CAJ | 학술논문

对于时变与非线性的结构系统，由于结构模态响应信号的瞬时频率并不等同于结构本身的瞬时频率，因此推导了单自由度与多自由度体系在自由振动和受迫振动下模态响应信号的瞬时频率与结构本身瞬时频率的关系，理论结果表明，对于时变的线性结构和弱非线性结构，模态响应的瞬时频率缓慢变化的部分与结构系统的瞬时频率近似相等。通过对一杜芬系统的数值模拟和对一调整索力变化而使其频率变化的斜拉索自由振动实验，验证了理论结果的正确性。对于具有密集模态的时变与非线性的多自由度体系，提出了把解析模式分解方法扩展到时变与非线性结构的模态分解。该方法通过小波变换选取二分时变截止频率，对结构的时变模态响应进行分离，从而实现多自由度结构时变参数识别。最后，对一具有密集模态的两层框架时变系统受白噪声激励和地震激励进行数值模拟，结果表明，提出的方法能有效的分解时变系统的密集模态响应并能较好的识别出结构系统的瞬时频率。
대우시변여비선성적결구계통，유우결구모태향응신호적순시빈솔병불등동우결구본신적순시빈솔，인차추도료단자유도여다자유도체계재자유진동화수박진동하모태향응신호적순시빈솔여결구본신순시빈솔적관계，이론결과표명，대우시변적선성결구화약비선성결구，모태향응적순시빈솔완만변화적부분여결구계통적순시빈솔근사상등。통과대일두분계통적수치모의화대일조정색력변화이사기빈솔변화적사랍색자유진동실험，험증료이론결과적정학성。대우구유밀집모태적시변여비선성적다자유도체계，제출료파해석모식분해방법확전도시변여비선성결구적모태분해。해방법통과소파변환선취이분시변절지빈솔，대결구적시변모태향응진행분리，종이실현다자유도결구시변삼수식별。최후，대일구유밀집모태적량층광가시변계통수백조성격려화지진격려진행수치모의，결과표명，제출적방법능유효적분해시변계통적밀집모태향응병능교호적식별출결구계통적순시빈솔。
The instantaneous frequency of modal response signals is not equal to the instantaneous frequency of the structural system for a time-varying and nonlinear structure.Here,the structural instantaneous frequencies were directly derived from the decomposed modal responses for single-DOF and multi-DOF systems under both free and forced vibrations.The theoretical results showed that the slowly varying part of a modal response’s instantaneous frequency is approximately equal to the systems instantaneous frequency for time-varying linear structures and weakly nonlinear structures.The correctness of the theoretical results was validated with a numerical simulation of a Duffing system and a free vibration test of a cable with time-varying tension force and frequency.For a time-varying and nonlinear structure with closely-spaced modes,the analytical modal decomposition method was extended to deal with its modal decomposition.The mathematical model for this new extension was provided and an approach with wavelet transformation was developed for the selection of time-varying bisecting frequencies.Finally,a two-story time-varying structure with closely-spaced modes subjected to both white noise and earthquake excitations was simulated,the results showed that the proposed method can effectively be used to decompose modal responses and accurately identify the instantaneous frequency of time-varying and nonlinear structures.