Shaping of a system's frequency response using an array of subordinate oscillators.

The frequency response of an oscillating structure can be tailored by attaching one or more subordinate oscillators. This paper shows how the magnitude and phase of the frequency response can be deliberately shaped by prescribing the distributions of the dynamic properties in an array of such subordinate oscillators. Exact analytic governing equations of motion are derived for the coupled system composed of the primary system and the subordinate array. For a relatively small number (<100) of attached oscillators whose total mass is small (<1%) relative to the primary structure, it is possible to engineer frequency-response functions of the primary oscillator to have, for example, nearly linear phase or constant amplitude over a frequency band of interest. The frequency range over which response shaping is achieved is determined by the band of the attached oscillators. It is shown that the common analytic methodology for designing a dynamic vibration absorber represents the limiting case of a single oscillator in the subordinate set. Moreover, increasing the number of subordinate oscillators (without increasing the total added mass) offers a number of advantages in reshaping the dominant system's frequency response.

Detection and localization of rib detachment in thin metal and composite plates by inversion of laser Doppler vibrometry scans.

The laboratory implementation of a fault detection and localization method based on inversion of dynamic surface displacements measured by a scanned laser Doppler vibrometer (SLDV) was investigated. The technique uses flexural wave and generalized force inversion algorithms which have previously been demonstrated using simulated noise-free vibration data generated for thick plates with a finite element model. Here these inversion algorithms to SLDV measurements made in the laboratory on a thin nickel plate and a thin carbon fiber composite plate, both having attached reinforcing ribs with intentional de-bonding of the rib/plate interface at a specific location on each structure are applied. The inverted displacement maps clearly detect and locate the detachment, whereas direct observation of the surface displacements does not. It is shown that the technique is relatively robust to the choice of frequency and to the presence of noise.