Free vibration investigations for the cantilever-symmetric and skew-symmetric trapezoidal plates with cracks

Abstract

Using the advantages of non-contact and full-field measurements, the optical technique called amplitude-fluctuation electronic speckle pattern interferometry (AF-ESPI) with out-of-plane setup is employed to investigate the free vibration of cantilever-symmetric and skew-symmetric trapezoidal plates with cracks. Three different types of crack locations will be discussed in detail in this study, one is along the middle chord line and the others are along the clamped edge. Prior to the study of cracked trapezoidal plates, a cantilever rectangular plate is used to carry out the AF-ESPI measurement, and then the experimental results are checked by theoretical and numerical calculations. Numerical calculations based on the finite element method are performed and compared with the experimental results, in which good agreement is obtained for resonant frequencies and mode shapes. Finally, the influences of crack length and location on the vibration behavior of the cracked trapezoidal plates are studied in terms of the dimensionless frequency parameter vs. the crack length ratio. With the aid of mode shape observation, the variation in resonant frequencies is specified; furthermore, it is found that the crack existence does not affect the resonant frequencies for some vibration modes.