电致伸缩圆柱体电场冲击响应研究

Research on the Electro-Elastic Response in an Electrostrictive Cylinder Subjected to an Electrical Shock

根据弹性力学轴对称平面应变问题的基本方程,采用有限Hankel变换及其逆变换辅以Laplace变换技术,得到了轴对称径向突加电场载荷条件下电致伸缩材料实心圆柱体的动态位移和应力响应的解析解.由于电冲击引起圆柱体内弹性波的传播,动态位移和应力随时间呈不同峰值的周期性变化.数值计算表明,随着半径增大,位移的响应相应增加,在圆柱表面达到静态位移数值的5倍以上;在圆柱表面附近,动态应力响应呈周期性拉压变化,最大幅度可达到静态应力的20倍左右.因此,在计算位移和应力场时,必须考虑电场冲击因素.

According to the basic equations of symmetric elastic plane strain problem,the analytic solutions of displacements and stress fields in an electrostrictive cylinder subjected to a symmetric electrical shock are derived with the finite Hankel and Laplace transformations and their inverse. The amplitudes of the transient displacement and the stress field oscillate,since elastic waves propagate in the cylinder subjected to the electrical shock. Numerical results show that,the values of transient displacement can be enhanced to 5 times of the static ones when the radius of cylinder increases; the dynamic stress varies in tensile and compressive status periodically,which can be around 20 times over the value of the static one. Therefore,the electrical shock must be taken into consideration in computation of the displacement and the stress fields.