Wave Propagation Analysis Of Nonlocal Piezoelectric Nanobeams And Nanoshells

Piezoelectric materials can produce charge under external loads, whereas under applied electric field they can produce stress or mechanical movement. With the development of preparation technology of materials and application of piezoelectric nanomaterials, piezoelectric nanostructures have attracted researchers’extensive attention in recent years. Piezoelectric nanomaterials not only have the electro-mechanical coupling property, but also have many novel characteristics in mechanics, electrics, magnetics, acoustics and optics etc., so it has been widely used in various types of nanodevices.Piezoelectric nanostructures have the dimension varying from several hundred nanometers to just a few nanometers. At this scale, the size effect becomes very important. Therefore, the size effect should be taken into account in theoretical and experimental studies of piezoelectric nanostructures. It should be pointed out that Eringen’s nonlocal theory has been widely accepted and applied to the mechanical properties of nanostructures. The bending buckling, linear vibration, nonlinear vibration, postbuckling and wave propagation problems of carbon nanotubes and grapheme sheets have been extensively studied using the nonlocal nanobeam, nanoplate and nanoshell models.In this paper, wave propagation of piezoelectric nanobeams is first studied by using the Euler beam theory, Timoshenko beam theory and nonlocal piezoelectricity elastic theory. Then, Love shell theory and first-order shear deformation shell theory are used to study the wave propagation problems in piezoelectric nanoshells. Based on Hamilton principle, we obtain the equations of motion of nanobeams and nanoshells. The analytical solution of the equations is solved to obtained the disperse relations. Finally, the effect of nonlocal parameters, temperature change, voltage on the wave propagation characteristics of piezoelectric nanobeams and nanoshells is discussed in detail.