CAJ | 학술논문

针对频率响应函数的级数展开法在中高频激励时计算发散的问题,提出一种新的级数展开改进算法.将系统的结构模态划分为低阶和截断的高阶模态,在模态叠加分析的基础上,将频率响应函数进行泰勒级数展开.根据高低阶模态对质量矩阵和刚度矩阵的耦合特性,用低阶模态及系统矩阵表达高阶模态对响应的影响.研究结果表明,该算法将频率响应函数的级数展开法扩展到高频激励和中频激励范围阶段,在非完备模态条件下提高了频率响应函数的计算精度,数值计算检验了该方法准确可靠并有很好的收敛性.
침대빈솔향응함수적급수전개법재중고빈격려시계산발산적문제,제출일충신적급수전개개진산법.장계통적결구모태화분위저계화절단적고계모태,재모태첩가분석적기출상,장빈솔향응함수진행태륵급수전개.근거고저계모태대질량구진화강도구진적우합특성,용저계모태급계통구진표체고계모태대향응적영향.연구결과표명,해산법장빈솔향응함수적급수전개법확전도고빈격려화중빈격려범위계단,재비완비모태조건하제고료빈솔향응함수적계산정도,수치계산검험료해방법준학가고병유흔호적수렴성.
Aiming at the computational divergence in the series expand method of frequency response function under medium and high frequency excitations, a new improved algorithm for dynamics system response is proposed. Structural modes are divided into available low-order modes and truncated higher-order modes. On the basis of modal superposition analysis, the frequency response function of high order truncation modes is expanded by Taylor series. According to the coupling characteristics between low-order and high-order modes, the contribution of truncated high-order modes to the frequency response function is expressed by low-order modes and system matrix. The improved algorithm extends the series expand method for the range of high frequency and medium frequency excitations; the calculation accuracy of the frequency response function is improved under the non-complete modal conditions. Numerical results validate the feasibility and convergence.