scholarly journals Some New Three-Dimensional Green's Functions in Antisotropic Piezoelectric Bimaterials

2007 ◽  
Vol 1 (2) ◽  
Author(s):  
E. Pan
Keyword(s):  
Piezoelectric Materials ◽  
Electrical Potential ◽  
Three Dimensional ◽  
Displacement Component ◽  
Superposition Method ◽  
Interface Conditions ◽  
Electrical Fields ◽  
Interface Models ◽  
Complementary Part ◽  
Electrical Displacement

In this paper, we derive three-dimensional Green’s functions of point-force/pointcharge in anisotropic and piezoelectric bimaterials for six different interface models. Mechanically, the six interface models are either in perfect or smooth contact along the interface; electronically, they can be closed, open interface, or with continuous electrical potential and normal electrical displacement component along the interface. By introducing certain modified bimaterial Stroh matrices, along with the extended Stroh formalism and the Mindlin’s superposition method, the bimaterial Green’s functions for the six interface conditions are expressed in terms of a concise and mathematically similar uniform form. That is, the physical-domain bimaterial Green’s functions can all be expressed as a sum of a homogeneous full-space Green’s function in an explicit form and a complementary part in terms of simple line-integrals over [0, π] suitable for standard numerical integration. Furthermore, utilizing a direct connection between the 2D and 3D Stroh matrices observed in this paper, the corresponding 2D bimaterial Green’s functions are also derived, in exact-closed form, for the six interface conditions. Based on the bimaterial Green’s functions, the effects of different interface conditions on the mechanical and electrical fields are discussed. It is noted that only the complementary part of the solution contributes to the differences of the mechanical and electrical fields arising from different interface conditions. Also, numerical examples are presented for the Green’s functions in the bimaterials made of two half-spaces with two typical piezoelectric materials, quartz and ceramic. Certain new features are observed which could be of great interest to the design of piezoelectric composites and to the numerical modeling of strained quantum devices using the boundary element method.

Three-Dimensional Green’s Functions in Anisotropic Elastic Bimaterials With Imperfect Interfaces

2003 ◽  
Vol 70 (2) ◽  
pp. 180-190 ◽  
Author(s):  
E. Pan
Keyword(s):  
Green's Functions ◽  
Green’S Functions ◽  
Three Dimensional ◽  
Imperfect Interface ◽  
Boundary Integral ◽  
Stress Fields ◽  
Superposition Method ◽  
Interface Conditions ◽  
Complementary Part ◽  
Anisotropic Elastic

In this paper, three-dimensional Green’s functions in anisotropic elastic bimaterials with imperfect interface conditions are derived based on the extended Stroh formalism and the Mindlin’s superposition method. Four different interface models are considered: perfect-bond, smooth-bond, dislocation-like, and force-like. While the first one is for a perfect interface, other three models are for imperfect ones. By introducing certain modified eigenmatrices, it is shown that the bimaterial Green’s functions for the three imperfect interface conditions have mathematically similar concise expressions as those for the perfect-bond interface. That is, the physical-domain bimaterial Green’s functions can be obtained as a sum of a homogeneous full-space Green’s function in an explicit form and a complementary part in terms of simple line-integrals over [0,π] suitable for standard numerical integration. Furthermore, the corresponding two-dimensional bimaterial Green’s functions have been also derived analytically for the three imperfect interface conditions. Based on the bimaterial Green’s functions, the effects of different interface conditions on the displacement and stress fields are discussed. It is shown that only the complementary part of the solution contributes to the difference of the displacement and stress fields due to different interface conditions. Numerical examples are given for the Green’s functions in the bimaterials made of two anisotropic half-spaces. It is observed that different interface conditions can produce substantially different results for some Green’s stress components in the vicinity of the interface, which should be of great interest to the design of interface. Finally, we remark that these bimaterial Green’s functions can be implemented into the boundary integral formulation for the analysis of layered structures where imperfect bond may exist.

Analysis of Commercial Vehicle Thrust Rod Load Simulation

2015 ◽  
Vol 713-715 ◽  
pp. 159-163
Author(s):  
Guo Yu Feng ◽  
Wen Ku Shi ◽  
Jun Ke ◽  
Lu Lu Guo
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Time History ◽  
Prototype Model ◽  
Superposition Method ◽  
Adams Software ◽  
Lower Load ◽  
Multi Body ◽  
Load Simulation ◽  
Three Dimensional Space

In order to obtain the accurate thrust rod load, based on the theory of multi body dynamics, establish the complete vehicle virtual prototype model by using ADAMS software, the dynamic simulation of the thrust rod load time history. Combined with MATLAB software to build three-dimensional space pavement model with harmonic superposition method, obtaining the thrust rod load under different conditions, the simulation results show that, the vehicle loaded with uphill turn thrust rod by the load of the largest, and bear in various working upper thrust rod load than the lower load. Consistent with the experimental results, illustrate the modeling method is correct, can quickly and accurately obtain the thrust rod load.

Three-dimensional records of surface displacement on the Superstition Hills fault zone associated with the earthquakes of 24 November 1987

1989 ◽  
Vol 79 (2) ◽  
pp. 376-389
Author(s):  
Robert V. Sharp ◽  
John L. Saxton
Keyword(s):  
Fault Zone ◽  
Power Law ◽  
Main Shock ◽  
Three Dimensional ◽  
Surface Displacement ◽  
Displacement Component ◽  
Observation Data ◽  
Fault Movement ◽  
Remarkable Agreement ◽  
Observation Period

Abstract Seven quadrilaterals, constructed at broadly distributed points on surface breaks within the Superstition Hills fault zone, were repeatedly remeasured after the pair of 24 November 1987 earthquakes to monitor the growing surface displacement. Changes in the dimensions of the quadrilaterals are recalculated to right-lateral and extensional components at millimeter resolution, and vertical components of change are resolved at 0.2 mm precision. The displacement component data for four of the seven quadrilaterals record the complete fault movement with respect to an October 1986 base. These data fit with remarkable agreement the power law U ( t ) = U f ( B t 1 + B t ) c , where U(t) is a displacement component at time t after the second main shock and Uf, B, and c are constants. This power law permits estimation of the final displacement, Uf, from the data obtained within the period of observation. Data from one quadrilateral, located near the epicenter of the second main shock and northeast-trending conjugate faults, allow that about 5 cm of right-lateral slip may have been associated with the first main shock there. Data from the other quadrilaterals confirm that the surface faulting on most of the Superstition Hills fault zone did initiate at the time of the second main shock of the 1987 earthquakes. The three-dimensional motion vectors all describe nearly linear trajectories throughout the observation period, and they indicate smooth shearing on their respective fault surfaces. The inclination of the shear surfaces is generally nearly vertical, except near the south end of the Superstition Hills fault zone where two strands dip northeastward at about 70°. Surface displacement on these strands is right reverse. Another kind of deformation, superimposed on the fault displacements, has been recorded at all quadrilateral sites. It consists of a northwest-southeast contraction or component of contraction that ranged from 0 to 0.1 per cent of the quadrilateral lengths between November 1987 and April 1988.

Energy Harvesting Aspects of Irregular Vibrating Forces Acting on Piezoelectric Devices

2015 ◽  
pp. 143-158
Author(s):  
Alessandro Massaro
Keyword(s):  
Energy Harvesting ◽  
Piezoelectric Materials ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Output Current ◽  
Vibrating System ◽  
External Forces ◽  
Piezoelectric Devices ◽  
Three Dimensional Space

After a brief introduction of piezoelectric materials, this chapter focuses on the characterization of vibrating freestanding piezoelectric AlN devices forced by different external forces acting simultaneously. The analyzed vibrating forces are applied mainly to piezoelectric freestanding structures stimulated by irregular vibration phenomena. Particular kinds of theoretical noise signals are commented. The goal of the chapter is to analyze the effect of the noise in order to model the chaotic vibrating system and to predict the output current signals. Moreover, the author also shows a possible alternative way to detect different vibrating force directions in the three dimensional space by means of curved piezoelectric layouts.

Modeling and stabilization of current-controlled piezo-electric beams with dynamic electromagnetic field

2020 ◽  
Vol 26 ◽  
pp. 8
Author(s):  
Ahmet Özkan Özer ◽  
Kirsten A. Morris
Keyword(s):  
Electromagnetic Field ◽  
Piezoelectric Materials ◽  
Electrical Potential ◽  
Gauge Condition ◽  
Current Control ◽  
Magnetic Vector Potential ◽  
Bounded Control ◽  
The Cauchy Problem ◽  
A Current ◽  
Piezo Electric

Piezoelectric materials can be controlled with current (or charge) as the electrical input, instead of voltage. The main purpose of this paper is to derive the governing equations for a current-controlled piezo-electric beam and to investigate stabilizability. The magnetic permeability in piezo-electric materials is generally neglected in models. However, it has a significant qualitative effect on properties of the control system such as stabilizability. Besides the consideration of current control, there are several new aspects to the model. Most importantly, a fully dynamic magnetic model is included. Also, electrical potential and magnetic vector potential are chosen to be quadratic-through thickness to include the induced effects of the electromagnetic field. Hamilton’s principle is used to derive a boundary value problem that models a single piezo-electric beam actuated by a current (or charge) source at the electrodes. Two sets of decoupled system of partial differential equations are obtained; one for stretching of the beam and another one for bending motion. Since current (or charge) controller only affects the stretching motion, attention is focused on control of the stretching equations in this paper. It is shown that the Lagrangian of the beam is invariant under certain transformations. A Coulomb type gauge condition is used. This gauge condition decouples the electrical potential equation from the equations of the magnetic potential. A semigroup approach is used to prove that the Cauchy problem is well-posed. Unlike voltage actuation, a bounded control operator in the natural energy space is obtained. The paper concludes with analysis of stabilizability and comparison with other actuation approaches and models.

A Variational-Asymptotic Theory of Smart Slender Structures

Aerospace ◽  
2005 ◽  
Author(s):  
Sitikantha Roy ◽  
Wenbin Yu
Keyword(s):  
Dimensional Analysis ◽  
Piezoelectric Materials ◽  
Three Dimensional ◽  
Reduction Process ◽  
Cross Sectional ◽  
Cross Sectional Analysis ◽  
Variational Asymptotic ◽  
Small Parameters ◽  
Sectional Analysis ◽  
Slender Structures

The goal of the present work is to develop an efficient simulation tool with high-fidelity to help the engineers design and analyze smart slender structures with embedded piezoelectric materials. Actuation and sensing capabilities of piezoelectric material embedded in smart beam including geometric nonlinearity will be explored. The dimensional reduction process has been carried out using the powerful Variational Asymptotic Method. Starting from the exact three-dimensional electric-mechanically coupled enthalpy functional, the asymptotical analysis is done on the functional itself with respect to the naturally occurring small parameters. The original three-dimensional electric-mechanical problem of the slender structure is decomposed into two separate problems: a two-dimensional analysis over the cross section and a one-dimensional analysis over the beam reference line. The coupled cross-sectional analysis is being implemented in VABS, a versatile cross-sectional analysis code.

scholarly journals Proton-Dependent Gating and Proton Uptake by Wzx Support O-Antigen-Subunit Antiport Across the Bacterial Inner Membrane

mBio ◽  
2013 ◽  
Vol 4 (5) ◽  
Author(s):  
Salim T. Islam ◽  
Paul D. W. Eckford ◽  
Michelle L. Jones ◽  
Timothy Nugent ◽  
Christine E. Bear ◽  
...  
Keyword(s):  
Cell Surface ◽  
Bacterial Cell ◽  
Electrical Potential ◽  
Three Dimensional ◽  
Structural Data ◽  
Inner Membrane ◽  
Content Type ◽  
Bacterial Cell Surface ◽  
Repeat Units ◽  
Dependent Transport

ABSTRACTWzx flippases are crucial for bacterial cell surface polysaccharide assembly as they transport undecaprenyl pyrophosphate-linked sugar repeat units from the cytoplasmic to the periplasmic leaflets of the inner membrane (IM) for final assembly. Our recently reported three-dimensional (3D) model structure of Wzx fromPseudomonas aeruginosaPAO1 (WzxPa) displayed a cationic internal vestibule and functionally essential acidic amino acids within transmembrane segment bundles. Herein, we examined the intrinsic transport function of WzxPafollowing its purification and reconstitution in phospholipid liposomes. WzxPawas capable of mediating anion flux, consistent with its cationic interior. This flux was electrogenic and modified by extraliposomal pH. Mutation of the above-mentioned acidic residues (E61, D269, and D359) reduced proton (H+)-modified anion flux, showing the role of these amino acid side chains in H+-dependent transport. Wzx also mediated acidification of the proteoliposome interior in the presence of an outward anion gradient. These results indicate H+-dependent gating and H+uptake by WzxPaand allow for the first H+-dependent antiport mechanism to be proposed for lipid-linked oligosaccharide translocation across the bacterial IM.IMPORTANCEMany bacterial cell surface polysaccharides that are important for survival and virulence are synthesized at the periplasmic leaflet of the inner membrane (IM) using precursors produced in the cytoplasm. Wzx flippases are responsible for translocation of lipid-linked sugar repeat units across the IM and had been previously suggested to simply facilitate passive substrate diffusion. Through our characterization of purified Wzx in a reconstitution system described herein, we have observed protein-dependent intrinsic transport producing a change in the electrical potential of the system, with H+identified as the coupling ion. These results provide the first evidence for coupled (i.e., secondary active) transport by these proteins and, in conjunction with structural data, allow for an antiport mechanism to be proposed for the directed transport of lipid-linked sugar substrates across the IM. These findings bring our understanding of lipid-linked polysaccharide transporter proteins more in line with the efflux pumps to which they are evolutionarily related.

A New Three-Dimensional Moving Timoshenko Beam Element for Moving Load Problem Analysis

2020 ◽  
Vol 142 (3) ◽  
Author(s):  
Yan Xu ◽  
Weidong Zhu ◽  
Wei Fan ◽  
Caijing Yang ◽  
Weihua Zhang
Keyword(s):  
Dynamic Analysis ◽  
Coordinate System ◽  
Timoshenko Beam ◽  
Moving Load ◽  
Three Dimensional ◽  
Beam Element ◽  
Superposition Method ◽  
Reference Coordinate System ◽  
Current Formulation ◽  
Timoshenko Beam Element

Abstract A new three-dimensional moving Timoshenko beam element is developed for dynamic analysis of a moving load problem with a very long beam structure. The beam has small deformations and rotations, and bending, shear, and torsional deformations of the beam are considered. Since the dynamic responses of the beam are concentrated on a small region around the moving load and most of the long beam is at rest, owing to the damping effect, the beam is truncated with a finite length. A control volume that is attached to the moving load is introduced, which encloses the truncated beam, and a reference coordinate system is established on the left end of the truncated beam. The arbitrary Lagrangian–Euler method is used to describe the relationship of the position of a particle on the beam between the reference coordinate system and the global coordinate system. The truncated beam is spatially discretized using the current beam elements. Governing equations of a moving element are derived using Lagrange’s equations. While the whole beam needs to be discretized in the finite element method or modeled in the modal superposition method (MSM), only the truncated beam is discretized in the current formulation, which greatly reduces degrees-of-freedom and increases the efficiency. Furthermore, the efficiency of the present beam element is independent of the moving load speed, and the critical or supercritical speed range of the moving load can be analyzed through the present method. After the validation of the current formulation, a dynamic analysis of three-dimensional train–track interaction with a non-ballasted track is conducted. Results are in excellent agreement with those from the commercial software simpack where the MSM is used, and the calculation time of the current formulation is one-third of that of simpack. The current beam element is accurate and more efficient than the MSM for moving load problems of long three-dimensional beams. The derivation of the current beam element is straightforward, and the beam element can be easily extended for various other moving load problems.

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