Axial Wave Modes Research Articles

Plateau lower-bounds to the imperfection sensitive buckling of composite shells

The buckling of thin FRP laminated shells are sensitive to initial geometric imperfections. A large number of geometric and material variables prohibit the traditional experiment-based lower-bound design method for metallic shells from being extended to composite ones. As an alternative, the so-called reduced stiffness method (RSM) has been applied to the lower bound buckling of FRP laminated shells. It has been shown for shorter shells the method predicted excellent lower bounds to the nonlinear buckling loads. This paper aims to extend the study to longer shells. It is shown for longer composite shells the lower-bound buckling modes generally occur in the long axial wave mode having one axial halfwave but require imperfection amplitudes of impractical largeness. Further studies of the geometric parameters identify the existence of intermediate and significant plateaus to the lower bounds. These plateau lower-bounds demonstrate the importance of the short axial wave modes having more than one axial halfwave, associated with the imperfection amplitudes of practical smallness. Using the plateau values and modes to predict lower bounds is suggested to provide an important alternative for improving shell buckling design.

3D permeance model of induction machines taking into account saturation effects and its connection with stator current and shaft speed spectra

This study presents a 3D-permeance model of induction machines that reproduces the axial evolution of the air-gap flux for skewed rotors. This evolution is presented using the terminology of axial magnetic modes. These axial waves are the result of the interaction between the rotor slot harmonics permeance series and the space harmonic index related to the magneto-motive force generated by the skewed rotor cage. Wavelength of this axial mode is compared with the results of a validated multi-slice finite element model. Axial wave modes in the slice model were processed using estimation techniques giving an excellent matching with the results of the permeance model. Experimental validation has been indirectly carried out comparing different spectral components for both skewed and non-skewed identical motors and comparing their magnitudes. Differences in the magnitude are associated with the existence of axial modes that change the total flux contained in the air gap of the motor. This study mainly focuses on the study of saturation harmonic.

Mechanical resonance characteristics of a cylindrical semiconductor heterostructure containing a high-mobility two-dimensional electron gas

We investigate the mechanical resonance characteristics of semiconductor rolled-up tubes containing a high-mobility two-dimensional electron gas (HM2DEG) by optical and electrical means. The observed mode frequencies are in an excellent agreement with the theoretically calculated frequencies for the ground bending and excited bending and axial modes. The effect of the curvature is to increase the frequencies of the ground bending modes and the axial wave modes, while decreasing the frequencies of the first excited bending modes. We find significant splitting of the bending and twisting modes by the residual stress effects due to axial shear relaxation in $z$-dependent modes. The HM2DEG interacts with the mechanical motion due to Eddy currents and embedded impedances. A prominent asymmetry appears in the vibration amplitude with respect to the direction of the magnetic field. This originates from the broken symmetry of the HM2DEG on the curved surfaces.

Characteristics of low-aspect ratio, large-diameter, high-density helicon plasmas with variable axial boundary conditions

A low-aspect ratio, high-density helicon plasma source with a large-diameter of ∼74 cm that utilizes an end-launch flat-spiral antenna has been characterized under three different axial boundary conditions. Whereas one end of the device is a quartz-glass window through which an excitation rf wave is injected, the other end is a movable plasma terminating plate of three different kinds: (1) metal with small holes, (2) solid metal, and (3) solid insulator. Using this movable plate, the device aspect ratio A (device axial length/device diameter) can be reduced to ∼0.075 corresponding to the device axial length of 5.5 cm. The plasma production efficiency (PPE, defined as the ratio of the total number of electrons in the plasma to the input rf power) and helicon wave structures are examined for plasmas with various aspect ratios and boundary conditions to characterize our helicon device. Even for the lowest aspect ratio case (A ∼0.075), a plasma with the electron density of 7.5 × 1011 cm−3 can be produced. The PPE of our device is higher than that of other helicon devices that utilize winding-type antennas. Discrete axial wave modes, which can be explained by a simple model, have been identified for helicon waves excited in our low-aspect ratio helicon plasmas. A comparison between the experimental results and helicon wave theory suggests that second order radial modes must have been excited when the electron density is sufficiently high.

Axial wave propagation in coupled nanorod system with nonlocal small scale effects

This article deals with the axial wave propagation properties of a coupled nanorod system with consideration of small scale effects. The nonlocal elasticity theory has been incorporated into classical rod/bar model to capture unique features of the coupled nanorods under the umbrella of continuum mechanics theory. Nonlocal rod model is developed for coupled nanorods. The strong effect of the nonlocal scale has been obtained which leads to substantially different wave behavior of nanorods from those of macroscopic rods. Explicit expressions are derived for wavenumber, cut-off frequency and escape frequency of nanorods. The analysis shows that the wave characteristics of nanorods are highly over estimated by the classical rod model, which ignores the effect of small-length scale. The studies also shows that the nonlocal scale parameter introduces certain band gap region in axial or longitudinal wave mode, where no wave propagation occurs. This is manifested in the spectrum cures as the region, where the wavenumber tends to infinite or wave speed tends to zero. The effect of the coupled spring stiffness is also capture in the present analysis. It has been also shown that the cut-off frequency increases as the stiffness of the coupled spring increases and also the coupled spring stiffness has no effect on escape frequency of the axial wave mode in the nanorod. This cut-off frequency is also independent of the nonlocal small scale parameter. The present study may bring in helpful insights while investigating multiple-nanorod-system-models for future nano-optomechanical systems applications. The results can also provide useful guidance for the study and design of the next generation of nanodevices that make use of the wave propagation properties of coupled single-walled carbon nanotubes or coupled nanorods.

Nonlocal scale effects on ultrasonic wave characteristics of nanorods

In this paper, the nonlocal elasticity theory has been incorporated into classical Euler–Bernoulli rod model to capture unique features of the nanorods under the umbrella of continuum mechanics theory. The strong effect of the nonlocal scale has been obtained which leads to substantially different wave behaviors of nanorods from those of macroscopic rods. Nonlocal Euler–Bernoulli bar model is developed for nanorods. Explicit expressions are derived for wavenumbers and wave speeds of nanorods. The analysis shows that the wave characteristics are highly over estimated by the classical rod model, which ignores the effect of small-length scale. The studies also shows that the nonlocal scale parameter introduces certain band gap region in axial wave mode where no wave propagation occurs. This is manifested in the spectrum cures as the region where the wavenumber tends to infinite (or wave speed tends to zero). The results can provide useful guidance for the study and design of the next generation of nanodevices that make use of the wave propagation properties of single-walled carbon nanotubes.

Wave dispersion characteristics in fluid-filled carbon nanotubes embedded in an elastic medium

This paper reports the result of an investigation into the wave dispersion characteristic in fluid-filled carbon nanotubes (CNTs) embedded in an elastic medium. Based on an analysis method for a coupled system between the fluid-filled and the deformation of CNTs, the effect of a surrounding medium on the response of a fluid loading term in the CNTs is described. The result obtained indicates that for different wave modes there exist corresponding critical frequencies at which the velocity of wave propagation drops dramatically and some cut-off frequencies before which the corresponding wave modes does not appear; the response of the fluid loading item in fluid-filled CNTs embedded in an elastic medium is dependent on the axial wave mode, the circumferential wave mode, the radial constraint of the surrounding elastic medium and the response frequency of the coupled system. New features for the wave dispersion characteristic and the response of a fluid loading term in fluid-filled CNTs and meaningful results are useful in the design of a nano device, where CNTs act as basic elements for a conveying fluid.

Short-wavelength instability and decay of a vortex pair in a stratified fluid

The evolution of a counter-rotating vortex pair in a stably stratified fluid is investigated using direct numerical simulations. The study focuses on the short-wavelength elliptic instability occurring in this flow and the subsequent decay of the vortices. Depending on the level of stratification, as characterized by the Froude number which indicates the time scale of buoyancy to that of the instability, and the stage of evolution, stratification effects may significantly alter the behaviour of the flow. In the case of weak to moderate stratification, the elliptic instability develops qualitatively in the same manner as in unstratified fluid. The primary effect of stratification is to reduce the vortex separation distance which enhances the mutually induced strain. Consequently, the instability has an earlier onset and higher growth rate with increasing stratification. The behaviour is essentially described by linear stability theory for unstratified flow if the varying separation distance is taken into account. On the other hand, the final breakdown and decay of the flow may be greatly modified by stratification since buoyancy effects eventually emerge after sufficient time has elapsed. The decay is enhanced owing to additional mechanisms not present in unstratified flow. Secondary vertical vortex structures form between the primary vortices promoting fluid exchange in the transverse direction. Detrainment of fluid from the primary vortices by the generated baroclinic torque also contributes to the more rapid breakdown of the flow. In the case of strong stratification, in which the time scale of buoyancy is comparable to that of the instability, the flow is significantly altered. As a result of strong baroclinic torque, the primary vortices are brought together and detrainment occurs earlier. The associated reduction in radii of the vortices results in a higher axial wave mode and a more complex radial structure of the instability. Detrainment and mixing accelerate their decay. Late time evolution is dominated by the successive generation of alternate signed baroclinic torque which results in an oscillation of the total flow circulation at the buoyancy frequency.

Wave propagation in a thin-walled liquid-filled initially stressed tube

Wave propagation through a thin-walled cylindrical orthotropic viscoelastic initially stressed tube filled with a Newtonian fluid is discussed. Special attention is drawn to the influence of the initial stretch on the wave propagation. It is shown that initial stretching of real arteries enhances the propagation of blood pressure pulses in mammalian arteries. The dispersion equation for the initial-value problem of a semi-infinite tube is also derived. It is shown that the speed of propagation and the attenuation vary with the distance from the support. The results obtained for the axial wave mode provide an explanation for the experimental observations, which is not possible with the results obtained for the infinite tube.