1. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai 200072, China; 2. Rizhao Polytechnic, Shandong 276826, China;3. Department of Mechanics, Shanghai University, Shanghai 200444, China
Abstract：The dynamic stability in transverse vibration of a viscoelastic pipe on Winkler elastic foundation for conveying pulsating fluid is investigated for the simply-supported case. The pipe’s material obeys the Kelvin model in which the material time derivative is used. The axial fluid speed is characterized as simple harmonic variation about a constant mean speed. When the viscoelastic damping and the periodical excitation are considered small, the method of multiple scales is applied directly to the governing equation to establish the solvability conditions in summation and principal parametric resonances. The effects of the pulsating fluid flow velocity, damping coefficient, mass ratios of the parametric instability are discussed. Some numerical examples are presented to demonstrate the effects of related parameters on the stability boundaries.
2013, Vol. 32 
