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The objective of this research effort has been to develop algorithms for in situ location and identification, by ultrasound, of flaws in plates or laminated layered elastic materials. Achieving this objective requires detailed knowledge of the excitation, propagation, scattering and detection of high frequency sound waves in the unflawed and flawed environments. Based on an understanding of these fundamental wave phenomena, one may then attempt to construct analytical models with accompanying algorithms, so as to parametrize the NDE problem in terms of good observables. During the contract period, carefully selected prototype problems have been investigated to determine 'good observables' for particular flawed environments. Two major phases have received attention: (a) phenomena within a flat layered plate, especially beam-to-mode conversion, and the consequent interaction with a weak debonding flaw; (b) characterization of transducer outputs in terms of good wave objects that facilitate coupling into and out of the plate environment. The analytical tools rely on spatial and spectral domain formulations, and they comprise self- consistent hybrid beam-mode methods; complex source modeling of Gaussian beams, with complex ray tracing to track such beams; and decomposition of general wavefields into Gaussian beams. Thus, Gaussian beams, which are 'good observables' are central to the problem strategy.

The acoustic radiation characteristics of a fluid filled concentric shell structure are investigated by making use of the simple source surface integral method. The fluid field is described in terms of surface expansion functions, while the in vacuo structural modes, obtained by using the BOSOR4 structural program, are used as a basis for the shell motions. The structural code can be applied to branched shells of revolution, thereby obviating the need to introduce structural coupling of the two shells in a manner which is external to the main code. For illustrative purposes three types of internal harmonic excitations have been considered: (1) an axisymmetric unit pressure acting on the central region, (2) a unit line load acting on the central region, and (3) concentrated axial loads acting at the poles of the spherical closures. The far field fluid pressures have been obtained for a wide range of frequencies for both the single shell and for the double shell with and without inner fluid. Because of numerical difficulties encountered when applying the integral methods to internal fluid problems, some simple approximations to the internal fluid problem were considered. The results obtained compare quite favorably with those of the exact solution over a wide range of frequencies. (Author), Prepared in cooperation with Polytechnic Inst. of New York, Brooklyn, Rept. no. POLY-M/AE-85-1.

A general method is presented for obtaining the dynamic equations of an elastic structure to which elastic and/or nonlinear substructural elements are attached. (Author)

The nonlinear dynamic response of a thin, clamped hemispherical shell subjected to a suddenly applied pressure is obtained. The governing fourth order, coupled, nonlinear equations are rewritten in finite difference form and the resulting matrix equation is partitioned into a form to which Lu factorization can be readily applied. A 'dynamic buckling' criterion is used, and both the axisymmetric and asymmetric responses are investigated. (Author)

The transient responses of a submerged spherical shell to a concentrated impulse and Heaviside load are obtained by using the classical mode method and the Laplace transform. For long time solutions, only a relatively small number of modes are sufficient, while for the short time response, a large number of modes must be used in order to achieve acceptable accuracy. For the lower modes, the inversion integral involves only simple poles and can be evaluated by Cauchy's residue theorem. For the higher modes it is necessary to use asymptotic approximations and the inversion involves branch points and poles. (Author)

An investigation has been carried out to determine the response of a cantilever beam having a time-varying cross section, to a prescribed harmonic displacement at its support. The assumption of classical beam theory leads to a set of ordinary differential equations of the Mathieu type. A general solution to these non-homogeneous equations is developed and programmed for the IBM 7040 digital computer. The strong dependence of the lateral motion to the frequency of the support displacement and to the frequency of the changing cross section is investigated for a wide range of ratios of these frequencies. (Author)

The natural frequencies and modes have been obtained for a stiffened and unstiffened composite shell composed of a cylinder with spherical end caps. Comparison of these are made to those obtained for an unreinforced cylindrical shell having various edge conditions. The results indicate that at the higher circumferential wave numbers, the frequencies of the unreinforced shell are independent of the end conditions. The frequencies of the ring-stiffened composite shell lie between the corresponding frequencies of the unstiffened shell and that of the isolated ring stiffener for circumferential wave numbers m greater than or equal to 1. Above a critical circumferential wave number, the stiffeners raise the value of the frequencies while below that number, they reduce their values. (Author)

A modified Particle-In-Cell (P.I.C.) method has been developed for solving two-dimensional nonlinear elasticity problems. The method is demonstrated by determining the stress concentration in an elastomeric sheet with a rigid circular inclusion subjected to large equi-biaxial deformations. The results indicate that the P.I.C. method might well be a desirable alternative to other numerical schemes for solving this class of problems. (Author)