约束Green函数与非线性地基梁模态分析
Constrained Green Function and Nonlinear Foundation Beam Modal Analysis
赵翔 1王琦 1朱伟东 2李映辉3
作者信息
- 1. 西南石油大学 土木工程与测绘学院,成都 610500
- 2. 马里兰大学 机械工程系,巴尔的摩县 MD21250
- 3. 西南交通大学 力学与工程学院, 成都 610000
- 折叠
摘要
在生物和医学领域,微机电系统(MEMS)中的微梁结构在植入人体的使用时,由于体内的细胞环境类似于水凝胶,在这种环境下工作,设备和仪器的精度和稳定性很大程度上受到细胞弹性的影响.为了分析此类地基梁的动力学问题,本文建立了非线性基础上的梁振动模型,研究了任意位置弹簧和非线性弹簧基础上的梁模态.通过Laplace变换和线性叠加原理,得到了一种约束Green函数,利用数值计算验证方案的有效性,并研究了各种重要物理参数的影响,发现弹簧位置向跨中移动时,模态对称性被打破,弹簧刚度增加,模态阶数改变.
Abstract
In the field of biology and medicine, for example, in the use of micro-electromechanical sys-tems (MEMS) with microbeam structure in human implantation, the accuracy and stability of the equip-ment and instruments are greatly affected by the elastic foundation because the cellular environment in the body is similar to that of hydrogels. In order to analyze this problem, a beam dynamics model based on nonlinear beam is established in this paper, and the free vibration of a beam with a spring at any posi-tion and based on nonlinear spring is studied. By using of Laplace transform and linear superposition principle, a kind of constrained Green's function is obtained. Numerical calculation is carried out to veri-fy the proposed solution, and the influence of various important physical parameters is studied. It is found that when the position of the spring moves towards the midspan, the modal symmetric is broken. The spring stiffness increases as the modal order changes.
关键词
约束Green函数/Laplace变换/非线性弹簧基础/模态分析/叠加原理Key words
constrain Green's function/Laplace transform/nonlinear spring foundation/modal analysis/superposition principle引用本文复制引用
基金项目
国家自然科学基金(12072301)
四川省自然科学基金(2022NSFSC0275)
出版年
2024
NETL
NSTL
万方数据