求解结构动力响应的卷积型DQ半解析法

Convolution Semi-analytical Differential Quadrature Method for Structural Dynamic Response

通过卷积将原始控制方程构造成包含初始条件的新的具有完整初值问题特征的控制方程.该方程既与Gurtin变分原理一样有合理的数学内涵,又避免了卷积型Gurtin变分原理泛函和计算的繁复.对新的控制方程在时间域取解析函数,在空间域采用离散的DQ法,经对梁的动力响应问题的计算表明,该方法是一种精度好效率高的求解动力响应问题的计算方法.

A convolution type semi-analytical approach is proposed for structural dynamic response. With convolution original governing equation is transformed into a complete initial-value problem with initial conditions. The equation is mathematically equivalent to Gutrin＇ s variational principle while it involves no functional and complicated calculation in variational principle. The new governing equation is solved by differential quadrature method in space domain and analytieal series in time domain to obtain dynamic response. Dynamic response of a beam is studied. It is shown that the proposed method is accurate and efficient.