Abstract
The existing studies indicate polymers will present obviously different properties in tension and compression (bimodular effect) which is generally ignored because of the complexity of the analysis. In this study, a functionally graded piezoelectric cantilever beam with bimodular effect was investigated via analytical and numerical methods, respectively, in which a one-dimensional theoretical solution was derived by neglecting some unimportant factors and a two-dimensional numerical simulation was performed based on the model of tension-compression subarea. A full comparison was made to show the rationality of one-dimensional theoretical solution and two-dimensional numerical simulation. The result indicates that the layered model of tension-compression subarea also makes it possible to use numerical technique to simulate the problem of functionally graded piezoelectric cantilever beam with bimodular effect. Besides, the modulus of elasticity E* and the bending stiffness D* proposed in the one-dimensional problem may succinctly describe the piezoelectric effect on the classical mechanical problem without electromechanical coupling, which shows the advantages of one-dimensional solution in engineering applications, especially in the analysis and design of energy harvesting/sensing/actuating devices made of piezoelectric polymers whose bimodular effect is relatively obvious.
Highlights
Piezoelectric materials have an electromechanical coupling characteristic, which makes them a good candidate for a variety of electromechanical devices, for example, sensors and actuators used extensively in electromechanical conversion
Shi and Chen [17] studied the problem of a functionally graded piezoelectric materials (FGPM) cantilever beam and obtained a set of analytical solutions for the beam subjected to different loadings
Due to the complexity of its analysis, the bimodular effect of materials is often neglected, especially in the analysis of some specialized materials and structures, for example, intelligent materials and structures mentioned above. He et al [27] introduced the bimodular effect into the analysis of FGPM structures, for the first time, and obtained a two-dimensional electroelastic analytical solution for a FGPM beam with different moduli in tension and compression
Summary
Piezoelectric materials have an electromechanical coupling characteristic, which makes them a good candidate for a variety of electromechanical devices, for example, sensors and actuators used extensively in electromechanical conversion. Shi and Chen [17] studied the problem of a FGPM cantilever beam and obtained a set of analytical solutions for the beam subjected to different loadings. Due to the complexity of its analysis, the bimodular effect of materials is often neglected, especially in the analysis of some specialized materials and structures, for example, intelligent materials and structures mentioned above He et al [27] introduced the bimodular effect into the analysis of FGPM structures, for the first time, and obtained a two-dimensional electroelastic analytical solution for a FGPM beam with different moduli in tension and compression. For the above two reasons, we think it is necessary to obtain the one-dimensional theoretical solution and perform the two-dimensional numerical simulation for the problem of bimodular FGPM cantilever beam.
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