Content area
Full Text
Journal of Mechanical Science and Technology 26 (8) (2012) 2511~2521
www.springerlink.com/content/1738-494x
DOI 10.1007/s12206-012-0629-7
Dynamic analysis of smart composite beams by using the frequency-domain spectral element method
Ilwook Park and Usik Lee*
Department of Mechanical Engineering, Inha University, 253 Yonghyun-dong, Nam-gu, Incheon 402-751, Korea
(Manuscript Received December 5, 2011; Revised March 23, 2012; Accepted April 4, 2012)
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
Abstract
To excite or measure the dynamic responses of a laminated composite structure for the active controls of vibrations or noises, wafer-type piezoelectric transducers are often bonded on the surface of the composite structure to form a multi-layer smart composite structure. Thus, for such smart composite structures, it is very important to develop and use a very reliable mathematical and/or computational model for predicting accurate dynamic characteristics. In this paper, the axial-bending coupled equations of motion and boundary conditions are derived for two-layer smart composite beams by using the Hamiltons principle with Lagrange multipliers. The spectral element model is then formulated in the frequency domain by using the variation approach. Through some numerical examples, the extremely high accuracy of the present spectral element model is verified by comparing with the solutions by the conventional finite element model provided in this paper. The effects of the lay-up of composite laminates and surface-bonded wafer-type piezoelectric (PZT) layer on the dynamics and wave characteristics of smart composite beams are investigated. The effective constraint forces at the interface between the base beam and PZT layer are also investigated via Lagrange multipliers.
Keywords: Smart composite beam; Spectral element method; Dynamic analysis; PZT ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
1. Introduction
Piezoelectric materials have received a great deal of attention due to the potential applications to the active controls of structural vibrations and noises. The converse piezoelectric effect is used for the actuator design while the direct piezoelectric effect is used for the sensor design [1]. In order to use these piezoelectric effects, the wafer-type piezoelectric transducers made of lead zirconate titanate (hereafter, PZTs) are often bonded on the surface of a structure, which builds a multi-layer structure [2]. Though there are various types of multilayer structures, the discussion in this paper will be confined to the two-layer smart composite beam which consists of a laminated composite base beam and a PZT layer.
For accurate prediction of the dynamics...