Functionally graded piezoelectric material has very enormous application in the field of engineering and science. It is very useful for smart device like micro electric mechanical system, nano electro mechanical system. In the present work the effect of diametric ratio has been observed for functionally graded piezoelectric circular plate. d15 effect has been utilized for exited shear induced flexural vibration. Plate has been readily polarized and electric effect is applied along the thickness direction.
Functionally graded piezoelectric materials is widely used material. Functionally graded material has been used in drone for making it self-powered. Functionally graded piezoelectric materials are using in gas litre and in gas stove for auto ignition. This plate can be use in crack detection in the pipes and rail wheel. Piezoelectric materials are used to measure change in pressure, acceleration.
II. MODEL DESCRIPTION
For analysis the effect of diametric ratio on functionally graded piezoelectric materials a circular plate of inner diameter of 1 mm and outer diameter of 24 has been consider. Thickness of the plate is 1mm. This plate has been radially polarized and electric field has been applied towards the thickness direction. Eigen frequency has been evaluated for free-free, fixed-free and for fixed-fixed boundary conditions.
IV. RESULT AND DISCUSSION
In this study, Eigen frequencies of functionally graded circular disks have been evaluated for free-free, fixed-free, and fixed-fixed boundary conditions. Hare the meaning of free-free boundary conditions is that inner surface of the plate is free and outer surface of the plate is also free, fixed free means that inner surface of the plate is fixed while outer surface of the plate is free. Fixed-fixed means that plate is fixed from inner and outer surface of the plate. Power law is used to vary the property in thickness direction. Upper surface of the plate is PZT-4 rich while inner surface of the plate is PZT-5H rich. Properties of the plate constantly varying.
A. Analysis of Eigen frequency of FGPM disk for measuring the effect of diametric ratio for free-free boundary condition
Table 1 shows the effect of natural frequency of FGPM disk for free-free boundary conditions. From this table it can be observed that the natural frequency of the disc is decreasing when the diametric ration is increases. ‘n’ denotes nodal diameter, ‘s’ denotes nodal circle hare, N is the power law index. Power law index N is 0.5 in this analysis. Thickness of the plate is 1 mm and outer diameter of the plate is 24 mm while inner diameter is varying constantly.
B. Analysis of Eigen frequency of FGPM disk for measuring the effect of diametric ratio for fixed-free boundary condition
From table 2 in can be observed that natural frequency of the circular disc increases when the inner and outer diameter ratio increases. Natural frequency of one nodal diameter and zero nodal circle increase in greater diameter. For the engineering application it is very good to find more flexible plate so this results can be utilized for developed more new engineering applications.
C. Analysis of Eigen frequency of FGPM disk for measuring the effect of diametric ratio for fixed-free boundary condition
It can be observed from table 3 that natural frequency increase when diameter ratio increases. Second column of this table show zero nodal diameter and zero nodal circle third Colum show the natural frequency for the one nodal diameter and zero nodal circle and forth column show result for two nodal diameter and zero nodal circle and similarly fifth, sixth and seventh column show the result for three, four and fifth nodal diameter.
Eigen frequency for the FGPM plate has been evaluated, and a comparative study of different geometrical parameters has been conducted with power law variation. It is observed here that natural frequency slightly creases when the value of the power law index increases. This FGPM circular disk can be used in ultrasonic motors, drones, and many smart devices. Here, the natural frequency is higher for fixed-fixed boundary conditions than the free and fixed-free boundary conditions. The free-free plate\'s natural frequency is much less than the other boundary condition for the same nodal circle and nodal diameter. The natural frequency obtained here is believed to be useful for designing smart systems based on FGPM round disks by exited shear vibration. Shear-induced flexural vibration for varying power law index on the elastic foundation can be explored in future work.
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