Abstract

As a first endeavor, thermo-electro-mechanical analysis of quadrilateral and triangular piezoelectric nanoplates are investigated based on the nonlocal theory and the Kirchhoff plate theory. It is assumed that the piezoelectric nanoplate is subjected to a biaxial force, an external electric voltage, and a uniform temperature rise. Hamilton’s principle is employed to derive the governing equations. The B3-spline finite strip method used to determine the natural frequencies, buckling loads, and corresponding mode shapes of displacement and the electric potential of quadrilateral and triangular piezoelectric nanoplates, for the first time. The comprehensive parametric study is conducted to explore the effect of the nonlocal parameter, geometrical shape, thermo-electro-mechanical loadings, boundary conditions, aspect ratio, and side length. It is shown that small-scale effect plays a considerable role in the buckling and vibration behavior of quadrilateral and triangular piezoelectric nanoplates.

摘要

作为第一次尝试，基于非局部理论和基尔霍夫板理论研究了四边形和三角形压电纳米板的热机电分析。假设压电纳米板受到双轴力、外部电压和均匀的温升。哈密​​顿原理用于推导控制方程。B3 样条有限条法首次用于确定四边形和三角形压电纳米板的固有频率、屈曲载荷以及相应的位移振型和电势。进行了综合参数研究，以探索非局部参数、几何形状、热机电载荷、边界条件、纵横比和边长的影响。