磁场中载有电流的微型梁结构在微机电系统中具有广泛而重要的应用，其动力学问题是涉及力、电、磁等多学科交叉的前沿课题。关于磁场中载流微型梁的动力学机理及其微尺度效应，至今尚无统一的结论和定量的非线性动力学理论模型。本项目拟开展以下工作：1）利用弯曲实验，测试微型梁弯曲变形的尺度效应；2）在前述实验基础上，应用和发展基于高阶连续介质力学的梁理论，建立磁场中载流微型梁振动的非线性理论模型；3）求解线性系统的特征值问题，分析微型梁的稳定性和振动特性；4）应用现代非线性动力学理论，研究非线性系统在恒定电磁力下的屈曲位形、自由振动、受迫振动、内共振和复杂动力响应，探讨非恒定电磁力下的参数共振规律，重点揭示有异于宏观尺度梁的新特性、新机理。研究结果将深化人们对微型梁力-电-磁耦合非线性动力学及其微尺度效应的理解，拓宽连续介质力学理论的应用范围，为工程MEMS结构的多场耦合分析与设计提供理论基础和技术储备。

Current-carrying microbeams subjected to magnetic fields have become one of the most important components in MEMS. The corresponding dynamical problem is fast becoming an attractive issue involving mechanical-electronic-magnetic coupling. As for current-carrying microbeams in external magnetic fields, there is a lack of unified conclusion regarding the dynamical behavior and its size effect, and hence quantitative theoretical models need to be developed. This project will deal with the following work: 1) According to the bending test of microbeams, the size effect of the microbeam’s flexural deflections will be examined. 2) Based on the experimental results obtained, by applying and developing beam theories with the aid of higher-order continuum mechanics, the nonlinear dynamical model for current-carrying microbeams subjected to magnetic fields will be established. 3) By solving eigenvalue problems, the stability and linear vibration characteristics of the microbeam will be analyzed. 4) Utilizing modern nonlinear dynamic theories, the buckled configuration, free vibration, forced vibration, internal resonance and other complex dynamics of the microbeam subjected to constant Lorentz force will be studied; the parametric resonance of the microbeam with time-dependent Lorentz force will also be investigated in detail. Emphasis will be placed on the possible new properties of such a micro-system different from those of macro-scale beams. The research results of this project are useful for better understanding the mechanical-electronic-magnetic coupled nonlinear dynamics of microbeams as well as its size effect. This work can expand the application field of the theory of continuum mechanics. The knowledge gained from this work is also expected for providing theoretical basis and technical reserve for analyzing the multi-field coupling problems and design in MEMS-based structures.