### ASA 125th Meeting Ottawa 1993 May

## 3aSA6. Spatial attenuation of bending waves in the infinite plates coupled
by a viscous damping layer.

**Jongmin Kang
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*Dept. of Mech. Eng. and Inst. for Manufacturing Res., Wayne State Univ.,
Detroit, MI 48202
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**Adnan Akay
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*Carnegie Mellon Univ., Pittsburgh, PA 15213
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Plate vibrations can be reduced by a viscous damping layer between a
primary excited plate and a secondary plate, of which frequency responses are
considered by Ingard and Akay [J. Vib., Struct. Rel. Design 108, 178--184
(1987)]. For a free vibration, complex wave numbers are determined from a
dispersion relation, where the imaginary part is related with the attenuation
due to the damping layer. The steady state responses both in the plates and
fluid layer are calculated when the primary plate is under a time harmonic
line-driven force. Energy and power flow of a complex wave number are also
considered. The complex wave number in a vibrating plate increases as the
thickness of the damping layer decreases, such that the attenuation is greater
and the period in space is shorter, and the waves in a damping layer become
unstable. For a given thickness of a damping layer, as the exciting frequency
is higher, the damping effects are weaker, since the boundary layer thickness
becomes thinner. When a secondary plate of a same material is attached to
attenuate the vibration of a primary plate, the secondary plate must be thicker
than the primary plate to achieve an efficient vibration reduction. The bending
waves in the primary plate are attenuated very fast, and become identical with
the bending waves in the secondary plate at far field.