离散周期性结构的多尺度力学研究

Owing to the spectacular advantages of the discrete periodic structures widely used in micro- and nano-electro-mechanical systems, such as highly effective energy adsorption, highly effective isolation, the multi-scale study of the discrete periodic structures is carried out. In view of the equivalence of the governing equations of discrete periodic structures and Eringen type nonlocal elasticity, we investigate the effects of the number, the characteristic sizes, the buckling (or vibrational) mode numbers and the boundary conditions of the discrete periodic structures on the nonlocal parameters, based on the macro phenomenological theory, microstructured model and numerical model. According to the analytical expressions of the buckling and vibrational parameters obtained from the asymptotic analysis of the ordinary differential equation(s) (ODEs), the nonlocal parameter is calibrated by curving fitting using the analytical expressions with the numerical results obtained from the discrete ODEs. The work gains insights on the physics of the nonlocal parameter, and on the other hand, is expected to be useful for the multi-scale model of the large scale discrete periodic structures.

项目以微纳米机电系统等领域为依托，针对以高效能量吸收、高效隔振等为特征的离散链式结构，开展大规模离散链式结构的多尺度力学研究。结合离散链式结构与Eringen型非局部弹性理论的相似性，采用宏观唯象理论、微细观模型和计算模型三种不同方法研究离散结构的数量、特征尺寸、屈曲（或振动）模态数、边界条件等对非局部参数的影响。基于常微分方程（组）的渐进分析理论，利用非局部模型得到不同边界条件下结构在屈曲、振动等响应参数的渐进形式，并通过拟合相应离散链式结构在屈曲、振动等响应参数，校核得到非局部参数。研究成果一方面有利于人们对非局部参数的物理认识，一方面为大规模离散链式结构的多尺度建模提供重要依据。

项目以离散链式结构的力学行为为研究对象，结合离散链式结构与Eringen型非局部弹性理论的相似性，研究了该类结构的力学等效性。内容包括静屈曲和固有频率等问题。研究了不同尺度参数对该类结构的力学行为的影响，并研究了高阶非经典边值问题的求解方法。其科学意义体现在两个方面：1. 建立了考虑尺度效应梁系统的力学边值问题；2. 给出求解其力学边值问题的求解方法，澄清不同边界条件的选择对结构力学行为的影响。