RESONANT AND ANTIRESONANT FREQUENCIES OF MULTIPLE CRACKED BAR

The natural frequencies or related resonant frequencies have been widely used for crack detection in structures by the vibration-based technique. However, antiresonant frequencies, the zeros of frequency response function, are less involved to use for the problem because they have not been thoroughly studied. The present paper addresses analysis of antiresonant frequencies of multiple cracked bar in comparison with the resonant ones. First, exact characteristic equations for the resonant and antiresonant frequencies of bar with arbitrary number of cracks are conducted in a new form that is explicitly expressed in term of crack severities. Then, the conducted equations are employed for analysis of variation of resonant and antiresonant frequencies versus crack position and depth. Numerical results show that antiresonant frequencies are indeed useful indicators for crack detection in bar mutually with the resonant one

The Effect of Patterned vs. Unpatterned Acoustic Bragg Reflector on Barium Strontium Titanate Solidly Mounted Resonator

ABSTRACTBarium strontium titanate solidly mounted resonators were fabricated with patterned and unpatterned acoustic Bragg reflectors on a sapphire substrate. The patterned and unpatterned solidly mounted resonator devices had acoustic Bragg reflectors consisting of Pt/SiO2/Pt/SiO2. The s-parameters of both devices were measured. The results showed that the quality factor increased for the device with the patterned acoustic Bragg reflector structure. The quality factors for the devices with patterned and unpatterned acoustic Bragg reflector structures were 54 and 115 and 28 and 86, respectively at the resonant and antiresonant frequencies. This investigation shows how an unpatterened acoustic Bragg reflector can contribute to the degradation of the overall quality factor of the device.

Identification of Linear Structures

Experimental frequency response data for a linear dynamic system is used to obtain system transfer functions. An easily implemented multi-degree-of-freedom technique which is applicable to linear structures having moderate, non-proportional viscous damping is presented. It is shown that experimental data at the resonant and antiresonant frequencies, together with high and low frequency data, are sufficient to identify the system.

The inverse problem for the vibrating beam

The beam is modelled by a system of rigid rods joined together by rotational springs and with masses at the joints. The left end is clamped while the right end is subject to one of a number of conditions: it is free, pinned, sliding or clamped. It is shown that the resonant and antiresonant frequencies of the system may be almost completely ordered. Necessary and sufficient conditions are found that these frequencies must satisfy to correspond to an actual system, with positive parameters, and two stripping procedures are devised for the determination of these system parameters, from a knowledge of certain frequency spectra.