Free vibration of functionally graded material beams with surface-bonded piezoelectric layers in thermal environment
The authors consider free vibrations of statically thermal postbuckled three-layer laminated functionally graded material beams with surface-bonded piezoelectric layers subject to temperature and voltage. The top and bottom layers are homogeneous piezoelectric materials, the middle layer is of a functionally graded material. The thickness of the top and bottom layers is the same. The authors investigate the change in the beam static thermal deformation and natural frequency through electrical control of the piezoelectric layers. The axial extension, eliminating the transverse shearing, is expressed accordingly to Euler-Bernoulli beam theory. The temperature rise in the beam is static and transversely non-uniform. In order to analyze beam free vibrations in static prebuckling and postbuckling configurations, the solutions of governing equations are divided in two parts: the solutions for static deformation and the solutions describing the vibrations in the vicinity of static equilibrium configurations. The authors find that three lowest frequencies of the prebuckled beam decrease with increase in the temperature, but for a buckled beam they increase monotonically with temperature rise. The tensional force produced in piezoelectric layers by voltage can efficiently reduce the critical buckling temperature and natural frequencies.
scientific article; zbMATH DE number 5619128