covariant stable approach for simultaneously treating Lorentzian, Galilean, and Lifshitz fluids within an effective field theory framework and sets the stage for future studies of non-relativistic intertwined patterns of symmetry breaking.

Bulky auxeticity, tensile buckling and deck-of-cards kinematics emerging from structured continua

Complex mechanical behaviours are generally met in macroscopically homogeneous media as effects of inelastic responses or as results of unconventional material properties, which are postulated or due to structural systems at the meso/micro-scale. Examples are strain localization due to plasticity or damage and metamaterials exhibiting negative Poisson’s ratios resulting from special porous, eventually buckling, sub-structures. In this work, through ad hoc conceived mechanical paradigms, we show that several non-standard behaviours can be obtained simultaneously by accounting for kinematical discontinuities, without invoking inelastic laws or initial voids. By allowing mutual sliding among rigid tesserae connected by pre-stressed hyperelastic links, we find several unusual kinematics such as localized shear modes and tensile buckling-induced instabilities, leading to deck-of-cards deformations—uncapturable with classical continuum models—and unprecedented ‘bulky’ auxeticity emerging from a densely packed, geometrically symmetrical ensemble of discrete units that deform in a chiral way. Finally, after providing some analytical solutions and inequalities of mechanical interest, we pass to the limit of an infinite number of tesserae of infinitesimal size, thus transiting from discrete to continuum, without the need to introduce characteristic lengths. In the light of the theory of structured deformations, this result demonstrates that the proposed architectured material is nothing else than the first biaxial paradigm of structured continuum —a body that projects, at the macroscopic scale, geometrical changes and disarrangements occurring at the level of its sub-macroscopic elements.

Investigation of the Effect of Inhomogeneous Material on the Fracture Mechanisms of Bamboo by Finite Element Method

Bamboo is a remarkably strong and sustainable material available for construction. It exhibits optimized mechanical characteristics based on a hollow-inhomogeneous structure which also affects its fracture behavior. In this study, the aim is to investigate the effect of material composition and geometrical attributes on the fracture mechanisms of bamboo in various modes of loading by the finite element method. In the first part of the investigation, the optimized transverse isotropy of bamboo to resist transverse deformation was numerically determined to represent its noticeable orthotropic characteristics which prevail in the axial direction. In the second part of this study, a numerical investigation of fracture mechanisms in four fundamental modes of loading, namely bending, compression, torsion, and shear, were conducted by considering the failure criterion of maximum principal strain. A crack initiation stage was simulated and compared by implementing an element erosion technique. Results showed that the characteristics of bamboo’s crack initiation differed greatly from solid geometry and homogeneous material-type models. Splitting patterns, which were discerned in bending and shear modes, differed in terms of location and occurred in the outside-center position and inside-lowermost position of the culm, respectively. The results of this study can be useful in order to achieve optimized strength in bamboo-inspired bionic designs.

A novel bi-directional shear mode magneto-rheological elastomer vibration isolator

In this article, a novel bi-directional shear mode magneto-rheological elastomer–based vibration isolator has been designed, fabricated, and characterized to improve the dynamic response and identification of this class of “intellectual” mechanical devices. A heuristic embodiment has been realized in order to design such an isolator wherein both the vertical and horizontal directions can be operated only in the shear mode not only individually but also simultaneously. Two fixtures have been designed for performing the characterization of the magneto-mechanical behavior of the proposed magneto-rheological elastomer isolator in the vertical and horizontal shear modes under wide ranges of strain amplitude (4%–32%), excitation frequency (1–8 Hz), and magnetic flux density (0–220 mT). Experimental results revealed maximum relative magneto-rheological effects of 35% and 27 % in the vertical and horizontal shear modes, respectively. Furthermore, basic mathematical models of single-degree-of-freedom systems, employing the magneto-rheological elastomer–based isolator in the vertical and horizontal shear modes, have been established. The proposed magneto-rheological elastomer isolator in the vertical mode exhibited natural frequency shift of 6.1% by a small increment in the magnetic flux density which approves the potential of the proposed bi-directional shear mode magneto-rheological elastomer–based vibration isolator for vibration control applications, such as seat suspension systems.

Bechmann’s Number for Harmonic Overtones of Thickness-Shear Vibrations of Rotated Y-Cut Quartz Crystal Plates

A procedure based on approximate solutions of three-dimensional equations of wave propagation is utilized for calculating Bechmann’s number for the harmonic overtones of thickness-shear modes in the rotated Y-cut quartz crystal plates. Bechmann’s number is used for the optimization and improvement of electrodes to yield superior performance in the design of quartz crystal resonators. Originally, Bechmann’s number is found through practical experiences, and analytical results were provided afterward to enable optimal design of novel resonator structures. The outcomes in this study are from a simplified theoretical prediction and they are consistent with known empirical results, making it is possible to design optimal quartz crystal resonators for cases without adequate experimental data for a higher frequency and smaller size.