Elliptical Trace Research Articles

Distorted wave response of ultrasonic annular stator incorporating non-uniform geometry

The traveling wave ultrasonic stator is normally fabricated with teeth. The tooth geometry improves the driving speed, but it creates natural frequency splitting and mode contamination, especially a distorted traveling wave. A dynamic model of a stepped-plate periodic stator is developed to examine the distortion. The stator is treated as an annular supported by a thin mid plate, and the support stiffness is formulated by using equivalent energy principle. The effects of the tooth and mid plate on the natural frequency and vibration mode are examined by using the perturbation method. The rules governing the frequency splitting, frequency perturbation as well as mode contamination are also identified. The traveling wave response and elliptical trace on stator surface are obtained by using the mode superposition method and they are proved to be distorted due to the tooth geometry. The response at the repeated doublets becomes coupled forward and backward traveling waves, but that at the split doublets becomes coupled forward traveling, standing and backward traveling waves. The results indicate that the tooth mass instead of the stiffness decreases the vibration amplitude and driving speed of the dominant wave, but their effects are different at the repeated and split doublets. Inspection of the model implies that the distortion can be suppressed by using a suitable combination of the wavenumber, tooth count, tooth height and occupying fraction. Numerical calculations are carried out to demonstrate the tooth geometry effect on the transient waveform, driving speed and elliptical trace. The optimization of the tooth geometry that can help achieve a purer traveling wave is discussed.

Coherent perfect absorption in photonic structures

The ability to drive a system with an external input is a fundamental aspect of light-matter interaction. The coherent perfect absorption (CPA) phenomenon extends to the general multibeam interference phenomenology the well known critical coupling concepts. This interferometric control of absorption can be employed to reach full delivery of optical energy to nanoscale systems such as plasmonic nanoparticles, and multi-port interference can be used to enhance the absorption of a nanoscale device when it is embedded in a strongly scattering system, with potential applications to nanoscale sensing. Here we review the two-port CPA in reference to photonic structures which can resonantly couple to the external fields. A revised two-port theory of CPA is illustrated, which relies on the Scattering Matrix formalism and is valid for all linear two-port systems with reciprocity. Through a semiclassical approach, treating two-port critical coupling conditions in a non-perturbative regime, it is demonstrated that the strong coupling regime and the critical coupling condition can indeed coexist; in this situation, termed strong critical coupling, all the incoming energy is converted into polaritons. Experimental results are presented, which clearly display the elliptical trace of absorption as function of input unbalance in a thin metallo-dielectric metamaterial, and verify polaritonic CPA in an intersubband-polariton photonic-crystal membrane resonator. Concluding remarks discuss the future perspectives of CPA with photonic structures.

The Sexual Shame of the Chaste: ‘Abortion Miracles’ in Early Medieval Saints’ Lives

The Sexual Shame of the Chaste: ‘Abortion Miracles’ in Early Medieval Saints’ Lives

Dynamic Behavior of Bi-Axial Self-Synchronous Shaker with Translation Elliptic Trace

According to the self-synchronous theory with two vibrating electric motors, a translation elliptic shaker is designed, and its finite element model for the sieving box is established. The dynamic behavior analysis of the sieving box is reached with CATIA software. The natural frequencies and modal oscillation modes of the sieving box are calculated, and the stress and deformation distribution in every part of the sieving box under rated load are obtained. All shows that, its structure design is reasonable. Under the designed working conditions, the maximum principal stress of the side boards is 39.7 MPa, and its dynamic strength is satisfied. The calculating results will be of significance to the design improvement, and give a basis for the experiment research of dynamic strength.

Dynamics and screening characteristics of a vibrating screen with variable elliptical trace

The ideal motion characteristics for the vibrating screen was presented according to the principle of screening process with constant bed thickness. A new vibrating screen with variable elliptical trace was proposed. An accurate mechanical model was constructed according to the required structural motion features. Applying multi-degree-of-freedom vibration theory, characteristics of the vibrating screen was analyzed. Kinematics parameters of the vibrating screen which motion traces were linear, circular or elliptical were obtained. The stable solutions of the dynamic equations gave the motions of the vibrating screen by means of computer simulations. Technological parameters, including amplitude, movement velocity and throwing index, of five specific points along the screen surface were gained by theoretical calculation. The results show that the traces of the new designed vibrating screen follow the ideal screening motion. The screening efficiency and processing capacity may thus be effectively improved.

Tilted lamellae in an affinely deformed 3D macrolattice and elliptical features in small‐angle scattering

AbstractLamellar reflections in small‐angle X‐ray and neutron scattering patterns of uniaxially drawn semicrystalline polymers appear to fall on elliptical or hyperbolic arcs. We attribute this to a 3D lattice of tilted lamellae, a macrolattice. Affine deformation of this lattice, such as during uniaxial draw, moves and spreads the reflections along elliptical arcs, and nonaffine deformation, such as during rolling, moves and spreads the reflections along an arc that deviates from an ellipse. Discrete reflections are the product of two functions: the elliptical trace that is the Fourier transform of the affinely deformed lattice and the radial streak that is the Fourier transform of the individual lamella in the reciprocal space. Four‐point patterns are obtained if the lamellar‐surface normal is tilted away from the fiber‐axis, and two‐point patterns if it is not. This model is used to discuss the transformation between four‐ and two‐point patterns and other changes in lamellar morphology that occur during drawing and annealing of oriented semicrystalline polymers. The deformation of the macrolattice of crystalline lamellae, need not be correlated to the tilt of the lamellae. The tilt of the lamellae is shown to be important. It reflects the cross‐sectional area mismatch at the lamellar surface between crystalline stems and amorphous chains segments, and this indicates the internal strain in the interfibrillar amorphous regions. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 1277–1286, 2006