Convolution-Type Semi-Analytic DQ Approach for Transient Response of Rectangular Plates
-
摘要: 卷积型的Gurtin变分原理是目前在数学上唯一能和动力学初值问题完全等价的变分原理，它完全反映了有关初值问题的全部特征．通过卷积将矩形薄板原始控制方程构造成包含初始条件的新的具有完整初值问题特征的控制方程．对新的控制方程在时间域取解析函数，在空间域采用离散的DQ(differential quadrature)法，从而构造了卷积型DQ半解析法．该方法既可以达到和Gurtin变分原理相同的效果，又避开了Gurtin泛函的繁复．经对矩形薄板的动力响应问题的计算表明，该方法是一种精度好效率高的求解动力响应问题的计算方法．
-
关键词:
- 卷积 /
- 瞬态响应 /
- DQ(differential quadrature)法 /
- 半解析法
Abstract: The convolution-type Gurtin variational principle is known as the only variational principle,that is,from mathematical point of view,totally equivalent to the initial value problem system.The equation of motion of rectangular thin plates was first transformed to a new governing equation containing initial conditions by using convolution method.A convolution-type semi-analytical DQ approach,which involves differential quadrature (DQ) approximation in space domain and an analytical series expansion in time domain,was proposed to obtain the transient response solution.This approach of-fers the same advantages as Gurtin variational principle and at the same time,is much simpler in the calculation.Numerical results show that it is very accurate,yet computationally efficient for the dynamic response of plates. -
[1] Gurtin M E.Variation principles for linear initial-value problem[J].Quarterly Journal of Applied Mechanics,1964,22(3):252-264. [2] 罗恩.关于线弹性动力学中各种类型变分原理[J].中国科学(A辑)，1987，9:936-948. [3] Peng J S,Zhang J Y,Lewis R W.A semi-analytical approach for solving forced vibration problems based on convolution-type variational principle[J].Computers and Structures,1996,59(1):167-179. doi: 10.1016/0045-7949(95)00203-0 [4] Bellman R,Casti J.Differential quadrature and long-term integration[J].Journal of Mathematical Analysis and Applications,1971,34(2):235-238. doi: 10.1016/0022-247X(71)90110-7 [5] Cortinez V H.DQM for vibration analysis of composite thin-walled curved beams[J].Journal of Sound and Vibration,2001,246(3):551-555. doi: 10.1006/jsvi.2001.3600 [6] Hsu M H.Vibration analysis of edge-cracked beam on elastic foundation with axial loading using the differential quadrature method[J].Computer Methods in Applied Mechanics and Engineering,2005,194(1):1-17. doi: 10.1016/j.cma.2003.08.011 [7] Claudio F,Tomasiello S.Static analysis of a Bickford beam by means of the DQEM[J].International Journal of Mechanical Sciences,2007,49(1):122-128. doi: 10.1016/j.ijmecsci.2006.07.016 [8] Malekzadeha P,Karamib G.Polynomial and harmonic differential quadrature methods for free vibration of variable thickness thick skew plates[J].Engineering Structures,2005,27(8):1563-1574. doi: 10.1016/j.engstruct.2005.03.017 [9] 彭建设，张鹰，杨杰.策动力下动力学初-边值问题的时域配点DQ空-时半解析法[J].计算物理，2000,17(2):54-58. [10] 熊铃华，彭建设.卷积型加权残值法解圆板的动力响应问题[J].西华师范大学学报，2008，29(1):72-75. [11] 李永莉，赵志岗，侯志奎.卷积型加权残值法求解薄板的动力学问题[J].工程力学，2006，23(1):43-46. [12] 曹国雄.弹性矩形薄板振动[M].北京：中国建筑工业出版社，1983. [13] 曹志远.板壳振动理论[M].北京：中国铁道出版社，1989. [14] Szilard R.板的理论和分析——经典法和数值法[M].陈太平,戈鹤翔，周孝贤 译.北京：中国铁道出版社，1984. -
点击查看大图
计量
- 文章访问数: 1797
- HTML全文浏览量: 150
- PDF下载量: 834
- 被引次数: 0
下载:
