Vibroacoustic response of an eccentric hollow cylinder

The linear 3D elasticity theory in conjunction with the classical method of separation of variables and the translational addition theorem for cylindrical wave functions are employed to investigate the three-dimensional steady-state sound radiation characteristics of an arbitrarily thick eccentric hollow cylinder of infinite length, submerged in an unbounded ideal acoustic medium, and subjected to arbitrary time-harmonic on-surface mechanical drives. The spatial Fourier transform along the shell axis and Fourier series expansion in the circumferential direction are utilized to obtain a formal integral expression for the radiated pressure field in the frequency domain. The method of stationary phase is subsequently implemented to evaluate the integral for an observation point in the far field. The analytical results are illustrated with numerical examples in which air-filled water-submerged concentric and eccentric steel cylinders are driven by harmonic concentrated radial and transverse surface loads. Effects of excitation and cylinder eccentricity on the far-field radiated pressure amplitudes/directivities are discussed and contributions from pseudo-Rayleigh, whispering gallery, and axially guided waves are examined through selected spatial dispersion patterns. Limiting cases are considered and the validity of results is established with the aid of a commercial finite element package as well as by comparison with the data in the existing literature.     

A simple model for a two-stage chemical reaction with diffusion

We analyse the evolution of a two-stage chemical reaction betweentwo neighbouring plumes of reactants. Under the assumption thatthe plumes are approximately Gaussian we derive a system ofordinary differential equations for the total amount, the centroidand the variance of each reactant. We compare the solution ofthese equations with full numerical simulation of the reaction.Excellent agreement is obtained, with solution of the near-Gaussianmodel requiring considerably less computational effort thanthe full simulations. Of key importance is the yield of thereaction, and we discuss this feature in particular.     

Acoustic resonance scattering from a multilayered cylindrical shell with imperfect bonding

The method of wave function expansion is adopted to study the three dimensional scattering of a time-harmonic plane progressive sound field obliquely incident upon a multi-layered hollow cylinder with interlaminar bonding imperfection. For the generality of solution, each layer is assumed to be cylindrically orthotropic. An approximate laminate model in the context of the modal state equations with variable coefficients along with the classical T-matrix solution technique is set up for each layer to solve for the unknown modal scattering and transmission coefficients. A linear spring model is used to describe the interlaminar adhesive bonding whose effects are incorporated into the global transfer matrix by introduction of proper interfacial transfer matrices. Following the classic acoustic resonance scattering theory (RST), the scattered field and response to surface waves are determined by constructing the partial waves and obtaining the non-resonance (backgrounds) and resonance components. The solution is first used to investigate the effect of interlayer imperfection of an air-filled and water submerged bilaminate aluminium cylindrical shell on the resonances associated with various modes of wave propagation (i.e., symmetric/asymmetric Lamb waves, fluid-borne A-type waves, Rayleigh and Whispering Gallery waves) appearing in the backscattered spectrum, according to their polarization and state of stress. An illustrative numerical example is also given for a multi-layered (five-layered) cylindrical shell for which the stiffness of the adhesive interlayers is artificially varied. The sensitivity of resonance frequencies associated with higher mode numbers to the stiffness coefficients is demonstrated to be a good measure of the bonding strength. Limiting cases are considered and fair agreements with solutions available in the literature are established.     

Effects of dynamic viscoelastic properties on acoustic diffraction by a solid sphere submerged in a viscous fluid

Summary  This study provides a general analysis for scattering of a planar monochromatic compressional sound wave by a homogeneous, isotropic, viscoelastic, solid sphere immersed in an unbounded viscous, heat-nonconducting, compressible fluid. The dynamic viscoelastic properties of the spherical scatterer and the viscosity of the surrounding fluid are rigorously taken into account in the solution of the acoustic-scattering problem. Havriliak–Negami model for viscoelastic material behaviour along with the appropriate wave-harmonic field expansions and the pertinent boundary conditions are employed to develop a closed-form solution in form of infinite series. Subsequently, the associated acoustic quantities such as the scattered far-field pressure directivity pattern, scattered intensity distribution, differential scattering cross section, and the acoustic radiation force are evaluated for given sets of viscoelastic material properties. Numerical results clearly indicate that, in addition to the traditional fluid viscosity-related mechanisms, the dynamic viscoelastic properties of the solid obstacle can be of major significance in sound scattering. Limiting cases are examined and fair agreements with well-known solutions are established. Received 15 January 2002; accepted for publication 2 July 2002 The authors wish to sincerely thank professors Daniel Levesque, Roderic Lakes, Yves Berthelot, S. Temkin, and Andrei Dukhin for valuable and productive consultations on dynamic theory of viscoelasticity and acoustics of (thermo)viscous media.     

Dynamic Viscoelastic and Multiple Scattering Effects in Fiber Suspensions

This study considers the most fundamental problem of 2‐D acoustic scattering in fiber suspensions. It treats the interaction of a plane compressional sound wave with a cluster of two flexible fibers submerged in a boundless viscous fluid medium. The dynamic viscoelastic properties of the fibers and the viscosity of the surrounding fluid are rigorously taken into account in the solution of the problem. The translational addition theorem for cylindrical wave functions, the Havriliak‐Negami model for viscoelastic material behaviors and the appropriate wave field expansions and the pertinent boundary conditions are employed to develop a closed‐form solution in the form of an infinite series. The prime objectives are to investigate the influence of dynamic viscoelastic properties of fiber material as well as multiple scattering interaction effects on acoustic scattering and its associated quantities. The analytical results are illustrated with a numerical example in which two identical viscoelastic fibers are insonified by a plane sound wave at broadside/end‐on incidence. The backscattering form function amplitude and the spatial distribution of the total acoustic pressure are numerically evaluated and discussed for representative values of the parameters characterizing the system. The effects of incident wave frequency, angle of incidence, material properties, and proximity of the two fibers are examined. A limiting case involving a pair of rigid cylinders in an ideal fluid is considered, and fair agreement with a well‐known solution is established.     

Gas-phase deprotonation of arylalkylamines. A collision-induced dissociation study

The collision-induced dissociation (CID) of deprotonated arylalkylamines of general formula R(1)C(6)H(4)CHR(2)CH(2)NR(3)(2) (where R(1) = H, OH, F or NO(2); R(2) = H or OH; R(3) = H or CH(3)) generated by negative chemical ionization with H(2)O and D(2)O as ionizing reagents, is discussed. The negative chemical ionization mass spectra show that, in the absence of a hydroxy group in the aromatic ring, deprotonation takes place at the benzylic position whereas the proton is lost from the OH group when present. The nitro compound forms only M(-.) ions. The CID spectra of the deprotonated molecules show that fragmentations are strongly dependent on the structural features of the molecules, namely the presence or absence of substituents in the aromatic ring or aliphatic chain. Copyright 1999 John Wiley & Sons, Ltd.     

Modelling and simulation of acoustic pulse interaction with a fluid-filled hollow elastic sphere through numerical Laplace inversion

A detailed study is undertaken to analyze the non-steady interaction of plane progressive pressure pulses with an isotropic, homogeneous, fluid-filled and submerged spherical elastic shell of arbitrary wall thickness within the scope of linear acoustics. The formulation is based on the general three dimensional equations of linear elasticity and the wave equation for the internal and external acoustic domains. The Laplace transform with respect to the time coordinate is invoked, and the classical method of separation of variables is used to obtain the transformed solutions in the form of partial-wave expansions in terms of Legendre polynomials. The inversion of Laplace transforms have been carried out numerically using Durbin’s approach based on Fourier series expansion. Special convergence enhancement techniques are invoked to completely eradicate spurious oscillations (Gibbs’ phenomenon), and obtain uniformly convergent solutions. Detailed numerical results for the transient and vibratory responses of water-submerged steel shells of selected wall thickness parameters with various internal fluid loadings under an exponential wave excitation are presented. Many of the interesting dynamic features in the transient shell–shock interaction such as shock transparency, shell-radiated negative pressure waves, formation of triple points, and focusing of the reflected waves are examined using appropriate 2D images of the internal pressure field. Also, the temporal behavior of the specularly-reflected, the lowest symmetric S₀- and antisymmetric A₀-Lamb waves, as well as appearance of the Franz’s creeping waves are discussed through proper visualization of the external scattered field. Likelihood of cavitation is addressed and regions proned to cavitation are identified. Moreover, the effects of internal fluid impedance in addition to shell wall thickness on the dynamic stress concentrations induced within the shell are analyzed. Limiting cases are considered and fair agreements with well-known solutions are established.