The steady-state response of a fluid-filled beam near resonance

In this report the steady-state near-resonant vibration of a hollow fluid-filled beam is considered. The energy dissipation caused by the beam-fluid interaction is approximated by introducing a viscous damping force into the Bernoulli-Euler beam equation. A theoretical expression is developed for the displacement of the hollow beam by solving this modified Bernoulli-Euler beam equation. Tests are made using a cantilevered fluid-filled box to simulate a unit of beam-fluid length. The band-width technique is used to determine the incremental viscous damping coefficient from test data. A variety of fluids are used in the box to determine the effect of the fluid characteristics and fluid height upon the incremental damping coefficients. The tests show that in general filling the box with any volume of liquid increases its damping characteristics. An increase in the kinematic viscosity of the fluid will result in a corresponding increase in the equivalent damping factor of the system for the box full of a fluid. However, when the box is partially filled with fluid this factor will decrease. Negligible longitudinal fluid interaction is assumed for the continuous system, and the incremental damping coefficient determined from incremental test data is then used in the theoretical expression developed for the displacement of the hollow beam. The analytical results thus obtained for the beam completely and partially filled with SAE 40W oil is verified experimentally. The measured magnification factors near resonance deviate by no more than thirty percent from the corresponding analytically determined magnification factors for all of the three cases selected --Abstract, pages ii-iii