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

Abstract

a b s t r a c tPiezoelectric 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.

Vibration Analysis of Composite Laminate Plate Excited by Piezoelectric Actuators

“…Proulx and Cheng [6] reported a dynamic model for the active vibration control of a rectangular plate using piezoceramic elements of arbitrary shape. Susanto [7] presented an analytical model of piezoelectric laminated slightly curved beams, which included the computation of natural frequencies, mode shapes and transfer function formulation using the distributed transfer function method. Qiu et al [8] used piezoelectric ceramic patches as sensors and actuators to suppress the vibration of a smart flexible clamped plate.…”

Analytical Solution for Free Vibration of Laminated Curved Beam with Magnetostrictive Layers

“…• Because of shallow curved beam assumption, the change in the radius of curvature due to magnetic field effects on the magnetostrictive layers is negligible [Susanto, 2009;Lee and Reddy, 2004].…”

“…Also they proposed the global-local HSDT suitable for symmetric and anti-symmetric laminates. Susanto [2009] computation of natural frequencies, mode shapes and transfer function formulation using the distributed transfer function method (DTFM). The DTFM was applied and extended to carry out the transfer function formulation of the PLSCB and PLSB models.…”

Influence of magneto-electric environments on size-dependent bending results of three-layer piezomagnetic curved nanobeam based on sinusoidal shear deformation theory

“…The bending results were derived using Taylor series expansion method. Influence of stretching–bending coupling due to curvature on the electro-elastic behaviors of the piezoelectric laminated slightly curved beams was mentioned by Susanto [7]. The numerical results showed that increasing the radius of curvature leads to increase of the natural frequencies of curved beam.…”