| The forced vibration response of nearly degenerate structural modes and radiated sound is considered for repeated structures such as the blades on a rotor. An approach to minimize the radiated sound power from the lowest order modes on a uniformly excited five-bladed rotor is developed.; The analytical study considers the first bending modes of a five-bladed rotor by approximating it as a spring-mass-damper lumped-parameter system. The model, which approximates each blade as independent masses being connected to a rotor hub as a common mass, is evaluated for even and uneven blade-mass distributions. The radiated sound power, W, decreases with increasing mass perturbation amplitude epsilon and is optimized for mass perturbation phase &phis; being odd multiples of 18 degrees. W is shown to scale on the mechanical damping of the system zeta such that a decibel reduction in Wzeta2 is simply related to epsilon/zeta.; The computational study uses finite element analysis to compute the vibration levels and an acoustic superposition method to calculate the resulting radiated sound. For cases with even blade-to-blade trim masses, the computed natural frequency spread of the degenerate modes is less than one percent and the mode shapes follow circumferential wave-number distributions. Whenever blade-to-blade trim-mass distributions are used, the spread of natural frequencies increases to 20 percent of the mean frequency and the mode shapes are sequentially dominated by lone blades. A reduction of 13 dB was obtained for the uneven trim-mass distribution compared to the even trim-mass distribution for the first bending mode.; The radiated sound power is measured experimentally by exciting the blades underwater with PZT actuators and comparing the sound power results for both the uneven and even trim-mass distributions. The radiated sound power is shown to be measured indirectly by using the shaft force. Measurements are performed for no-, even-, and uneven-trim-mass conditions in air and in water. In general, the radiated sound power is reduced by applying uneven trim masses. However, the sound power increases at the side bands, a result which is consistent with the computational cases. |
