具有刚性间隙约束输流管的碰撞振动

管道与间隙约束间的碰撞振动是工程输流管结构的一个重要动力学现象. 迄今,人们通常采用光滑的非线性弹簧来模拟管道与间隙约束之间的碰撞力,但这种光滑的碰撞力无法真实反映碰撞前后管道状态向量的非光滑传递特征. 本文基于非光滑理论建立了具有刚性间隙约束简支输流管的非线性碰撞振动模型,利用 Galerkin 法离散了无穷维的管道模型, 并引入恢复系数构造了碰撞前后管道各处状态向量的传递矩阵,运用四阶龙格库塔法分析了脉动内流激励下管道与刚性间隙约束的非光滑碰撞振动现象,着重讨论了刚性间隙约束参数对管道动态响应随流速脉动频率变化的影响规律,特别是碰撞振动的周期性运动规律. 研究结果表明,刚性约束间隙值对管道碰撞振动行为的影响较大,在某些脉动频率下管道会出现多周期和非周期性的运动形态,还可出现非光滑系统特有的黏滑现象. 此外,碰撞恢复系数对管道振动的影响也比较显著,较小的恢复系数值更容易使管道在大范围脉动频率区间出现复杂的非周期碰撞振动. 

VIBRO-IMPACT DYNAMICS OF PIPE CONVEYING FLUID SUBJECTED TO RIGID CLEARANCE CONSTRAINT

The vibro-impact dynamics due to loose constraints have become one of the key scientific problems in the dynamical system of pipes conveying fluid. The impact force modeled by smoothed nonlinear springs varies continuously with time and displacement of the vibrating pipe, which cannot exactly capture the non-smooth characteristics of the saltation of state vectors for the pipes before and after an impact. In this paper, a non-smooth mathematical model of simply supported pipes conveying pulsating fluid, subjected to a rigid constraint somewhere along the pipe length is established, with consideration of the effect of the values of clearance and coefficient of restitution of the constraint. Especially, the periodic and aperiodic oscillations are investigated under various pulsating frequencies of the internal fluid. The transition matrices of the displacement and velocity of all nodes along the pipe before and after impact were derived based on a Galerkin's approach. The nonlinear equations of motion are solved via a fourth-order Runge-Kutta method, by applying the impact boundary conditions. Results show that the pipe is capable of displaying interesting vibro-impact behaviors in the presence of the rigid clearance constraint with the variation of pulsating frequency of the flowing fluid. With a clearance close to the maximum displacement of the pipe without constraint, periodic vibro-impact behaviors are observed with multiple impacts. The vibration velocities before the pipe impacts on the edge of the rigid clearance constraint decrease to zero gradually with the displacement invariant, which is called a dynamical stick-slip motion, also known as a typical non-smooth phenomenon. By decreasing the value of coefficient of restitution, the responses of the pipe may change from periodic vibrations to chaotic ones. This work provides an attractive strategy for further understanding of the nonlinear impact dynamics of pipes conveying fluid subjected to rigid clearance constraint based on non-smooth theories.