Vibration of beams with delaminations and embedded piezoelectric sensors and actuators - Della, Christian Ngalatan (2008)
Nondimensional parameters are introduced to study the vibration of bimaterial beams with a single delamination. The use of these parameters provides a physical understanding on the ‘constrained mode’ and ‘free mode’ assumptions that are used in delamination vibration. In addition, an analytical solution for the vibration of three-layer beams with double delaminations is presented. Lower and upper bounds of the frequency are proposed by assuming totally ‘free’ and totally ‘constrained’ deformations of the delaminated layers. Analytical solutions for the free vibration of composite beams with multiple delaminations are presented. The delaminated beams are modeled as interconnected Euler-Bernoulli beams using the delaminations as their boundaries. The effects of the delaminations on the natural frequencies and mode shapes of the composite beams are investigated. A mathematical model for the vibration of beams with embedded piezoelectric sensors and actuators is presented. These embedded piezoelectrics are analyzed using Eshelby’s equivalent inclusion method. The natural frequency of the beam is determined from the variational principle in Rayleigh quotient form. The effects of the volume fraction, aspect ratio and location of the piezoelectric inclusions on the natural frequency of the beam are investigated.