引入减基法的压电层合板瞬态响应分析  

Transient response analysis for a piezoelectric laminate with reduced-basis method

作　　者：黄芬[1] 韩旭[1] 龚双[1] 黄永辉 

机构地区：[1]湖南大学机械与运载工程学院汽车车身先进设计制造国家重点实验室,长沙410082 [2]长沙中联重工科技股份有限公司,长沙410013

出　　处：《振动与冲击》2011年第4期254-258,共5页Journal of Vibration and Shock

基　　金：国家杰出青年基金(10725208);高等学校博士点专项科研基金(2007053201)

摘　　要：用减基法(RBM)结合有限元法、傅里叶变换和Newmark直接积分法,研究了压电层合板在机电耦合载荷下的瞬态响应。用层单元将层合板沿厚度方向进行离散,得到时间域内的运动方程,通过傅里叶变换得到波数域内的控制方程。应用Newmark直接积分法求解波数域内的位移和电势,并在Newmark法求解过程嵌入减基法,构造减基空间,把结构的等效刚度矩阵、质量矩阵和载荷列向量映射到减基空间降阶,得到减缩的Newmark增量式,从而快速求解得到原结构波数域响应,通过傅里叶逆变换得到时域内的响应。以PZT-5A/0°PVDF铺层两相材料复合压电层合板为算例,分析了机电耦合线载荷激励下,位移场和电势场的瞬态响应情况。计算结果表明,求解过程引入减基法能更快得到结构的瞬态响应,并保证了精度。The combination of reduced-basis method（RBM）,finite element method,Fourier transformation and Newmark direct integral method was introduced for transient response analysis of a piezoelectric laminate subjected to coupled electro-mechanical loads.The laminate was discretized in the thickness direction with plate elements,and the governing equations were obtained.The governing equations in wavenumber domain were gained with Fourier transformation.The Newmark direct integral method was employed to calculate the displacement responses and the electrical potential responses in wavenumber domain.The reduced-basis method was introduced during using Newmark direct integral method and a reduced basis space was constructed.The equivalent stiffness matrix,mass matrix and the load vector were projected into the space.The reduced Newmark formulation was obtained and the responses in wavenumber domain were calculated effectively.The transient responses were obtained by using the inverse Fourier transformation.The numerical results provided the transient responses excited by the coupled electro-mechanical line load in a PZT-5A/0° PVDF composite plate.They showed that the transient responses of a piezoelectric laminate can be solved rapidly by employing the proposed reduced-basis method.

关 键 词：减基法 瞬态响应 NEWMARK法 压电层合板 

分 类 号：TB123[理学—工程力学]