Piezoelectricity theoretical models

Kogan S, Kaduchak G, Sinha DN (2004) Acoustic concentration of particles in piezoelectric tubes theoretical modeling of the effect of cavity shape and symmetry breaking. J Acoust Soc Am 116 1967-1974... 

DiolOCtriC Thoory. The piezoelectricity in amorphous polymers differs from that in semicrystalline polymers and inorganic crystals in that the polarization is not in a state of thermal equilibrium, but rather a quasi-stable state because of the freezing-in of molecular dipoles. The result is a piezoelectric-hke effect. A theoretical model for polymers that have frozen-in dipolar orientation was presented to explain piezoelectricity and p5Toelectricity in amorphous polymers such as poly(vinyl chloride) (39). 

Due to the complicated nature of the piezoelectric properties of polymeric materials, it is extremely difficult to exactly determine which theoretical model is closest to presenting the real mechanisms. However, the theoretical models proposed by researchers are useful in providing insight into the physical basis of the observed piezoelectricity. 

Another cylindrical hydrophone design approach that features piezoelectric polymer as the active sensing clement is shown in Figure 9. In this concept, PVDF coaxial cable is wrapped around a compliant cylindrical structure (11], A theoretical model with supporting experiments of such a concept has suggested t cylindrical hydrophones featuring PVDF cable wound around an air-filled cylinder (with exposed ends) results in enhanced performance as compared to a similar piezoelectric polymer coil around a free flooded cylindrical structure as demonstrated by the FFVS of Ftgure 10. 

In order to investigate the theoretical model presented in section n, an experimental setup consisting of a water tank and piezoelectric elements is used (Figure 2). The transmitter consists of a 2 cm diameter piezoelectric transducer (PZT-4) with a resonance frequency of 1 MHz, excited by a signal generator producing a sine wave at 1.1 MHz. Another piezoelectric transducer (2 cm diameter, resonance frequency of 1.7 MHz) is connected to a data-acquisition board via a preamplifier. 

This chapter discusses materials known as electroactive composites. These are mixtures of an electroactive (or in the present context, ferroelectric) ceramic phase and a polymer phase. Early sections will look at the individual phases, making use of piezoelectric parameters defined in Chapter 5. A summary of theoretical models will then be given, before preparation and characterization are discussed. Finally, the problems associated with producing an active device and examples of working systems will be considered. 

Wada and Hayakawa have developed the theory of piezo- and pyroelectricity based on the model that spheres with spontaneous polarization Psc are dispersed in a matrix. The sphere represents a crystal lamella with sur-rouning oriented amorphous phase. Their theoretical expression for piezoelectric e constant is as follows. 

H. Banno, Theoretical equations far dielectric and piezoelectric properties of fatrocloctric composites based on modified cubes model, Jpn. J. AppL Pkys. St pL 24-2 445 (1965). 

Lee J, Kim H (2007) Elasto-plastic analysis of adhesively bonded symmetric single lap joints under in-plane tension and edge moments. J Adhes 83(9) 837-870 Liljedahl CDM, Crocombe AD, hab I4A, Ashcroft lA (2006) Damage modelling of adhesively bonded joints. Int J Fract 141(1—2) 147—161 Luo Q, Tong L (2002) Exact static solutions to piezoelectric smart beams including peel stresses-1 theoretical formulation. Int J Solids Struct 39( 18) 4677-4695... 

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