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- W2075508743 abstract "Further work is reported for the canonical model of an elastic coaxial cylinder, with inner radius R − 12 h and outer radius R + 12 h immersed in a compressible fluid, with the full set of elastodynamic equations, rather than a simplified shell model, used as a starting point for analysis. This dynamical system admits wave solutions of constant angular frequency ω, in which all of the appropriate field variables vary with azimuthal angle φ and axial coordinate x through a common factor eikxxeinφ with n = kyR not necessarily being an integer. One seeks simplified expressions for the dispersion relation F(ω,kx,ky) = 0 and for the polarization relations that determine the ratio of the complex amplitudes of displacements and stresses on the middle surface of the shell, and on the outer and inner surfaces. Systematic exact analytical (not numerical) expansions of the dispersion relations and the polarization relations in powers of parameters (such as h/R) are derived by a procedure that involves use of a computer-assisted symbol manipulation program and concepts of modern algebra. Alternate parameterizations are discussed and explored for incorporation of fluid loading into the expansion scheme, with appropriate assignments of the relative order of magnitudes of dimensionless groups, compared with that of the a priori small h/R. The other groups include, for example, the ratio of the fluid mass per unit area in a slab 1 wavelength thick to the shell mass per unit surface area. The parameterization presumes kxR and kyR are of the order of unity (neither small or large), but makes no initial assumption for the magnitude of the angular frequency. [Work of ADP is supported by ONR and by the William E. Leonhard endowment to Penn State Univ.; work of MGM is supported by the PSU Applied Research Laboratory Exploratory and Foundational Research Program.]" @default.
- W2075508743 created "2016-06-24" @default.
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- W2075508743 date "1990-11-01" @default.
- W2075508743 modified "2023-09-27" @default.
- W2075508743 title "Waves on fluid‐loaded cylindrical shells: Systematic expansions based on full elastodynamic equations" @default.
- W2075508743 doi "https://doi.org/10.1121/1.2029154" @default.
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