电－热－力载下 BNNTs 增强压电板的非线性动力响应

摘要

研究了电－热－力载荷作用下硼氮纳米管（BNNTs）增强压电板的非线性动力响应。运用板的非线性应变几何关系及考虑温度效应的压电理论，建立了 BNNTs 增强压电板的本构关系。通过变分推导出了结构的非线性动力控制方程。在空间上采用差分法离散，在时间上采用 Newton-Newmark 方法离散，整个问题采用迭代法进行求解。算例中，详细讨论了电压、温度、载荷、体积比以及外激励频率等因素对 BNNTs 增强压电板非线性动力响应的影响。%The nonlinear dynamic response of a piezoelectric plate reinforced with boron nitride nanotubes (BNNTs)under electro-thermo-mechanical loadings was studied.Using nonlinear strains based on the plate theory and the piezoelectric theory considering thermal effects,the constitutive relations of the piezoelectric plate reinforced with BNNTs were established.Then,the dynamic governing equations of the structure were derived with the variational principle.Using the difference method in space and Newton-Newmark method in time,the whole problem was solved with the iteration method.In numerical examples,the effects of voltage,temperature,mechanical load,volume ratio and external excitation frequency on the nonlinear dynamic response of the piezoelectric plate reinforced with BNNTs were discussed.