CAJ | 학술논문

采用矩阵谱分解中常用的Sylvester理论和Fourier级数展开法,推导了单自由度参数振动系统的频响函数,并得到了系统外激励共振条件.在此基础上,以直齿轮副参数振动系统为例仿真了系统的频响特性,并讨论了系统参数稳定性、时变参数以及阻尼的影响.结果表明,参数振动系统的频响特性主要有以下一些特点:(1) 系统具有多个频响函数,分别对应于多频响应中的各个频率成分;(2) 系统存在多个外激励共振区.除了外激励频率等于系统固有频率的共振区外,当激励频率等于系统固有频率与参数激励频率的组合值时,同样存在共振现象;(3) 参数振动系统共振响应时,主导频率成分为系统固有频率;(4) 阻尼使得频响函数峰值有明显下降,而对非共振区的频响曲线影响不大.
채용구진보분해중상용적Sylvester이론화Fourier급수전개법,추도료단자유도삼수진동계통적빈향함수,병득도료계통외격려공진조건.재차기출상,이직치륜부삼수진동계통위례방진료계통적빈향특성,병토론료계통삼수은정성、시변삼수이급조니적영향.결과표명,삼수진동계통적빈향특성주요유이하일사특점:(1) 계통구유다개빈향함수,분별대응우다빈향응중적각개빈솔성분;(2) 계통존재다개외격려공진구.제료외격려빈솔등우계통고유빈솔적공진구외,당격려빈솔등우계통고유빈솔여삼수격려빈솔적조합치시,동양존재공진현상;(3) 삼수진동계통공진향응시,주도빈솔성분위계통고유빈솔;(4) 조니사득빈향함수봉치유명현하강,이대비공진구적빈향곡선영향불대.
Utilizing Sylvester's theorem and Fourier series expansion method, commonly used in the spectral decomposition for matrix, the frequency response functions (FRFs) of parametrically excited system were derived theoretically and the external resonance condition was obtained . Then, a spur-gear-pair parametric vibration system was selected as an example to simulate its frequency response characteristics. The effects of parametric stability, time-varying parameters (parametric frequency and contact ratio) and system damping were taken into consideration in the simulation. It is shown from both the theoretical and simulation results that the frequency response of the parametric system has the following properties: there are multi-FRFs corresponding to the multi-frequency responses;there exist multi-outer-excitation resonance regions;besides the resonance due to that the exciting frequency approaches to the natural frequency, external resonances will also appear, if the excitating frequency meets the combination of natural frequency and parametric frequency;when the system is in external resonance, the dominant frequency component in the response is the natural frequency;damping makes the peak values of FRFs drop evidently, while it has almost no impact on the FRFs in no-resonance regions.