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本文发展一个可以计算固体火箭发动机瞬态线性粘弹性响应的方法。该方法是根据固体火箭发动机部件线弹性有限元模型组成子结构运动方程。通过以下的方法完成有效的计算:1)按谐波坐标设立运动方程;2)应用界面约束模态作为固体装药子结构相对位移场的近似振型函数。假设经典的麦克韦尔松弛模型可以描述固体装药的粘弹性特性。最后的线性积分-微分运动方程的解法是修正的 New-mark β积分法。通过两个实例证明本方法的适用范围。第一个实例是三自由度粘弹性系统的数值解,它与闭型拉普拉斯变换解非常一致。第二个实例是典型固体火箭发动机有限元模型傅立叶变换瞬态响应解。它与 MSC/NASTRAN 直接频响解十分一致。
This article develops a method that can calculate the transient linear viscoelastic response of a solid rocket motor. The method is based on the solid rocket engine linear elastic finite element model composed of substructure equations of motion. Effective computations are done by: 1) setting up the equations of motion in terms of harmonic coordinates; and 2) applying the interface-constrained modes as the approximate modal functions of the relative displacement field of the solid charge substructure. It is assumed that the classical Mcwell relaxation model can describe the viscoelastic properties of solid charge. The final solution to the linear integral-differential equation of motion is the modified New-mark β integral method. Two examples prove the scope of this method. The first example is the numerical solution of a three-degree-of-freedom viscoelastic system, which is very consistent with the closed-form Laplace transform solution. The second example is the Fourier Transform transient response of a finite element model of a typical solid rocket motor. It is very consistent with the MSC / NASTRAN direct frequency response.