Shell Resonances Research Articles

The radiation of sound waves from a lightly loaded finite elastic shell, I: Duct and shell resonances for linear motions

This paper is the first half of a study into the scattering of acoustic waves by a finite circular cylindrical elastic shell. The flexible body is set into a rigid cylinder of infinite extent, and the shell motions are excited by waves which propagate from infinity inside the duct. In this paper we assume a linear response for the shell/fluid system. By employing the assumption that the fluid density is much smaller than the plate density, the scattered field both outside and interior to the cylinder is calculated from the shell deflections. At a forcing frequency near to that of the free vibration frequency of the shell, the asymptotic expansions must be modified to take into account the increased amplitude of the structural vibrations. We employ the method of multiple scales to calculate the solution near to these shell resonances, and the method is also applied near to the duct resonances. In a followup to this paper the effects of non-linearities in the shell equations will be investigated by the same method, and the modifications to the position and magnitudes of the resonant peaks in the scattered field will be discussed.

Water-borne waves at the interface of evacuated elastic spherical shells and pseudo-Stoneley resonances.

Monochromatic plane waves are known to excite resonances on submerged elastic spherical evacuated shells. The resonances are related to symmetric and antisymmetric Lamb modes found in free vibrations and can be observed by examining the backscattered echo’s (form functions) that lead to characteristic ‘‘tell-tale’’ resonance signatures. A partial wave analysis of the individual modes can reveal the nature of the resonances, provided one is able to subtract the correct acoustical background from the shell. The recent development of the correct acoustical background is taken advantage of to analyze the partial wave components of shell resonances. It is easy to distinguish between the Lamb modes that are also apparent in the form functions. However, an additional resonance is observed at high frequencies that correspond to waves which are broad in partial wave space and which propagate in the fluid at the fluid–shell interface at about the speed of sound of the ambient fluid. It may be assumed that they are related to Stoneley waves observed at the interface of a flat plate evacuated on one side and with a fluid on the other and may therefore be referred to as pseudo-Stoneley resonances. The significance of these waves at coincidence frequency will be discussed.

Dynamic spectra of pulsation events at L ∼ 1.9 and L ∼ 3.3

High resolution dynamic spectra of 12 pulsation events are compared at NCK ( L ∼ 1.9) and KVB ( L ∼ 3.3), lying on the same meridian. Common features of the pulsation activity at the two stations include periods, period shifts and switches on and off. These parameters are investigated for the sample of pulsation activity and demonstrate that the two stations record activity from both a common and from different sources. Shell resonances are discussed in relation to the common source of activity.

Lamb and creeping waves around submerged spherical shells resonantly excited by sound scattering

Acoustic wave scattering by spherical shells in water in the resonance region is studied. The interaction is studied classically and by the resonance scattering theory (RST). The connection between internal resonances and the Lamb waves excited in the shell is analyzed. Conditions are derived that govern the propagation of Lamb waves in a spherical shell when it is fluid-loaded or in vacuo. These general conditions reduce to the usual conditions for Lamb waves in plates, in the large radii limit. The connection is established between the outer scattering problem and the internal vibrational problem that excites the shell resonances, and it is demonstrated that the creeping-wave series that synthesizes the Franz waves around the shell, can be obtained quite simply without the use of the Watson–Sommerfeld Method (WSM). All that is required is suitable one-term expansions of the denominators of the scattering amplitudes. This eliminates the need for the cumbersome excursions through the complex angular momentum plane ν of the WSM. Calculations are presented for the summed form functions of seven shells of three compositions and thicknesses over quite broad frequency bands. Subtraction of rigid or soft backgrounds permits one to draw many conclusions as to the behavior of the shell response in various spectral regions. The relative phase between the form function and the background is also displayed. This phase is helpful for the identification of actual resonances and for the choice of proper background. It is shown how the poles of the scattering amplitude in the x plane split into two subsets. One set, the Franz set, depends only on shell shape, and is related to the external Franz (creeping) waves in the water. This set does not change with varying shell thickness or composition. The other set, the Lamb set, depends only on material composition, and is related to the Lamb waves in the shell. These poles are displayed in various cases, and it is shown that for thin shells, only one family of Lamb poles (the zeroth-order symmetric family, s0) is dominant, which explains the relatively simple structure of the form function of a thin shell. For thicker shells, many modes interact, and one is forced to go to the usual partial-wave analysis of the RST. A very accurate picture of the scattering process taking place around and inside the shell emerges from this analysis.

Classification of resonances and remote aspect‐ratio determination of submerged spheroidal elastic shells

Acoustic scattering was studied from submerged, steel, spheroidal shells in their resonance region. Arbitrary angular incidences were considered to analyze the possible aspect‐angle dependence of the resonances. The shells are sufficiently thin so that the “proper backgrounds” of the RST [G. C. Gaunaurd and M. F. Werby, Int. J. Solids Structures 22, 1149–1159 (1986)] can be suitably suppressed, and the resonances can be adequately isolated. It is shown that the shell resonances are caused by surface standing waves propagating at discrete frequencies with an almost constant phase velocity. From this (surface) standing‐wave interpretation (viz., geodesics) accurate resonance locations have been derived. Only two basic vibrational modes seem to exist, one along and the other normal to the axis of symmetry. Thus, only resonances corresponding to these two directions are possible. Furthermore, the fixed resonance locations seem to have amplitudes that change with incidence angle. Hence, this procedure permits the classification of resonances, and it can he exploited to extract the aspect ratio of the spheroidal shell from its returned echo. These points are illustrated with numerous computational examples. [Work supported by NAVELEX and ONR.]

Resonances in the K shell excitation spectra of benzene and pyridine: Gas phase, solid, and chemisorbed states

K shell excitation spectra of the aromatic molecules benzene and pyridine in the gas phase are compared to those for the solids (ices) and for monolayers chemisorbed on Pt(111). The gas phase and solid spectra are essentially identical and even the spectra for the chemisorbed molecules exhibit the same resonances. Because of the orientation of the molecules upon chemisorption the latter spectra show a strong polarization dependence as a function of x-ray incidence. This polarization dependence in conjunction with a multiple scattering Xα calculation for the benzene molecule allows us to assign the origin of all K shell resonances. The resonances are found to arise from transitions to π* antibonding orbitals and to σ* shape resonances in the continuum. The shape resonances are characterized by potential barriers in high (l=5 and 6) angular momentum states of the excited photoelectron. The polarization dependence and energy position of the resonances allow the molecular orientation on the surface to be determined and show that the change in the carbon–carbon bond length is less than 0.02 Å.

Criteria for suitable background choices in resonance acoustic scattering by shells

We present an analytical and computational study of acoustic wave scattering by air‐filled spherical/spheroidal shells in water. The calculations displayed here are all performed by means of a recently improved T‐matrix approach for shells that is more efficient than usual earlier ones. This study permits the accurate determination of the relative shell thickness at which the usual rigid background of metal shells in water switches to the soft background of gas bubbles in water. The correct choice of background is crucial for the isolation of the shell resonances contained within the echoes. A key criterion to establish this transition thickness, and to decide on the suitability of the background choice, is provided by the relative phase between the (elastic) form function of the target and either the rigid or the soft background. That relative phase will exhibit jumps of π radians as the fluid‐loaded system goes through its modal resonances. In the case of an incorrectly chosen background this relative phase will undergo countless meaningless oscillations at all frequencies. Metal shells of the types studied here have transition thicknesses of h/a ≃ 0.001, and the thinner the shells, the narrower their resonances become. These points are all illustrated with examples. We show that soft backgrounds are possible only for shells so thin that they buckle under very light external pressures.

Acoustic resonance scattering by a cylindrical shell

We present a study of the resonance scattering process that takes place when plane acoustic waves are incident on elastic cylindrical shells in water. The analysis proceeds along the lines described by us earlier [D. Brill and G. Gaunaurd, J. Acoust. Soc. Am. 73, 1448–1455 (1983)] for solid elastic cylinders, and extends it to (hollow) shells. For aluminum gas‐filled cylindrical shells of various thicknesses, we construct the families of zeros in the complex k1a (≡ x) plane that give rise to the Rayleigh and the whispering gallery waves circumnavigating the shell. We have isolated the proper modal shell resonances from their modal backgrounds and we have generated monostatic plots of background‐supressed form functions (i.e., cross sections) that agree well with recent experimental observations made by a team in France. We have noticed that as the shells become thinner, fewer families at poles seem to offer contributions, until for very thin shells, only one type of circumnavigating surface wave seems to ...

Changes of pulsation activity during two solar cycles

Monthly and yearly averages of the pulsation activity in the mid-latitude station Nagycenk are compared to solar wind velocity and ionospheric-plasmaspheric electron concentration data. It is found that pulsation amplitudes are correlated with solar wind velocities with the exception of some month around December in solar maximum years, when they are significantly lower than computed from the corresponding solar wind velocities. This decrease can be caused either by a cutoff of the magnetospheric shell resonances or by local ionospheric damping. In addition to these effects, pulsations amplitudes slightly depend also on the geomagnetic activity and have a semi-annual activity change with maxima around equinoxes.

Nearfield acoustic radiation from spherical shells

In this study, the acoustic nearfield of excited spherical shells is investigated. The interaction of the acoustic medium with the vibration response of an elastic spherical shell due to an excitation by a point force or an acoustic point source is investigated analytically and experimentally. Thus, only axisymmetric, nontorsional motion of the spherical shell is considered, with a thin shell theory that includes extensional and bending deformation. The elastic spherical shell resonances were computed when in vacuo and when submerged in light (air) and heavy (water) acoustic medium. These were verified experimentally by testing two duralumin shells, a = 8 in. in radius and wall thicknesses h = 0.0514 and 0.1069 in. The measured resonance frequencies were within 5% of those predicted in air and in water for identified mode numbers up to 34. The measured mean‐line driving point admittance also agreed well with the predicted ones to within 3 dB. [Work supported by NAVSEA.]

Isolation of the resonant component in acoustic scattering from fluid-loaded elastic spherical shells

We investigate the process of resonance excitation of a spherical, fluid (or gas) filled elastic shell imbedded in another fluid, in the course of scattering of a plane incident sound wave from the shell, using the recently developed formalism of resonance scattering theory. Numerical studies are performed for air-filled aluminum shells immersed in water. We isolate the resonant component in the scattering amplitude by subtracting a nonresonant ’’intermediate’’ background, thus exhibiting the pure resonance peaks in the frequency region 0<ka?100, for shell thicknesses (inner-to-outer ratio) b/a=0.2, 0.7, and 0.9, and for the normal modes up to n=3. It is found that up to b/a=0.7, the background amplitude is adequately represented by that of a rigid body, but that above b/a=0.9, intermediate-background theory must be used. A physical explanation of the existence of the shell resonances is presented in terms of elastic circumferential waves created on the shell during the scattering process; each of these will build up to a resonance in the nth mode if n+1/2 of its wavelengths span the circumference of the sphere, the half-integer stemming from the fact that the circumferential wave loses 1/4 wavelength at each of the convergence points at the north and south pole.

Stationary states for electron oscillators in a rare-gas afterglow plasma

An explanation is advanced for the presence of populations of low energy oscillating paired electrons in rare-gas afterglow plasmas arranged in a system of coaxial shells, and enclosing a core plasma of free electrons. The common axis of the system is that of the long glass tube containing the plasma. The explanation is based on Fermi's analysis of the collisional interaction of very low energy electrons with gas atoms or molecules. A model afterglow is evolved based on the coaxial shell hypothesis, and is used to interpret two sets of afterglow phenomena, namely the plasma shell resonances obtained when energy is radiated by electrons making transitions from inner to outer shells, and the multiple values for accelerated decay times observed for afterglows of this type.

Modified, More Rapidly Converging Modal Series Representation for Mechanical Admittance

The standard modal series representation of mechanical admittance may be slowly convergent, especially at antiresonance, for structures that may exhibit a spatially localized response to a spatially localized excitation, e.g., beams on elastic foundation as well as plates and shells. A William's modal acceleration approach is used to arrive at a modified, faster converging, modal series representation for the displacement admittance of a general, finite, linear elastic structure which contains damping. A freely supported, damped, circular cylindrical shell, driven by a radial point force, is employed as an example for a comparison of the modified and the standard modal representations for driving-point and transfer displacement admittance in various frequency bands. At a shell antiresonance, the convergence of the modified driving-point admittance representation is very rapid in comparison to that of the standard modal representation. This is particularly true for that shell antiresonance that lies between the two most widely separated shell resonances. As one proceeds from the case of very light to intermediate shell damping, the convergence, at antiresonance, of both types of admittance representation improves considerably.

Measurement of High-Q Resonances in Liquid-Filled Spheres

One of the most important and difficult to measure elastic constants is the bulk modulus and its Q factor. In order to measure the Q factor of a small solid specimen, a high-Q liquid-filled system must be obtained. For the past year, an attempt has been made to excite the radial modes of a water-filled sphere suspended in a vacuum. At first, excitation at the wall was tried and proved unsuccessful, since it put energy into many of the shell resonances and produced a highly complex resonance pattern. In the past few months, a successful method was found. A small barium titanate crystal was cemented to the end of a brass tube and placed at the center of the sphere. Using this crystal for both driving and receiving, Q's as high as 72 000 have been obtained for several resonances, in two water-filled spheres of different wall thickness and diameter. Small samples were placed at the center and changes in the Q were measured. [Work supported by the U. S. Air Force Office of Scientific Research (AF-AFOSR-43-63).]