微纳尺度柔性结构的非线性振动特性研究

Recent studies on nonlinear vibration properties of continuous systems at micro and nano scales are mainly focused on beam and plate models with the classical continuum mechanics theory. Several results about effects of micro structures are limited to the relation between the amplitude and frequency for the nonlinear free vibration, which cannot present the nonlinear vibration characteristics widely. In this project, based on the nonlocal continuum theory, the nonlinear vibration models for continuous structures at the micro and nano scales are established, in which the matrix damping is considered. With the small scale effects, a series of nonlinear vibration behaviors are analyzed (e.g. the nonlinear free vibration, forced vibration, parameter vibration and chaos properties). It is hoped that this research can provide a simple and effective method for the nonlinear vibration properties of small scale structures, as well as perform the positive influences for enriching and developing the nonlinear dynamical theory of flexible structures at micro and nano scales.

关于微纳米尺度连续系统的非线性振动问题，目前的研究结果主要集中于采用经典连续介质力学理论的梁板模型。少数考虑了系统微结构影响的研究，则局限于分析系统非线性自由振动的幅频关系，未能全面地揭示其非线性振动特性。本课题基于非局部连续介质力学理论，建立考虑基体阻尼作用时，微纳米尺度连续结构的非线性振动模型。分析考虑内部小尺度效应时，微纳米梁板结构的非线性自由振动、受迫振动、参数振动、以及混沌特性等一系列非线性动力学行为。本课题的研究结果，可望为研究小尺度结构的非线性振动特性，提供简单而行之有效的方法，为微纳尺度柔性结构非线性动力学理论的丰富与发展起到积极作用。

本课题采用非局部连续介质力学理论，考虑了系统纳米尺度微结构的影响，建立了考虑基体阻尼作用时，微纳米尺度连续结构的非线性振动模型。分析了考虑内部小尺度效应时，微纳米梁板结构的非线性自由振动、受迫振动、参数振动、以及混沌特性等一系列非线性动力学行为，并给出了调节其非线性动力学行为的方法以及控制参数。