Vibration analysis of piezoelectric laminated slightly curved beams using distributed transfer function method

Piezoelectric laminated slightly curved beams (PLSCB) is currently one of the most popular actuators used in smart structure applications due to the fact that these actuators are small, lightweight, quick response and relatively high force output. This paper presents an analytical model of PLSCB, which includes the computation of natural frequencies, mode shapes and transfer function formulation using the distributed transfer function method (DTFM). By setting the radius of curvature of the proposed model to infinity, a piezoelectric laminated straight beams (PLSB) model can be obtained. The DTFM is applied and extended to carry out the transfer function formulation of the PLSCB and PLSB models. This method will be used to solve for the natural frequencies, mode shapes and transfer functions of the PLSCB and PLSB models in exact and closed form solution without using truncated series of particular comparison or admissible functions. The natural frequencies of the cantilevered PLSCB and PLSB are calculated by the DTFM and the Rayleigh–Ritz method. The analysis indicates that the stretching–bending coupling due to curvature has a considerable effect on the frequency parameters. Increasing the radius of curvature of the PLSCB has its largest effect on the natural frequencies. But the inhomogeneity of the boundary conditions does not have any effects on the natural frequencies or system spectrum due to the both receptance and boundary transfer functions have the same characteristic equations. The method can also be generalized to the vibration analysis of non-piezoelectric composite beams with arbitrary boundary conditions.