Analysis on the Radial Vibration of Longitudinally Polarized Radial Composite Tubular Transducer

The radial vibration of a radial composite tubular transducer with a large radiation range and power capacity is studied. The transducer is composed of a longitudinally polarized piezoelectric ceramic tube and a coaxial outer metal tube. Assuming that the longitudinal length is much larger than the radius, the electromechanical equivalent circuits of the radial vibration of a piezoelectric ceramic long tube and a metal long tube are derived and obtained for the first time following the plane strain theory. As per the condition of the continuous forces and displacements of two contact surfaces, the electromechanical equivalent circuit of the tubular transducer is obtained. The radial resonance/anti-resonance frequency equation and the expression of the effective electromechanical coupling coefficient are obtained. Then, the effects of the radial geometry dimension of the transducer on the vibration characteristics are analyzed. The theoretical resonance frequencies, anti-resonance frequencies, and the effective electromechanical coupling coefficients at the fundamental mode and the second mode are in good agreement with the finite element analysis (FEA) results. The study shows that when the overall size of the transducer is unchanged, as the proportion of piezoelectric ceramic increases, the radial resonance/anti-resonance frequency and the effective electromechanical coupling coefficient of the transducer at the fundamental mode and the second mode have certain characteristics. The radial composite tubular transducer is expected to be used in high-power ultrasonic wastewater treatment, ultrasonic degradation, and underwater acoustics, as well as other high-power ultrasonic fields.

The Effect of Strain Hardening on the Dynamic Response of Human Artery Segments

Background:When subjected to time-dependent blood pressure, human arteries undergo large deformations, exhibiting mainly nonlinear hyperelastic type of response. The mechanical response of arteries depends on the health of tissues that comprise the artery walls. Typically, healthy arteries exhibit convex strain hardening under tensile loads, atherosclerotic parts exhibit stiffer response, and aneurysmatic parts exhibit softening response. In reality, arterial dynamics is the dynamics of a propagating pulse, originating in heart ventricle, propagating along aorta, bifurcating,etc. Artery as a whole cannot be simulated as a lump ring, however its cross section can be simulated as a vibrating ring having a phase lag with respect to the other sections, creating a running pressure wave. A full mathematical model would require fluid-solid interaction modeling continuity of blood flow in a compliant vessel and a momentum equation. On the other hand, laboratory testing often uses small-length arteries, the response of which is covered by the present work. In this way, material properties that change along the artery length can be investigated.Objective:The effect of strain hardening on the local dynamic response of human arteries (excluding the full fluid-structure interaction) is examined through appropriate hyperelastic models related to the health condition of the blood vessel. Furthermore, this work aims at constituting a basis for further investigation of the dynamic response of arteries accounting for viscosity.Method:The governing equation of motion is formulated for three different hyperelastic material behaviors, based on the constitutive law proposed by Skalaket al., Hariton, and Mooney-Rivlin, associated with the hardening behavior of healthy, atherosclerotic, and aneurysmatic arteries, respectively. The differences between these modelling implementations are caused by physiology, since aneurysmatic arteries are softer and often sclerotic arteries are stiffer than healthy arteries. The response is investigated by proper normalization of the involved material parameters of the arterial walls, geometry of the arteries, load histories, time effects, and pre-stressing. The effect of each problem parameter on the arterial response has been studied. The peak response of the artery segment is calculated in terms of radial displacements, principal elongations, principal stresses, and strain-energy density. The validity of the proposed analytical models is demonstrated through comparison with previous studies that investigate the dynamic response of arterial models.Results:Important metrics that can be useful to vascular surgery are the radial deformation and the maximum strain-energy density along with the radial resonance frequencies. These metrics are found to be influenced heavily by the nonlinear strain-hardening characteristics of the model and the longitudinal pre-stressing.Conclusion:The proposed formulation permits a systematic and generalizable investigation, which, together with the low computational cost of analysis, makes it a valuable tool for calculating the response of healthy, atherosclerotic, and aneurysmatic arteries. The radial resonance frequencies can explain certain murmures developed in stenotic arteries.

AIRBORNE ACOUSTICS OF EXPLOSIVE VOLCANIC ERUPTIONS

A recently developed theoretical model of the airborne acoustic field from an explosive volcanic eruption of the Strombolian type is described in this article. The magma column is assumed to be a circular cylinder, which is open to the atmosphere at the top, and which opens into a large magma chamber below. The magma itself is treated as a fluid, and the surrounding bedrock is taken to be rigid. An explosive source near the base of the magma column excites the natural resonances of the conduit. These resonances result in displacement of the magma surface, which acts as a piston radiating sound into the atmosphere. The source is modeled in much the same way as an underwater explosion from a high-explosive chemical such as TNT, although in the case of the volcano the detonation mechanism is the ex-solution of magmatic gases under extremely high hydrostatic pressure. The new theory shows compelling agreement with airborne acoustic signatures that were recorded in July 1994 at a distance of 150 m from the western vent of Stromboli volcano, Italy. The theoretical and observed power spectra both display the following features: (1) four energetic peaks below 20 Hz, identified as the first four longitudinal resonances of the magma column; (2) a broad minimum around 30 Hz, interpreted as a source-depth effect, occurring because the source lay close to nulls in the fifth and sixth longitudinal resonances and thus failed to excite these modes; and (3) radial resonance peaks between 35 and 65 Hz. On the basis of the theory, an inversion of the acoustic data from Stromboli yields estimates of the depth (≈100 m) and radius (≈16 m) of the magma column as well as the depth (≈83 m), spectral shape and peak shock wave pressure (≈1 GPa) of the explosive source. Most of the parameters estimated from the acoustic inversion compare favorably with the known geometry and source characteristics of Stromboli.

Vibrations of Aircraft Gear Systems and Their Isolation

One of the most destructive factors in gear components with thin cylindrical rims, is the excessive stresses caused by the radial resonance modes. Dry friction dampers are an effective means of reducing structural vibratory response of gear components. This paper is the continuation of a previous report on vibration damping of aircraft gears [Buyukataman, AIAA-91-2550]. Similar notation and examples are used in this work. However, unlike the previous work which had stressed the damping mechanics and the design of the dampers, this report concentrates on computer implementation and design optimization of dampers.

Field distributions and resonance absorption in a laser plasma filament

In this paper we have theoretically studied the field distributions and resonance absorption in a laser-produced plasma filament. Under the condition of the cold plasma we derive the field equations, as well as their analytical solutions, to the radial and axial components of the electric field. Then, by the numerical calculations, we find that there exists a tunnel effect along the radial direction of the filament, i.e., the electric field reaches a maximum near the radial resonance point r0. Thus, the curves of variance of the radial and axial field components are obtained.