Analytical Modeling of Sandwich Beam for Piezoelectric Bender Elements
-
摘要: 压电弯曲元是一类传感和作动器件,已得到广泛的应用.基于一阶剪切变形理论发展了压电弯曲元夹层梁解析模型,对梁截面采用统一转角并将耦合电势沿厚度的分布假设为二次函数,进一步修正了横向剪应变对电位移的影响.以弯曲元简支梁自由振动为例进行数值分析,解析模型解与二维精确解相比具有良好的精度,为分析弯曲元动力机电响应提供了良好的解析模型.Abstract: Piezoelectric bender elements are widely used as electromechanical sensors and actuators. An analytical sandwich beam model for piezoelectric bender elements was developed based on the first-order shear deformation theory (FSDT), which assumes a single rotation angle for the whole cross-section and a quadratic distribution function for coupled electric potential in piezoelectric layers, and corrects the effect of transverse shear strain on the electric displacement integration. Free vibration analysis of simply-supported bender elements was carried out and the numerical results showed that solutions of the present model for various thickness-to-length ratios compare well with the exact two-dimensional solutions, which presents an efficient and accurate model for analyzing dynamic electromechanical responses of bender elements.
-
Key words:
- bender elements /
- piezoelectric /
- sandwich beam /
- shear correction factor /
- analytical model
-
[1] Shirley D J, Hampton L D. Shear-wave measurements in laboratory sediments[J].Journal of the Acoustic Society of America,1978,63(2):607-613. doi: 10.1121/1.381760 [2] ZHOU Yan-guo, CHEN Yun-min.Influence of seismic cyclic loading history on small strain shear modulus of saturated sands[J].Soil Dynamics and Earthquake Engineering,2005,25(5):341-353. doi: 10.1016/j.soildyn.2005.03.001 [3] Leong E C, Yeo S H,Rahardjo H.Measuring shear wave velocity using bender elements[J].Geotechnical Testing Journal,2005,28(5):488-498. [4] Viggiani G, Atkinson J H.Interpretation of bender element tests[J].Geotechnique,1995,45(1):149-154. doi: 10.1680/geot.1995.45.1.149 [5] Arulnathan R, Boulanger R W,Riemer M F. Analysis of bender element tests[J].Geotechnical Testing Journal,1998,21(2):120-131. doi: 10.1520/GTJ10750J [6] Wood D Muir, Arroyo M,Greening P D. Source near-field effects and pulse tests in soil samples[J].Geotechnique,2003,53(3):337-345. doi: 10.1680/geot.2003.53.3.337 [7] Lee J S, Santamarina J C.Bender elements: performance and signal interpretation[J].Journal of Geotechnical and Geoenvironmental Engineering, ASCE,2005,131(9):1063-1070. doi: 10.1061/(ASCE)1090-0241(2005)131:9(1063) [8] Madabhusi-Raman P, Davalos J F. Static shear correction factor for laminated rectangular beams[J].Composites Part B: Engineering,1996,27(3):285-293. doi: 10.1016/1359-8368(95)00014-3 [9] Fernandes A, Pouget J.Analytical and numerical approaches to piezoelectric bimorph[J].International Journal of Solids and Structures,2003,40(17):4331-4352. doi: 10.1016/S0020-7683(03)00222-1 [10] ZHOU Yan-guo,CHEN Yun-min, DING Hao-jiang. Analytical solutions to piezoelectric bimorphs based on improved FSDT beam model[J].Smart Structures and Systems,2005,1(3):309-324. [11] DING Hao-jiang, WANG Guo-qing, CHEN Wei-qiu. Green's functions for a two-phase infinite piezoelectric plane[J].Proceedings of the Royal Society of London A,1997,453(1966): 2241-2257. doi: 10.1098/rspa.1997.0120 [12] ZHOU Yan-guo, CHEN Yun-min, DING Hao-jiang. Analytical modelling and free vibration analysis of piezoelectric bimorphs[J].Journal of Zhejiang University A Science,2005,6(9):938-944. [13] Wang Q, Quek S T,Sun C T.et al.Analysis of piezoelectric coupled circular plate[J].Smart Materials and Structures,2001,10(2):229-239. doi: 10.1088/0964-1726/10/2/308 [14] 丁皓江,江爱民.压电梁的多项式解(Ⅰ)——若干精确解[J].应用数学和力学,2005,26(9):1009-1022. [15] Timoshenko S P.On the transverse vibrations of bars of uniform cross section[J].Philosophical Magazine, Ser 6,1922,43:125-131. doi: 10.1080/14786442208633855 [16] 周燕国. 土结构性的剪切波速表征及对动力特性的影响[D].博士论文.杭州:浙江大学, 2007.
点击查看大图
计量
- 文章访问数: 2689
- HTML全文浏览量: 96
- PDF下载量: 588
- 被引次数: 0