Volume 115, Issue 5, May 2004
 GENERAL LINEAR ACOUSTICS [20]


Analysis of transient Lamb waves generated by dynamic surface sources in thin composite plates
View Description Hide DescriptionA theoretical analysis is carried out in an effort to understand certain unusual properties of transient guided waves produced in a thin unidirectional graphite/epoxy composite plate by a localized dynamic surface load. The surface motion is calculated using an approximate plate theory, called the shear deformation plate theory (SDPT), as well as a recently developed finite element analysis(FEA), for their mutual verification. The results obtained by the two methods are shown to have excellent agreement. An interesting, nearly periodic “phase reversal” of the signal with propagation distance is observed for each propagation direction relative to the fiber direction. For clarification, a closed form analytical expression for the vertical surface displacement in an aluminum plate to an impulsive point force is obtained using the steepest descent method. It is found that the strong dispersion of the first antisymmetric waves at low frequencies is the main reason behind the phase reversal. This is verified further by measuring the surface response of a relatively thick aluminum plate to a pencil lead break source. The understanding developed in the paper is expected to be helpful in detecting and characterizing the occurrence of damage in composite structures.

Guided circumferential shear horizontal waves in an isotropic hollow cylinder
View Description Hide DescriptionGuided timeharmonic shear horizontal (SH) waves propagating in the circumferential direction of an isotropic hollow cylinder are studied. The dispersion equation as well as the displacement and stress field across the wall thickness is derived analytically. Compared with the SH waves in a plate, a quantitative guideline of how well a plate model can approximate a pipe in the circumferential direction is given for defect characterization purpose. The work is also crucial for initiating work efforts on threedimensional wave scattering for pipeline inspection.

Wave propagation and damping in linear viscoelastic laminates
View Description Hide DescriptionThis analysis is concerned with wave propagation and damping in linear viscoelasticlaminates. A spectral finiteelement method is developed and used to calculate the dispersionproperties of the first few wave types of a given laminate; the proposed approach provides a robust and numerically efficient alternative to the transfer matrix method in certain applications. The proposed approach is also well suited to the calculation of the wave types of sections whose material properties vary continuously throughout the thickness of the section. A onedimensional finiteelement mesh is used to describe the throughthickness deformation of the laminate, and the dispersion equation for planewave propagation is formulated as a linear algebraic eigenvalue problem in wave number at each frequency of interest. The resulting eigenvectors and eigenvalues can be computed using standard numerical routines and used to investigate the dispersion characteristics of the propagating wave types of the section. The damping loss factor of each wave type is estimated from the crosssectional strain energy distribution of the laminate. The proposed approach is well suited to modeling the structuralacoustic response of sandwich panels, constrained layer damping treatments, and general viscoelastic laminate sections in statistical energy analysis (SEA) codes.

Acoustic scattering from rigid bodies of arbitrary shape—Double layer formulation
View Description Hide DescriptionIn this work, a numerical method is presented, based on the wellknown method of moments (MoM), to calculate the acoustic fields scattered by a threedimensional, arbitrarily shaped, acoustically rigid body subjected to a plane wave incidence. The mathematical formulation is based on the potential theory and, in this work, the numerical method is applicable to the socalled double layer formulation (DLF). The scattering body is approximated by planar triangular patches. For the MoM solution using triangular patch modeling, edgebased basis functions are utilized to approximate the source distribution efficiently. These basis functions along with an appropriate testing proceduregenerates a simple numerical algorithm that is versatile enough to be applicable to closed, as well as open bodies. Finally, the present solution method is validated with several representative examples.

Rapid calculations of timeharmonic nearfield pressures produced by rectangular pistons
View Description Hide DescriptionA rapid method for calculating the nearfield pressure distribution generated by a rectangular piston is derived for timeharmonic excitations. This rapid approach improves the numerical performance relative to the impulse response with an equivalent integral expression that removes the numerical singularities caused by inverse trigonometric functions. The resulting errors are demonstrated in pressure field calculations using the timeharmonic impulse response solution for a rectangular source 5 wavelengths wide by 7.5 wavelengths high. Simulations using this source geometry show that the rapid method eliminates the singularities introduced by the impulse response. The results of pressure field computations are then evaluated in terms of relative errors and computational speeds. The results show that, when the same number of Gauss abscissas are applied to both approaches for timeharmonic pressure field calculations, the rapid method is consistently faster than the impulse response, and the rapid method consistently produces smaller maximum errors than the impulse response. For specified maximum error values of 10% and 1%, the rapid method is 2.6 times faster than the impulse response for pressure field calculations performed on a 61 by 101 point grid. The rapid approach achieves even greater reductions in the computation time for smaller errors and larger grids.

An efficient grid sectoring method for calculations of the nearfield pressure generated by a circular piston
View Description Hide DescriptionAn analytical expression is derived for timeharmonic calculations of the nearfield pressure produced by a circular piston. The nearfield pressure is described by an efficient integral that eliminates redundant calculations and subtracts the singularity, which in turn reduces the computation time and the peak numerical error. The resulting single integral expression is then combined with an approach that divides the computational grid into sectors that are separated by straight lines. The integral is computed with Gauss quadrature in each sector, and the number of Gauss abscissas in each sector is determined by a linear mapping function that prevents large errors from occurring in the axial region. By dividing the nearfield region into 10 sectors, the raw computation time is reduced by nearly a factor of 2 for each expression evaluated in this grid. The grid sectoring approach is most effective when the computation time is reduced without increasing the peak error, and this is consistently accomplished with the efficient integral formulation. Of the four single integral expressions evaluated with grid sectoring, the efficient formulation that eliminates redundant calculations and subtracts the singularity demonstrates the smallest computation time for a specified value of the maximum error.

Realtime focusing using an ultrasonic one channel timereversal mirror coupled to a solid cavity
View Description Hide DescriptionFocusing and beam steering is achieved by using a timereversal process and a single transducer coupled to a solid cavity that is immersed in water. This lowcost technique makes it possible to focus acoustic energy anywhere on a 3D domain with a spatiotemporal resolution comparable to that of multiple transducers array. A short pulse is emitted from a transducer stuck at the surface of the solid cavity. The multiplescattered field is measured in front of the solid cavity using a hydrophone needle at a reference point. This signal is then time reversed and remitted by the transducer. Around the reference point, one can observe a spatiotemporal recompression. The sidelobe level as well as the focal width no longer depend on the transducer aperture but on the dimensions of the solid cavity and the multiple paths covered by the acoustic waves in the solid. Moreover, it is shown how the experimental impulse responses on the front face of the cavity can be used to control the emitting ultrasonic field. This “synthetic timereversal” technique is shown to be as powerful as a real timereversal process.
