Showing papers on "Transverse plane published in 2009"
Patent•
15 Jul 2009
TL;DR: In this paper, a method of treating a compression fracture in a bone comprising the steps of forming a transverse cavity within a bone defined by at least one substantially flat surface lying substantially in a transversal plane formed by and communicating with said transverse cavities is described.
Abstract: A method of treating a compression fracture in a bone comprising the steps of forming a transverse cavity within said bone defined by at least one substantially flat surface lying substantially in a transverse plane formed by and communicating with said transverse cavity, the transverse cavity having a substantially uniform transverse extent and a maximum height, the maximum height being less than said transverse extent and applying a force within said transverse cavity generally normal to said surface to displace said surface and restore said bone to its substantially normal anatomic position.
299 citations
TL;DR: Patients with clinically suspected FAI may have a substantial contour abnormality that can be underestimated or missed if only oblique axial plane images are reviewed, and radial plane imaging should be considered in the MRI investigation of FAI.
Abstract: Insufficient femoral head-neck offset is common in femoroacetabular impingement (FAI) and reflected by the alpha angle, a validated measurement for quantifying this anatomic deformity in patients with FAI. We compared the alpha angle determined on magnetic resonance imaging (MRI) oblique axial plane images with the maximal alpha angle value obtained using radial images. The MRIs of 41 subjects with clinically suspected FAI were reviewed and alpha angle measurements were performed on both oblique axial plane images parallel to the long axis of the femoral neck and radial images obtained using the center of the femoral neck as the axis of rotation. The mean oblique axial plane and mean maximal radial alpha angle values were 53.4° and 70.5°, respectively. In 54% of subjects, the alpha angle was less than 55° on the conventional oblique axial plane image but 55° or greater on the radial plane images. Radial images yielded higher alpha angle values than oblique axial images. Patients with clinically suspected FAI may have a substantial contour abnormality that can be underestimated or missed if only oblique axial plane images are reviewed. Radial plane imaging should be considered in the MRI investigation of FAI.
260 citations
TL;DR: In this paper, a review of the theory of wave and oscillation in a homogeneous straight magnetic cylinder with the particular emphasis on fast kink waves is presented, where the authors consider the effects of stratification, loop expansion, loop curvature, non-circular cross-section, loop shape and magnetic twist.
Abstract: On 14 July 1998 TRACE observed transverse oscillations of a coronal loop generated by an external disturbance most probably caused by a solar flare. These oscillations were interpreted as standing fast kink waves in a magnetic flux tube. Firstly, in this review we embark on the discussion of the theory of waves and oscillations in a homogeneous straight magnetic cylinder with the particular emphasis on fast kink waves. Next, we consider the effects of stratification, loop expansion, loop curvature, non-circular cross-section, loop shape and magnetic twist. An important property of observed transverse coronal loop oscillations is their fast damping. We briefly review the different mechanisms suggested for explaining the rapid damping phenomenon. After that we concentrate on damping due to resonant absorption. We describe the latest analytical results obtained with the use of thin transition layer approximation, and then compare these results with numerical findings obtained for arbitrary density variation inside the flux tube. Very often collective oscillations of an array of coronal magnetic loops are observed. It is natural to start studying this phenomenon from the system of two coronal loops. We describe very recent analytical and numerical results of studying collective oscillations of two parallel homogeneous coronal loops. The implication of the theoretical results for coronal seismology is briefly discussed. We describe the estimates of magnetic field magnitude obtained from the observed fundamental frequency of oscillations, and the estimates of the coronal scale height obtained using the simultaneous observations of the fundamental frequency and the frequency of the first overtone of kink oscillations. In the last part of the review we summarise the most outstanding and acute problems in the theory of the coronal loop transverse oscillations.
197 citations
TL;DR: Reflection of an arbitrary plane wave, incident with a complex propagation vector, is analyzed for the planar DB boundary and it is shown that waves polarized transverse electric and transverse magnetic with respect to the normal of the boundary are reflected as from respective perfect electric conductor and perfect magnetic conductor planes.
Abstract: A set of boundary conditions requiring vanishing of the normal components of the D and B vectors at the boundary surface is introduced and labeled as that of DB boundary Basic properties of the DB boundary are studied in this paper Reflection of an arbitrary plane wave, incident with a complex propagation vector, is analyzed for the planar DB boundary It is shown that waves polarized transverse electric (TE) and transverse magnetic (TM) with respect to the normal of the boundary are reflected as from respective perfect electric conductor and perfect magnetic conductor planes The basic problem of current source above the planar DB boundary is solved by applying TE and TM decomposition for the source Realization of the DB boundary in terms of an interface of uniaxially anisotropic metamaterial half-space with zero axial medium parameters is considered It is also shown that such a medium with small axial parameters acts as a spatial filter for waves incident at the interface which could be used for narrowing the beam of a directive antenna Application of DB boundary as an isotropic soft surface with low interaction between antenna apertures also appears possible
139 citations
TL;DR: The first analysis of transverse loop oscillations observed by both Solar TErrestrial Relations Observatories (STEREO) and Extreme Ultraviolet Imager (EUVI) is presented in this paper.
Abstract: The first analysis of a transverse loop oscillation observed by both Solar TErrestrial RElations Observatories (STEREO) spacecraft is presented, for an event on the 2007 June 27 as seen by the Extreme Ultraviolet Imager (EUVI). The three-dimensional loop geometry is determined using a three-dimensional reconstruction with a semicircular loop model, which allows for an accurate measurement of the loop length. The plane of wave polarization is found from comparison with a simulated loop model and shows that the oscillation is a fundamental horizontally polarized fast magnetoacoustic kink mode. The oscillation is characterized using an automated method and the results from both spacecraft are found to match closely. The oscillation period is 630 {+-} 30 s and the damping time is 1000 {+-} 300 s. Also, clear intensity variations associated with the transverse loop oscillations are reported for the first time. They are shown to be caused by the effect of line-of-sight integration. The Alfven speed and coronal magnetic field derived using coronal seismology are discussed. This study shows that EUVI/STEREO observations achieve an adequate accuracy for studying long-period, large-amplitude transverse loop oscillations.
128 citations
TL;DR: In this article, a surface load normal to a plane connecting the ends of the micro-cracks is used as an approximate representation of contact stresses during frictionless sliding. But the model applied here gives significantly later occurrence of a maximum overall shear stress than that found by using hydrostatic pressure, the present model does predict a maximum in all the cases analyzed.
Abstract: When voids are present in a ductile material subject to a shear dominated stress state under low stress triaxiality the voids collapse to micro-cracks, which subsequently rotate and elongate in the shear field. In the present plane strain analyses for cylindrical voids a surface load normal to a plane connecting the ends of the micro-crack is used as an approximate representation of contact stresses during frictionless sliding. In a previous study of the same problem the author applied hydrostatic pressure inside the nearly closed micro-crack to approximate contact conditions. The transverse surface loads used in the present analyses avoid the tendency to unrealistically elongate the voids. It is found that even though the model applied here gives significantly later occurrence of a maximum overall shear stress than that found by using hydrostatic pressure, the present model does predict a maximum in all the cases analyzed and thus illustrates the micro-mechanism leading to failure of the material by localization of plastic flow.
123 citations
TL;DR: An analytic replenishment model is introduced that incorporates the hemodynamic properties of the flow system (velocity distribution and vascular cross section), includes the elevation and axial plane pressure distributions and accounts for the distinct high and low MI disruption and detection boundaries.
Abstract: Contrast-enhanced ultrasound (CEUS) is a promising clinical tool capable of noninvasively quantifying flow and relative vascular volume within the microcirculation. Quantification can be performed by recording the replenishment intensity time course of the imaging plane after the local disruption of agent during a constant infusion. Traditional analyses of the time-intensity curves have relied on mathematical functions (e.g., mono-exponential) that fail to consider the underlying physical principles of the flow system and the influence of the measurement device. In reality, the time-intensity curve reflects the hemodynamics and morphology of the vascular system being measured, the ultrasound field distribution and microbubble properties. We introduce a general analytic disruption replenishment model that attempts to account for these parameters and compare its performance to the established model in a flow phantom. Specifically, the proposed model incorporates the hemodynamic properties of the flow system (velocity distribution and vascular cross section); includes the elevation and axial plane pressure distributions; and accounts for the distinct high and low mechanical index (MI) disruption and detection boundaries. In addition, we demonstrated the importance of the ultrasound beam profile for accurate velocity quantification. It was shown that velocity estimates vary by up to 56% if the depth-dependent elevation thickness is not properly accounted for. Compared with the currently accepted mono-exponential model, the presented formalism was shown to be more robust in the presence of simulated motion artifacts and demonstrated better agreement in both the quality of the fit and estimation of velocity (∼3 to 10% vs. 90% error) for the same flow and acoustic conditions. (E-mail: hudsonjm@gmail.com )
115 citations
TL;DR: In this article, the Stokes flow through microchannels employing superhydrophobic surfaces with alternating micro-grooves and ribs was analyzed and the effects of patterning the grooves on one or both channel walls were also analyzed.
Abstract: Superhydrophobic surfaces have been demonstrated to be capable of reducing fluid resistance in micro- and nanofluidic applications. The objective of this paper is to present analytical solutions for the Stokes flow through microchannels employing superhydrophobic surfaces with alternating micro-grooves and ribs. Results are presented for both cases where the micro-grooves are aligned parallel and perpendicular to the flow direction. The effects of patterning the grooves on one or both channel walls are also analyzed. The reduction in fluid resistance has been quantified in terms of a dimensionless effective slip length, which is found to increase monotonically with the shear-free fraction and the periodic extent of each groove–rib combination normalized by the channel half-height. Asymptotic relationships have been derived for the normalized effective slip length corresponding to large and small limiting values of the shear-free fraction and the normalized groove–rib period. A detailed comparison has been made between transverse and longitudinal grooves, patterned on one or both channel walls, to assess their effectiveness in terms of enhancing the effective slip length. These comparisons have been carried out for small and large limiting values, as well as finite values of the shear-free fraction and normalized groove–rib period. Results for the normalized effective slip length corresponding to transverse and longitudinal grooves are further applied to model the Stokes flow through microchannels employing superhydrophobic surfaces containing a periodic array of micro-grooves inclined at an angle to the direction of the applied pressure gradient. Results are presented for the normalized effective slip lengths parallel to the direction of the applied pressure gradient and the normalized cross flow rate perpendicular to the direction of the applied pressure gradient.
109 citations
TL;DR: The radiation force on a Rayleigh dielectric sphere induced by focused coherent and partially coherent flat-topped beams is investigated theoretically and it is found that the transverse trapping range at the planes near the focal plane can be increased by increasing the flatness of the flat- topped beam.
Abstract: Propagations of coherent and partially coherent flat-topped beams through a focusing optical system are formulated. The radiation force on a Rayleigh dielectric sphere induced by focused coherent and partially coherent flat-topped beams is investigated theoretically. It is found that we can increase the transverse trapping range at the planes near the focal plane by increasing the flatness (i.e., beam order) of the flat-topped beam, and increase the transverse and longitudinal trapping ranges at the focal plane by decreasing the initial coherence of the flat-topped beam. Moreover the trapping stiffness of flat-topped beam becomes lower as the beam order increases or the initial coherence decreases. The trapping stability is also analyzed.
106 citations
TL;DR: In this paper, cooling of the plasma influences the oscillation properties (e.g., eigenfunctions and eigenfrequencies) of transverse (i.e., kink) magnetohydrodynamic (MHD) waves in a compressible magnetic flux tube embedded in a gravitationally stratified and uniformly magnetized atmosphere.
Abstract: Here we present an investigation into how cooling of the plasma influences the oscillation properties (e.g., eigenfunctions and eigenfrequencies) of transverse (i.e., kink) magnetohydrodynamic (MHD) waves in a compressible magnetic flux tube embedded in a gravitationally stratified and uniformly magnetized atmosphere. The cooling is introduced via a temperature-dependent density profile. A time-dependent governing equation is derived and an approximate zeroth-order solution is then obtained. From this the influence of cooling on the behavior of the eigenfrequencies and eigenfunctions of the transverse MHD waves is determined for representative cooling timescales. It is shown analytically, as the loop cools, how the amplitude of the perturbations is found to decrease as time increases. For cooling timescales of 900-2000 s (as observed in typical EUV loops), it is shown that the cooling has important and relevant influence on the damping times of loop oscillations. Next, the theory is put to the test. The damping due to cooling is fitted to a representative observation of standing kink oscillation of EUV loops. It is also shown with an explicit approximate analytical form, how the period of the fundamental and first harmonic of the kink mode changes with time as the loop cools. A consequence of this is that the value of the period ratio P 1/P 2, a tool that is popular in magneto-seismological studies in coronal diagnostics, decreases from the value of a uniform loop, 2, as the temperature decreases. The rate of change in P 1/P 2 is dependent upon the cooling timescale and is well within the observable range for typical EUV loops. Further to this, the magnitude of the anti-node shift of the eigenfunctions of the first harmonic is shown to continually increase as the loop cools, giving additional impetus to the use of spatial magneto-seismology of the solar atmosphere. Finally, we suggest that measurements of the rate of change in the eigenfunctions and eigenfrequencies of MHD oscillations can provide values for the cooling timescale and a further insight into the physics of coronal loops.
89 citations
TL;DR: In this paper, a pair of equal-sized circular cylinders of low nondimensional mass (m * = 10 ) in a tandem arrangement were analyzed for flow-induced vibrations in two dimensions, where the structural damping was set to zero for enabling maximum amplitudes of oscillation.
TL;DR: Bona fide two-dimensional rectification effects are reported, which cannot be explained by an approximate Fick-Jacobs kinetics, such as the characteristic curve of the current pumped by a transverse ac bias and the selective gating exerted on a driven longitudinal current.
Abstract: Driven transport of noninteracting Brownian particles in two-dimensional asymmetric channels is investigated by fully accounting for longitudinal and transverse diffusions. Bona fide two-dimensional rectification effects are reported, which cannot be explained by an approximate Fick-Jacobs kinetics, such as the characteristic curve of the current pumped by a transverse ac bias and the selective gating exerted by a transverse ac bias on a driven longitudinal current. Possible experimental demonstrations of these effects in superconducting devices are also discussed.
TL;DR: In this paper, a unified yield criterion for metallic sandwich structures considering the effect of core strength is proposed, which is valid for sandwich cross-sections with various core strengths and geometries.
TL;DR: In this article, a theoretical treatment of Timoshenko [S. Timoshenko, Philos. Mag. 41, 744 (1921)] beams is presented, in which the influences of shear deformation, rotary inertia, and scale coefficient are taken into account.
Abstract: This letter presents a theoretical treatment of Timoshenko [S. Timoshenko, Philos. Mag. 41, 744 (1921)] beams, in which the influences of shear deformation, rotary inertia, and scale coefficient are taken into account. Based on the nonlocal elasticity theory, coupled equations for transverse deflection and rotation of cross section are derived. Free vibration of several typical beams is analyzed. Explicit expressions for modal shapes of vibration are presented. Natural frequencies are evaluated for free vibration of simply supported beams, clamped beams, cantilever beams, and clamped-hinged beams. The effects of the nonlocal parameter on natural frequencies and modal shapes are discussed in detail.
TL;DR: In this article, the authors evaluated the axial and transverse stiffness of optical tweezers using radial polarization and found that radial polarization enhances axial trapping properties while reducing the transverse trapping properties.
Abstract: The trapping efficiency and stiffness of optical tweezers using radial polarization are evaluated; the ray-tracing method and a proposed measurement method are used for numerical and experimental analyses, respectively. The maximum axial trapping efficiency with radial polarization is 1.84 times that with linear polarization, while the maximum transverse trapping efficiency decreases by 0.58 times. Further, the axial and transverse trapping efficiencies are found to be 1.19 times larger and 0.83 times smaller, respectively, than the values with linear polarization. From the experiments, the axial and transverse stiffness values are 1.2 times larger and 0.8 times smaller, respectively, with radial polarization. Hence, radial polarization enhances the axial trapping properties while reducing the transverse trapping properties.
21 Apr 2009-Nuclear Instruments & Methods in Physics Research Section A-accelerators Spectrometers Detectors and Associated Equipment
TL;DR: In this paper, the shape of the Z boson transverse momentum distribution at hadron colliders was studied on an event-by-event basis, and it was shown that the transverse component is almost insensitive to the momentum resolution of the individual leptons.
Abstract: We present a novel method for studying the shape of the Z boson transverse momentum distribution, Q T , at hadron colliders in p p ¯ / pp → Z / γ * → l + l - . The Q T is decomposed into two orthogonal components; one transverse and the other parallel to the di-lepton thrust axis. We show that the transverse component is almost insensitive to the momentum resolution of the individual leptons and is thus more precisely determined on an event-by-event basis than the Q T . Furthermore, we demonstrate that a measurement of the distribution of this transverse component is substantially less sensitive to the dominant experimental systematics (resolution unfolding and Q T dependence of event selection efficiencies) reported in the previous measurements of the Q T distribution.
TL;DR: In this article, the Collins mechanism for the single transverse spin asymmetry in the collinear factorization approach is studied and the corresponding twist-three fragmentation function is identified, and it is shown that the Collins function calculated in this approach is universal.
Abstract: We study the Collins mechanism for the single transverse spin asymmetry in the collinear factorization approach. The corresponding twist-three fragmentation function is identified. We show that the Collins function calculated in this approach is universal. We further examine its contribution to the single transverse spin asymmetry of semi-inclusive hadron production in deep inelastic scattering and demonstrate that the transverse momentum dependent and twist-three collinear approaches are consistent in the intermediate transverse momentum region where both apply.
TL;DR: In this article, an extended Melnikov method was employed to analyze the Shilnikov-type multi-pulse homoclinic bifurcations and chaotic dynamics for the non-planar oscillations of a cantilever beam subjected to a harmonic axial excitation and two transverse excitations at the free end.
TL;DR: In this article, the effect of the slow continuum on the damping of transverse thread oscillations was explored for the first time both analytically and numerically, and it was shown that damping due to slow resonance is much less efficient than that due to the Alfven resonance.
Abstract: Transverse oscillations of small amplitude are commonly seen in high-resolution observations of filament threads, i.e., the fine structures of solar filaments/prominences, and are typically damped in a few periods. Kink wave modes supported by the thread body offer a consistent explanation of these observed oscillations. Among the proposed mechanisms to explain the kink mode damping, resonant absorption in the Alfven continuum seems to be the most efficient as it produces damping times of about three periods. However, for a nonzero-β plasma and typical prominence conditions, the kink mode is also resonantly coupled to slow (or cusp) continuum modes, which could further reduce the damping time. In this Letter, we explore for the first time both analytically and numerically the effect of the slow continuum on the damping of transverse thread oscillations. The thread model is composed of a homogeneous and straight cylindrical plasma, an inhomogeneous transitional layer, and the homogeneous coronal plasma. We find that the damping of the kink mode due to the slow resonance is much less efficient than that due to the Alfven resonance.
Patent•
18 Feb 2009
TL;DR: In this paper, the authors describe a conductor assembly of the type which, when conducting current, generates a magnetic field or in which, in the presence of a changing magnetic field, a voltage is induced.
Abstract: A conductor assembly of the type which, when conducting current, generates a magnetic field or in which, in the presence of a changing magnetic field, a voltage is induced. According to an exemplary embodiment a conductor is positioned along a path of variable direction relative to a reference axis. The conductor has a width measurable along an outer surface thereof and along a series of different planes transverse to the path direction. The measured conductor width varies among the different planes. In one example, the conductor path is helical, positioned about the axis between turns of helical spaces, and the conductor width varies as a function of the azimuth angle.
TL;DR: It is shown that for few-cycle laser pulses the cavity shape becomes asymmetric and depends strongly on the carrier-envelope phase, and the degree of plasma cavity asymmetry as a function of the laser-plasma parameters is calculated.
Abstract: Carrier-envelope phase effects during the interaction of relativistically intense few-cycle laser pulses with a plasma are studied in the ''bubble'' regime when an electron cavity (bubble) is formed behind the pulse. We show that for few-cycle laser pulses the cavity shape becomes asymmetric and depends strongly on the carrier-envelope phase. The carrier-envelope phase varies when the laser pulse propagates in plasma, which causes transverse oscillations of the cavity. Furthermore, the beam of electrons trapped by the cavity becomes modulated in the polarization plane. To describe these effects we derive an analytical model extended beyond the ponderomotive approximation. The degree of plasma cavity asymmetry as a function of the laser-plasma parameters is calculated. The obtained results are verified by particle-in-cell simulations.
TL;DR: It is discovered that when circularly polarized light is obliquely incident on a two-dimensional metallic photonic crystal slab, electrical voltage is induced perpendicular to the incident plane, which is brought about by the angular momentum of the incident light.
Abstract: We discovered that when circularly polarized light is obliquely incident on a two-dimensional metallic photonic crystal slab, electrical voltage is induced perpendicular to the incident plane. The sign of the signal is reversed by changing the sense of polarization or incident angle. The origin of this transverse photoinduced voltage is explained in terms of the force proportional to the light intensity induced by the asymmetry, which is brought about by the angular momentum of the incident light, along with the modification of local near-surface electromagnetic fields in the slab and field enhancement due to surface plasmon resonance.
Patent•
09 Apr 2009
TL;DR: In this paper, the storage locations are accessible by operating vehicles (8) over a set of horizontal planes (6,7), which are movable over rails in longitudinal and transverse directions, and a movable ramp, a conveyor and a vertical lift are provided between the horizontal storage planes.
Abstract: The system (1) has horizontal storage planes (2-5) in which storage locations are provided. The storage locations are accessible by operating vehicles (8) over a set of horizontal planes (6,7). The operating vehicles are movable over rails in longitudinal and transverse directions. A movable, ramp, a conveyor and a vertical lift are provided between the horizontal storage planes. Locking and unlocking devices are provided in the storage locations. The storage locations are lifted and lowered by a lifting mechanism.
TL;DR: In this paper, the authors considered free transverse vibrations of nonuniform homogeneous beams and derived their fourth order differential equations of transverse vibration into a pair of second-order differential equations, leading to general solutions in terms of hypergeometric functions.
TL;DR: In this article, a SKD61 tool steel was friction stir processed using polycrystalline cubic boron nitride tool and microstructure, tensile properties and wear characteristic were evaluated.
TL;DR: In this article, it was shown that the transverse shift of a high-order circularly polarized vortex-beam in a uniaxial crystal depends on neither a magnitude nor a sign of the vortex topological charge, being defined only by a handedness of the initial circular polarization and the inclination angle of the beam.
Abstract: We have found the asymmetric splitting of a high-order circularly polarized vortex-beam in a uniaxial crystal. The l-order vortex-beam splits into the same one and the beam with the l-1 vortices at the beam axis while one optical vortex is shifted along the direction perpendicular to the inclination plane of the beam. Such a vortex displacement causes the transverse shift of the partial beam. We consider this effect both in terms of the conservation law of the angular-momentum flux and on the base of the solutions to the paraxial wave equation. We revealed that the transverse shift of the crystal-traveling beam depends on neither a magnitude nor a sign of the vortex topological charge being defined only by a handedness of the initial circular polarization and a sign of the inclination angle of the beam.
TL;DR: In this article, pull-out tests with cyclic tensile loading and different preadjusted crack widths along the pullout bar have been conducted to evaluate the bond behavior between ribbed bars and normal strength concrete under transverse tension and repeated loading.
TL;DR: In this article, a converted-wave (C-wave) splitting estimation and compensation (SEAC) method was proposed to estimate the fast principal direction of the fractures and the amount of traveltime splitting from input radial and transverse azimuth-sectored stacks.
Abstract: Converted-wave (C-wave) splitting estimation and compensation (SEAC) estimates and removes the effects of shear-wave splitting from C-wave data. A locally 1D earth is assumed where a priori rotation of the field data to radial-transverse coordinates is valid. Subsurface fractures (horizontal transverse isotropy [HTI] layers are assumed) polarize C-wave reflection energy onto the transverse component, and introduce azimuth-dependent traveltime variations to the radial component. SEAC estimates the fast principal direction of the fractures, and the amount of traveltime splitting, from input radial and transverse azimuth-sectored stacks. SEAC also produces a splitting-compensated radial component, and a data misfit transverse component. Local fracture variations not accounted for in the coarse-interval inversion may be interpreted in the data misfit. Synthetic data generated by anisotropic reflectivity modeling for a model containing two HTI layers having different principal directions was used to illustrate...
TL;DR: In this paper, a 3D analysis model for considering the transverse edge effect caused by the finite widths of the primary and secondary is proposed, and a simple method measuring the transversal edge effect by using the patterns of currents induced in the secondary reaction plate is proposed.
Abstract: In this paper, linear induction motor is analyzed by 3-D finite-element method (3-D FEM) to consider influence of construction of secondary reaction plate on the transverse edge effect. A effective 3-D analysis model for considering the transverse edge effect caused by the finite widths of the primary and the secondary is not only proposed, but also the simple method measuring the transverse edge effect by using the patterns of currents induced in the secondary reaction plate is proposed. With this effective analysis method, various models with overhang and cap have been analyzed to consider the relationship between the construction of secondary reaction plate and the transverse edge effect.
TL;DR: In this paper, the linear theory of micropolar thermoelasticity for materials with voids is studied and the existence theorems of non-trivial solutions and eigenfrequencies of interior homogeneous boundary value problems of steady vibrations are proved.
Abstract: The present paper concerns with the linear theory of micropolar thermoelasticity for materials with voids. Some basic properties of wave numbers of the longitudinal and transverse plane harmonic waves are treated. The existence theorems of non-trivial solutions and eigenfrequencies of the interior homogeneous boundary value problems of steady vibrations are proved. The connection between plane harmonic waves and eigenfrequencies of the aforementioned problems is established.