Thermo-electro-mechanical vibration analysis of piezoelectric nanoplates resting on viscoelastic foundation with various boundary conditions

• Published in: International journal of mechanical sciences 2017-10, Vol.131-132, p.1001-1015
• Main Authors: Zhang, D.P., Lei, Y.J., Shen, Z.B.
• Format: Article
• Language: English
• Subjects: Galerkin strip distributed transfer function method; Nonlocal kirchhoff plate theory; Piezoelectric nanoplates; Thermo-electro-mechanical vibration
• ISSN: 0020-7403; 1879-2162
• DOI: 10.1016/j.ijmecsci.2017.08.031

•Thermo-electro-mechanical loadings, viscoelastic medium, nonlocal and piezoelectric effects are considered simultaneously.•A new numerical approach called the GSDTFM is developed to obtain the semi-analytical solutions of natural frequencies.•The validity of the proposed model is verified by the different numerical methods reported in the literature.•A detailed parametric study is conducted to examine the effects of internal and external parameters. Based on the nonlocal Kirchhoff plate theory, the thermo-electro-mechanical vibration responses are studied for a rectangular piezoelectric nanoplate resting on viscoelastic foundation with various boundary conditions. In doing this, the governing equations of motion are first derived for vibration analysis, where thermo-electro-mechanical loadings, nonlocal effect, piezoelectric effect and viscoelastic foundation have been taken into consideration. Subsequently, the Galerkin strip distributed transfer function method is proposed to solve the governing equations, which enables one to obtain the semi-analytical solutions of natural frequencies for piezoelectric nanoplates with arbitrary boundary conditions. Here, the developed mechanics model is first validated by comparing the obtained results with those available in the literature. Also, the effects of nonlocal parameter, boundary conditions, viscoelastic foundation, external electric voltage, increment temperature, biaxial force and geometric dimensions on the vibration behaviors are carefully examined for the piezoelectric nanoplate. The results demonstrate the efficiency and robustness of the developed model for vibration analysis of a complicated multi-physics system comprising piezoelectric nanoplates, viscoelastic foundation and thermo-electro-mechanical loadings. [Display omitted] A rectangular piezoelectric nanoplate of length la, width lb and uniform thickness h rests on a viscoelastic foundation. The viscoelastic foundation is characterized by a visco-Pasternak foundation model, whose Winkler's modulus parameter is kw, Pasternak's (shear) modulus parameter is kG, and damping parameter is ct. The piezoelectric nanoplate is modeled as a nonlocal Kirchhoff plate subjected to a biaxial force P0, a uniform temperature change ∆T and an applied voltage Φ(x, y, z, t). In addition, the rectangular coordinate system oxyz is defined, in which the x-, y- and z-axes are taken along the length, width and thickness directions of the nanoplate, respectively.