The high strain-rate behaviour of three molecular weights of polyethylene examined with a magnesium alloy split-Hopkinson pressure bar

A traditional split-Hopkinson pressure bar system has been modified by the addition of ZK60A magnesium alloy pressure bars in order to increase the resolution of data when examining specimens of low-density, high-density and ultra-high molecular weight polyethylene. It was found that the low density of the ZK60A allowed a decent increase in transmitted pulse amplitude, whilst its relatively high yield strength afforded long-term reliability of the system. The accuracy of data obtained from the fitted strain gauges was verified with the use of a high-speed video camera, and was found to be an excellent match.Comment: Will be shortly submitted to 'Polymer Testing

On the strike note of bells

A strike note, characteristic of the particular bell, is heard when a bell is struck. It is observed that the pitch of this note sometimes does not correspond to the frequency of any one of the bell’s normal modes. The origin of this strike note has been a subject of controversy for over 100 years. Previous empirical investigations have mainly made use of musically trained listeners and real or recorded bell sounds. The short duration of the actual strike note and possible influence of musical training on observations may invalidate the conclusions of previous investigators. In this work use has been made of computer generated simulated bell sounds and untrained listeners. It is demonstrated that a strike note may be isolated by beating with a pure test tone and this technique is used to investigate 28 bell-like sounds using a total of 60 listeners. It is concluded that virtual pitch theory provides the best method of predicting the presence or absence of a strike note and its frequency, but that it does not work in every case

Rayleigh's bell model revisited

It is now well over a century since Lord Rayleigh published his model for western-style bells. He used a hyperboloid of revolution plus a flat circular plate for the crown. By limiting himself to inextensional modes of a very restricted type, and exploiting the hyperbola’s parametric form, he produced an equation whose roots give the locations of nodal circles. Remarkably this equation involves neither the wall thickness nor physical properties of the bell material and this approach remains the only available analytical way of making such predictions. Although he gave adequate accounts of the derivation and method of solution of his equation, Rayleigh did not present much in the way of comparison of its predictions with experiment. Rather he focussed on using it to explain the fact that the Hum note never has any nodal circles. In the present paper we consider how well profiles of some modern church and handbells can be fitted by hyperbolae. We compare the model’s predictions for these bells with data for a range of inextensional modes and report a new, surprisingly accurate, approximate analytical solution of Rayleigh’s equation

Matryoshka locally resonant sonic crystal

The results of numerical modeling of sonic crystals with resonant array elements are reported. The investigated resonant elements include plain slotted cylinders as well as their various combinations, in particular, Russian doll or Matryoshka configurations. The acoustic band structure and transmission characteristics of such systems have been computed with the use of finite element methods. The general concept of a locally resonant sonic crystal is proposed that utilizes acoustic resonances to form additional band gaps that are decoupled from Bragg gaps. An existence of a separate attenuation mechanism associated with the resonant elements that increases performance in the lower frequency regime has been identified. The results show a formation of broad band gaps positioned significantly below the first Bragg frequency. For low frequency broadband attenuation, a most optimal configuration is the Matryoshka sonic crystal, where each scattering unit is composed of multiple concentric slotted cylinders. This system forms numerous gaps in the lower frequency regime, below Bragg bands, while maintaining a reduced crystal size viable for noise barrier technology. The finding opens alternative perspectives for the construction of sound barriers in the low frequency range usually inaccessible by traditional means including conventional sonic crystals

Studies with a small gamelan gong

A gamelan is an ensemble of ethnic musical instruments from parts of Indonesia where it is central to musical art and commands huge respect. It is also found in some neighboring countries. While it involves many different types of instruments its backbone consists of metalophones and gongs. show a vertical cross-section through the centre of a typical small gamelan gong placed on a horizontal surface. It consists of a central dome A on top of a flat plate which is terminated by a shoulder BC and then a deep inward sloping rim CD. The vertical line AE is the axis of symmetry. These gongs are rung by being stuck on the central dome with a mallet. Large gongs are suspended vertically by strings. Smaller ones are mounted horizontally from underneath on parallel strings. Since a “perfect” gong has complete axial symmetry one can conclude that its normal modes have nodal patterns consisting of m equally spaced “diameters” and n circles parallel to the rim’s edge. Modes with m = 0 are axisymmetric singlets while those with m > 0 occur in degenerate pairs with the diameters of one bisecting those of its partner. Modes can be designated by (m, n) with the addition of a subscript outside the brackets if it is desired to distinguish between a doublet’s components. In practice gamelan gongs are cast, sometimes rather roughly, and so have geometrical and metallurgical imperfections which break the basic axial symmetry. Consequently the doublets split and distortions appear in some nodal patterns. In the present work we are concerned with a small steel gong of 20.7cm diameter originating from Sarawak

Normal Modes of the Indian Elephant Bell

The geometrical structure of the Indian elephant bell is presented and the requirements on its normal modes from group representation theory are described. These are in good agreement with the results of a finiteelement model (FEM) for a specific 16-tine case. The spectrum consists of a sequence of families of modes lying on saturation curves and so is completely different from those of conventional bells. Physical explanations for the occurrence of these families are presented in terms of the tines behaving as a closed loop of coupled cantilevers with constraints from the dome. Each family is found to consist of modes in one of two specific sequences of symmetry types. Experimental measurements of the modes of this same 16-tine bell, using Electronic Speckle Pattern Interferometry (ESPI), have been made and are compared with the FEM predictions. Although the interpretation of the interferograms is difficult in all but the simpler cases, agreement in terms of frequencies is surprisingly good for the first few family sequences. The ESPI study also showed up numerous harmonics and subharmonics of true normal modes, showing the system to be rather non-linear and making comparisons with the FEM results tricky

Acoustic band gap formation in metamaterials

We present several new classes of metamaterials and/or locally resonant sonic crystal that are comprised of complex resonators. The proposed systems consist of multiple resonating inclusion that correspond to different excitation frequencies. This causes the formation of multiple overlapped resonance band gaps.We demonstrate theoretically and experimentally that the individual band gaps achieved, span a far greater range ( 2kHz) than previously reported cases. The position and width of the band gap is independent of the crystal’s lattice constant and forms in the low frequency regime significantly below the conventional Bragg band gap. The broad envelope of individual resonance band gaps is attractive for sound proofing applications and furthermore the devices can be tailored to attenuate lower or higher frequency ranges, i.e. from seismic to ultrasonic

In situ synchrotron x-ray study of ultrasound cavitation and its effect on solidification microstructures

Considerable progress has been made in studying the mechanism and effectiveness of using ultrasound waves to manipulate the solidification microstructures of metallic alloys. However, uncertainties remain in both the underlying physics of how microstructures evolve under ultrasonic waves, and the best technological approach to control the final microstructures and properties. We used the ultrafast synchrotron X-ray phase contrast imaging facility housed at the Advanced Photon Source, Argonne National Laboratory, US to study in situ the highly transient and dynamic interactions between the liquid metal and ultrasonic waves/bubbles. The dynamics of ultrasonic bubbles in liquid metal and their interactions with the solidifying phases in a transparent alloy were captured in situ. The experiments were complemented by the simulations of the acoustic pressure field, the pulsing of the bubbles, and the associated forces acting onto the solidifying dendrites. The study provides more quantitative understanding on how ultrasonic waves/bubbles influence the growth of dendritic grains and promote the grain multiplication effect for grain refinement