一种高阶频率可控的大变形梁单元  

A Large Deformation Beam Element with Controllable High-frequency

作　　者：张志刚 王栋银 马新旋 王良文 王才东 ZHANG Zhigang;WANG Dongyin;MA Xinxuan;WANG Liangwen;WANG Caidong(Henan Key Laboratory of Intelligent Manufacturing of Mechanical Equipment,Zhengzhou University of Light Industry,Zhengzhou 450002,China;Henan New Energy Vehicle Lightweight Design and Manufacturing Engineering Research Center,Zhengzhou University of Light Industry,Zhengzhou 450002,China)

机构地区：[1]郑州轻工业大学河南省机械装备智能制造重点实验室,郑州450002 [2]郑州轻工业大学河南省新能源汽车轻量化设计与制造工程研究中心,郑州450002

出　　处：《噪声与振动控制》2024年第5期14-20,68,共8页Noise and Vibration Control

基　　金：国家自然科学基金资助项目(52075500);河南省高校科技创新人才支持计划资助项目(22HAS-TIT023);2022年度河南省重点研发专项资助项目(221111240200)。

摘　　要：针对大变形梁刚柔耦合系统数值仿真效率低的问题,提出一种高阶频率可控的平面梁单元。选取节点位置矢量和首末两端节点处的轴向位置梯度矢量为整体参数,利用三次样条插值构造梁的形心线;依据Euler-Bernoulli梁变形假设,由形心线切向确定梁截面转角。从在模型层面滤除系统高频分量入手,采用一小段时间域内的平均内力代替虚功率方程中的瞬时内力,推导包含附加惯性项和阻尼项的大变形梁的控制方程。通过调整平均内力的时间区间长度参数,实现对系统方程中高频分量的控制,从而使常规显式算法也能被应用于传统刚性问题的仿真求解。数值算例表明应用所提出的大变形梁单元对刚柔耦合系统建模,能够在保证计算精度的同时大幅提升仿真求解效率。A planer beam element with controllable high-frequency is proposed to solve the low efficiency problem in numerical simulation of rigid-flexible coupled systems including large deformation beams.The position vector of each node and the axial gradient vector at the two-end nodes are selected as the global parameters,and the beam centroid line is interpo-lated using the cubic spline.The rotation angle of the beam cross-section is determined by employing the tangent direction of the centroid line according to the deformation assumption of Euler-Bernoulli beam.To filter out the high-frequency compo-nents of the system from the model level,the average internal force defined in a short time domain is used to replace the in-stantaneous internal force in the virtual power equation,and the governing equation of the large deformation beam with addi-tional inertia and damping terms is derived.By adjusting the time interval length parameter of the average internal force,the high-frequency components in the system equation can be controlled,so that the conventional explicit algorithm can also be used to solve the traditional stiff problem.Numerical examples illustrate that the computational efficiency of the rigid flexi-ble coupling system can be greatly improved without losing calculation accuracy when the proposed large deformation beam element is used.

关 键 词：振动与波 大变形梁 高频分量 三次样条 刚性问题 刚柔偶合 

分 类 号：O313.7[理学—一般力学与力学基础]