The modeling of viscoelastic circular plates for use as waveguide absorbers.
Hettema, Charles Dean.
Shin, Young S.
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A long standing concern of the Navy has been the need to reduce structural vibrations in plates, such as ship's hulls. Recently, it was proposed to use waveguide absorbers as a means to reduce structural vibrations. A waveguide absorber is a device which is made from damping material but mounted to the structure at a point rather than the full surface. A waveguide absorber removes and then dissipates vibrational energy from the structure through traveling waves. The performance of a waveguide absorber is determined from the driving point impedance, the ratio of force to velocity at the attachment point. This study has determined the theoretical driving point impedance for viscoelastic circular plates. The constitutive relations for viscoelastic material were evaluated and it was proven that a complex Young's modulus and shear modulus can be used to represent the viscoelastic material. Mindlin's theory for elastic isotropic plates, with complex moduli, was used to solve for the driving point impedance. The solutions are in terms of Bessel functions. Poisson's boundary conditions were used at the free edge of the circular plate, and clamped boundary conditions were used at the attachment point, which is at the center of the plate. A non-numeric language, REDUCE, was used to solve for the driving point impedance given the appropriate equations of motion and boundary conditions. The complex Bessel functions, needed for the results of the REDUCE program, were generated by a FORTRAN program. To validate the results of this study, elastic and viscoelastic plates were tested to determine their driving point impedance. A comparison of the theoretical results and the experimental results shows that there is agreement for all cases studied.
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