摘要
首先引入模态坐标变换及矩阵函数变换,将阻尼系统转化为无阻尼系统,再通过分析无阻尼系统的模态参数的特点,推导出计算其频率响应矩阵的公式,然后使用矩阵函数逆变换和模态坐标反变换,推导出原阻尼系统响应的精确表达式,方法应用于经典阻尼系统时,取得了与传统的振型迭加法等价的解析表达式,同时对于无法直接使用振型迭加法处理的非经典阻尼系统,也获得了解析解。数值算例表明了该方法的正确性及有效性。
Firstly,by introducing modal coordinate transformation and matrix function transformation,an original damped system was transformed into a non-damped one.Secondly,by analyzing the properties of modal parameters of the non-damped system, its frequency response function matrix was derived. Furthermore, by using inverse matrix transformation and inverse modal coordinate transformation,the precise expression for the response of the original damped system was derived.When the presented method was applied to a classical damped system,the analytical expression equivalent to the traditional modal superposition method was obtained.And then,the analytical expression for a non-classical damped system which could not be solved with the modal superposition method was obtained as well.Finally,the correctness and effectiveness of the proposed method were verified with two examples.
出处
《振动与冲击》
EI
CSCD
北大核心
2014年第4期161-166,共6页
Journal of Vibration and Shock
基金
吉林省自然科学基金项目(201215115)
关键词
非经典阻尼系统
频率响应矩阵
动力响应
矩阵函数变换
模态参数
non-classically damped system
frequency response function matrix
dynamic response
matrix function transformation
modal parameters