scholarly journals Tunable Bandgaps in Phononic Crystal Microbeams Based on Microstructure, Piezo and Temperature Effects

Crystals ◽  
2021 ◽  
Vol 11 (9) ◽  
pp. 1029
Author(s):  
Jun Hong ◽  
Zhuangzhuang He ◽  
Gongye Zhang ◽  
Changwen Mi
Keyword(s):  
Wave Equation ◽  
Temperature Effects ◽  
Piezoelectric Materials ◽  
Phononic Crystal ◽  
Potential Temperature ◽  
Geometrical Parameters ◽  
Plane Wave Expansion ◽  
Special Cases ◽  
Microstructure Effects ◽  
Magnetic Potentials

A new model of non-classical phononic crystal (PC) microbeam for the elastic wave bandgap generation is provided, incorporating microstructure, piezomagnetism, piezoelectricity and temperature effects. The wave equation of a general magneto–electro–elastic (MEE) phononic crystal microbeam is derived, which recovers piezoelectric- and piezomagnetic-based counterparts as special cases. The piezomagnetic and piezoelectric materials are periodically combined to construct the PC microbeam and corresponding bandgaps are obtained by using the plane wave expansion (PWE) method. The effects of the piezomagnetism, piezoelectricity, microstructure, geometrical parameters and applied multi-fields (e.g., external electric potential, external magnetic potential, temperature change) on the bandgaps are discussed. The numerical results reveal that the bandgap frequency is raised with the presence of piezo and microstructure effects. In addition, the geometry parameters play an important role on the bandgap. Furthermore, large bandgaps can be realized by adjusting the external electric and magnetic potentials at micron scale, and lower bandgap frequency can be realized through the temperature rise at all length scales.

Environmental impacts of aquifer thermal energy storage investigated by field and laboratory experiments

2013 ◽  
Vol 4 (2) ◽  
pp. 77-89 ◽  
Author(s):  
Matthijs Bonte ◽  
Boris M. Van Breukelen ◽  
Pieter J. Stuyfzand
Keyword(s):  
Energy Storage ◽  
Thermal Energy ◽  
Thermal Energy Storage ◽  
Temperature Effects ◽  
Laboratory Experiments ◽  
Potential Temperature ◽  
Arsenic Concentration ◽  
Observation Data ◽  
Aquifer Thermal Energy Storage ◽  
Field Investigations

Aquifer thermal energy storage (ATES) uses groundwater to store energy for heating or cooling purposes in the built environment. This paper presents field and laboratory results aiming to elucidate the effects that ATES operation may have on chemical groundwater quality. Field data from an ATES site in the south of the Netherlands show that ATES results in chemical quality perturbations due to homogenisation of the initially present vertical water quality gradient. We tested this hypothesis by numerical modelling of groundwater flow and coupled SO4 transport during extraction and injection of groundwater by the ATES system. The modelling results confirm that extracting groundwater from an aquifer with a natural quality stratification, mixing this water in the ATES system, and subsequent injection in the second ATES well can adequately describe the observation data. This mixing effect masks any potential temperature effects in typical low temperature ATES systems (<25 °C) which was the reason to complement the field investigations with laboratory experiments focusing on temperature effects. The laboratory experiments indicated that temperature effects until 25 °C are limited; most interestingly was an increase in arsenic concentration. At 60 °C, carbonate precipitation, mobilisation of dissolved oxygen concentration, K and Li, and desorption of trace metals like As can occur.

scholarly journals Relativistic equations for elementary particles

1948 ◽  
Vol 192 (1029) ◽  
pp. 195-218 ◽  
Keyword(s):  
Elementary Particle ◽  
Wave Equation ◽  
Equations Of Motion ◽  
Rest Mass ◽  
Wave Form ◽  
Total Charge ◽  
Field Equations ◽  
Relativistic Approximation ◽  
Special Cases ◽  
Linear Differential

From the general principles of quantum mechanics it is deduced that the wave equation of a particle can always be written as a linear differential equation of the first order with matrix coefficients. The principle of relativity and the elementary nature of the particle then impose certain restrictions on these coefficient matrices. A general theory for an elementary particle is set up under certain assumptions regarding these matrices. Besides, two physical assumptions concerning the particle are made, namely, (i) that it satisfies the usual second-order wave equation with a fixed value of the rest mass, and (ii) either the total charge or the total energy for the particle-field is positive definite. It is shown that in consequence of (ii) the theory can be quantized in the interaction free case. On introducing electromagnetic interaction it is found that the particle exhibits a pure magnetic moment in the non-relativistic approximation. The well-known equations for the electron and the meson are included as special cases in the present scheme. As a further illustration of the theory the coefficient matrices corresponding to a new elementary particle are constructed. This particle is shown to have states of spin both 3/2 and 1/2. In a certain sense it exhibits an inner structure in addition to the spin. In the non-relativistic approximation the behaviour of this particle in an electromagnetic field is the same as that of the Dirac electron. Finally, the transition from the particle to the wave form of the equations of motion is effected and the field equations are given in terms of tensors and spinors.

Acoustic wave frequency filtering in constant total length phononic crystals of Al/Pb multilayer

2021 ◽  
Author(s):  
Chittaranjan Nayak ◽  
Mehdi Solaimani ◽  
Alireza Aghajamali ◽  
Arafa H. Aly
Keyword(s):  
Acoustic Wave ◽  
Phononic Crystal ◽  
Phononic Crystals ◽  
Geometrical Parameters ◽  
One Dimensional ◽  
Internal Geometry ◽  
Total Length ◽  
Acoustic Filters ◽  
System Length ◽  
Phononic Band Gaps

In this study, we have scrutinized the frequency gap generation by changing the geometrical parameters of a one-dimensional phononic crystal. For this purpose, we have calculated the transmission coefficient of an incident acoustic wave by using the transfer matrix method. We have retained and fixed the total length of the system and changed the system internal geometry not to increase the system length too much. Another reason was to adjust the phononic band gaps and get the desired transmission properties by finding the optimum internal geometry without increasing or decreasing the total length of phononic crystals. In addition, we also propose few structures with the opportunity of applications in acoustical devices such as sonic reflectors. Our results can also be of high interest to design acoustic filters in the case that transmission of certain frequencies is necessary.

Numerical research on dynamic stress of phononic crystal ROD in longitudinal wave band gap

2014 ◽  
Vol 28 (32) ◽  
pp. 1450231 ◽  
Author(s):  
Hai-Sheng Shu ◽  
Xiao-Na Shi ◽  
Shi-Dan Li ◽  
Shao-Gang Liu ◽  
Wei-Yuan Wang ◽  
...  
Keyword(s):  
Wave Equation ◽  
Dynamic Stress ◽  
Phononic Crystal ◽  
Wave Band ◽  
Longitudinal Stress ◽  
Theoretical Derivation ◽  
Modal Frequency ◽  
Element Simulation ◽  
Arbitrary Section ◽  
Numerical Research

For the propagation of harmonic longitudinal stress wave in phononic crystal rod (PCR), transfer matrix of elastic wave in PCR was derived based on the wave equation and band structure of infinite PCR was calculated. For semi-infinite PCR, theoretical derivation of dynamic stress solutions of arbitrary section and internal interfaces was conducted with Bloch theorem. Inherent relationship between dynamic stress and surface wave modal frequency (SWMF) was analyzed. Afterwards, numerical computation mainly focusing on dynamic stress level of the internal interfaces of PCR was given in detail. Finally, numerical analysis for finite PCR was carried out and verified by finite element simulation. Our results show that SWMF has a significant influence on the dynamic stress, and exactly it is the formal pole of stress solution whose nature is directly determined by the sort order of the two materials constituting the PCR.

scholarly journals EN The wave model of secondary flows and coherent structures in pipes

2020 ◽  
Vol 55 (5-6) ◽  
pp. 273-281
Author(s):  
S. Surkov
Keyword(s):  
Wave Equation ◽  
Stream Function ◽  
Coherent Structures ◽  
Large Scale ◽  
Experimental Studies ◽  
Viscous Friction ◽  
Orthogonal Decomposition ◽  
Secondary Flows ◽  
Friction Forces ◽  
Special Cases

In this article, a theoretical analysis of the flows arising in the cross sections of fluid and gas flows is performed. Such flows are subdivided into secondary flows and coherent structures. From experimental studies it is known that both types of flows are long-lived large-scale movements (LSM) stretched along the flow. The relative stability of the vortices is traditionally explained by the fact that the viscous friction forces that inhibit the rotation are compensated by the intensification of the swirl when moving slowly rotating peripheral layers to the center of the vortex due to longitudinal tension. An analysis of this mechanism made it possible to develop a relatively simple model of vortex structures in which the viscous friction forces and axial expansion are considered to be infinitesimal. Under these assumptions, one can use the equations of motion of an ideal fluid in the variables “stream function - vorticity”. It is shown that under certain assumptions these equations take the form of a wave equation, and the boundary conditions are the condition that the stream function on the solid walls of the flow equals zero. The obtained solutions of the wave equation describe the following special cases: Goertler’s vortices between rotating cylinders, secondary flows in a pipe with a square cross section, swirling flow in a round pipe, paired vortex after bend of the pipe. The physical sense of more complex solutions of the wave equation has become clear relatively recently. Very similar structures were found in experimental studies using orthogonal decomposition (POD) of a turbulent pulsations field. This may mean that the eigenfunctions in the POD correspond to coherent structures that really arise in the flow. The results obtained confirm the hypothesis that secondary flows and coherent structures have a common nature. The solutions obtained in this paper can be used in processing the experiment as eigenfunctions for the orthogonal decomposition method. In addition, they can be used in direct numerical simulation (DNS) of turbulent flows

scholarly journals Interaction of a Screw Dislocation with Interface and Wedge-Shaped Cracks in One-Dimensional Hexagonal Piezoelectric Quasicrystals Bimaterial

2019 ◽  
Vol 2019 ◽  
pp. 1-7
Author(s):  
Lian he Li ◽  
Yue Zhao
Keyword(s):  
Screw Dislocation ◽  
Electric Fields ◽  
Electric Displacement ◽  
Image Force ◽  
Coupling Constants ◽  
Geometrical Parameters ◽  
Intensity Factors ◽  
One Dimensional ◽  
Special Cases ◽  
Analytical Expressions

Interaction of a screw dislocation with wedge-shaped cracks in one-dimensional hexagonal piezoelectric quasicrystals bimaterial is considered. The general solutions of the elastic and electric fields are derived by complex variable method. Then the analytical expressions for the phonon stresses, phason stresses, and electric displacements are given. The stresses and electric displacement intensity factors of the cracks are also calculated, as well as the force on dislocation. The effects of the coupling constants, the geometrical parameters of cracks, and the dislocation location on stresses intensity factors and image force are shown graphically. The distribution characteristics with regard to the phonon stresses, phason stresses, and electric displacements are discussed in detail. The solutions of several special cases are obtained as the results of the present conclusion.

scholarly journals The Cauchy Problem to a Shallow Water Wave Equation with a Weakly Dissipative Term

2012 ◽  
Vol 2012 ◽  
pp. 1-23
Author(s):  
Ying Wang ◽  
YunXi Guo
Keyword(s):  
Wave Equation ◽  
Shallow Water ◽  
Water Wave ◽  
Sufficient Conditions ◽  
Global Weak Solution ◽  
Dissipative Term ◽  
Shallow Water Wave ◽  
Global Strong Solution ◽  
Special Cases ◽  
The Cauchy Problem

A shallow water wave equation with a weakly dissipative term, which includes the weakly dissipative Camassa-Holm and the weakly dissipative Degasperis-Procesi equations as special cases, is investigated. The sufficient conditions about the existence of the global strong solution are given. Provided that(1-∂x2)u0∈M+(R),u0∈H1(R),andu0∈L1(R), the existence and uniqueness of the global weak solution to the equation are shown to be true.

Phononic Band Gaps in Al2O3/Epoxy Composite

2018 ◽  
Vol 912 ◽  
pp. 112-117 ◽  
Author(s):  
Edson Jansen Pedrosa Miranda Jr. ◽  
J.M.C. dos Santos
Keyword(s):  
Cross Section ◽  
Transverse Vibration ◽  
Elastic Waves ◽  
Epoxy Composite ◽  
Phononic Crystal ◽  
Band Gaps ◽  
Square Lattice ◽  
Plane Wave Expansion ◽  
Phononic Band Gaps ◽  
Angle Of Rotation

In this study, we have investigated the band structure of elastic waves propagating in a phononic crystal, consisting of an epoxy matrix reinforced by Al2O3 inclusions in a square and hexagonal lattices. We also studied the influence of the inclusion geometry cross section – circular, hollow circular, square and rotated square with a 45° angle of rotation with respect to the x, y axes. The plane wave expansion (PWE) method is used to solve the wave equation considering the wave propagation in the xy plane (longitudinal-transverse vibration, XY mode, and transverse vibration, Z mode). The complete band gaps between the XY and Z modes are observed to circular, square and rotated square cross section inclusion and the best performance is for rotated square cross section inclusion in a square lattice. We suggest that the Al2O3/epoxy composite is feasible for vibrations management.

Wave propagation in a non-local piezoelectric phononic crystal Timoshenko nanobeam

2020 ◽  
pp. 2150064
Author(s):  
Feiyang He ◽  
Denghui Qian ◽  
Musai Zhai
Keyword(s):  
Wave Propagation ◽  
Phononic Crystal ◽  
Local Effect ◽  
Geometric Parameters ◽  
Width Ratio ◽  
Plane Wave Expansion ◽  
Mechanical Coupling ◽  
Non Local ◽  
Influencing Parameters ◽  
Scale Coefficient

By applying non-local elasticity theory and plane wave expansion (PWE) method to Timoshenko beam, the calculation method of band structure of a non-local piezoelectric phononic crystal (PC) Timoshenko nanobeam is proposed and formulized. In order to investigate the properties of wave propagating in the nanobeam in detail, bandgaps of first four orders are picked, and the corresponding influence rules of thermo-electro-mechanical coupling fields, non-local effect and geometric parameters on bandgaps are studied. During the research works, temperature variation, external electrical voltage and axial force are chosen as the influencing parameters related to the thermo-electro-mechanical coupling fields. Scale coefficient is chosen as the influencing parameter corresponding to non-local effect. Length ratio between materials PZT-4 and epoxy and height-width ratio are chosen as the influencing parameters of geometric parameters. Moreover, all the band structures and influence rules of Timoshenko nanobeam are compared to those of Euler nanobeam. The results are expected to be of help for the design of micro and nanodevices based on piezoelectric periodic nanobeams.

Sign in / Sign up

Export Citation Format

Share Document