Vibration analysis of a circular thin polymeric piezoelectric diaphragm with fluid interaction
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Vibration analysis of a circular thin polymeric piezoelectric diaphragm with fluid interaction Amir Monemian Esfahani . Mohsen Bahrami
Received: 7 March 2015 / Accepted: 29 April 2015 Springer Science+Business Media Dordrecht 2015
Abstract This paper presents vibration analysis of a circular piezoelectric micro-plate in fluidic environment. PVDF film is used as the piezoelectric material. PVDF is a material with asymmetric matrix of piezoelectric constants and shows different piezoelectric properties in different directions. The governing equations, which are more complicated compared to piezo-ceramics, are derived. The boundary conditions for the plate are assumed fully clamped at outer edge, as is the case in many micro devices. Liquid is modeled as a damping foundation under the plate. The equations of motion are solved using generalized differential quadrature method to obtain Eigen frequencies and mode shapes of the plate. The results are compared by developed finite element analysis. Keywords Smart materials Polymer piezoelectric PVDF Micro plate GDQ Diaphragm
A. Monemian Esfahani M. Bahrami (&) Department of Mechanical Engineering, Amirkabir University of Technology (Tehran Polytechnic), #424, Hafez Ave, Tehran, Iran e-mail: [email protected] A. Monemian Esfahani e-mail: [email protected]
1 Introduction The inherent structural capabilities of polymers and their potential smartness make it possible to be used in a variety of applications in different engineering areas. Polymer implementation in different high-tech areas indicates the impact of research that have been pursued on polymers in the last decades. Some polymers, the so-called electro active polymers (EAP), may exhibit either piezoelectricity or electrostriction (Furukawa 1984; Riande and Calleja 2004). The capability to couple mechanical and electrical properties, piezoelectricity and electrostriction, is currently used in some well-known piezoelectric polymers such as polyvinylidene fluoride (PVDF) that is commercially available (MEAS 2008). Some researchers investigated the piezoelectricity properties of polymers. Kawai (1969) examined the piezoelectricity of poly (vinylidene fluoride). Furukawa (1984) explored piezoelectricity in ferroelectric polymers. Fukuda (2000) made a review on piezoelectric polymers. Riande and Calleja (2004) worked on electrical properties of polymers. Tanaka et al. (2008) used PVDF films for evaluating tactile sensing. Carpi et al. (2009) studied biomedical application of EAP. Addition to these studies, some researchers explored numerical analysis of the piezoelectricity to predict the behavior of these materials. Tzou and Tseng (1990) presented finite element method to solve a two dimensional piezoelectric material for use as an
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actuator or sensor. Kagawa et al. (1996) used FEM for simulating a piezoelectric actuator. Khutoryansky et al. (1998) investigated boundary element method (BEM) to model and simulate active materials. Benjeddou (2000) studied FEM for some
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