西北工业大学学报
西北工業大學學報
서북공업대학학보
JOURNAL OF NORTHWESTERN POLYTECHNICAL UNIVERSITY
2013年
6期
931-934
,共4页
哈密尔顿%多辛%薄圆板%冲击荷载
哈密爾頓%多辛%薄圓闆%遲擊荷載
합밀이돈%다신%박원판%충격하재
Hamiltonians%algorithms%dynamic response%multi-symplectic symmetric form%centrosymmetric thin circular plate
基于Bridges建立的多辛理论,构造了中心对称薄圆板振动方程的多辛对称形式及其多种局部守恒律,针对振动方程的多辛形式,采用Euler Box差分离散方法构造其多辛格式,利用计算机模拟,研究了冲击荷载作用下中心对称薄圆板的振动问题,并在模拟过程中重点关注多辛算法是否精确保持振动系统的局部几何性质,该研究结果为薄板振动问题提供了新的数值研究途径。
基于Bridges建立的多辛理論,構造瞭中心對稱薄圓闆振動方程的多辛對稱形式及其多種跼部守恆律,針對振動方程的多辛形式,採用Euler Box差分離散方法構造其多辛格式,利用計算機模擬,研究瞭遲擊荷載作用下中心對稱薄圓闆的振動問題,併在模擬過程中重點關註多辛算法是否精確保持振動繫統的跼部幾何性質,該研究結果為薄闆振動問題提供瞭新的數值研究途徑。
기우Bridges건립적다신이론,구조료중심대칭박원판진동방정적다신대칭형식급기다충국부수항률,침대진동방정적다신형식,채용Euler Box차분리산방법구조기다신격식,이용계산궤모의,연구료충격하재작용하중심대칭박원판적진동문제,병재모의과정중중점관주다신산법시부정학보지진동계통적국부궤하성질,해연구결과위박판진동문제제공료신적수치연구도경。
To preserve the local geometric properties of a dynamic system , one of the important factors for determi-ning its dynamic response , we analyze the vibration of the centrosymmetric thin circular plate under impact load in the Hamiltonian space .Section 1 of the full paper derived Eq .( 4) as the multi-symplectic symmetric form of the centrosymmetric thin circular plate and Eqs .(5), (6) and (7) for its local conservation laws.Section 2 uses the Euler Box difference discretization method to construct Eq .( 8 ) as the multi-symplectic difference discretization scheme of the multi-symplectic symmetric form .Section 3 simulates the vibration of the centrosymmetric thin circular plate under impact load and fixed boundary conditions to analyze its dynamic response .The simulation re-sults, given in Figs.1 and 2, show preliminarily that our multi-symlectic algorithm can accurately keep for a long time the local geometric properties of the centrosymmetric thin circular plate under impact load , indicating that the dynamic response analysis obtained with the multi-symlectic algorithm is reliable .