The multiplicity of the zero at 1 of polynomials with constrained coefficients

2013 ◽  
Vol 159 (4) ◽  
pp. 387-395 ◽  
Author(s):  
Peter Borwein ◽  
Tamás Erdélyi ◽  
Géza Kós
Keyword(s):  
Constrained Coefficients

The Natural Characteristics of Fluid Conveying Pipe under Different Supporting Conditions

2013 ◽  
Vol 372 ◽  
pp. 612-619 ◽  
Author(s):  
Ri Dong Bao
Keyword(s):  
Boundary Conditions ◽  
Natural Frequency ◽  
Vibration Mode ◽  
Fluid Pressure ◽  
Vertical Vibration ◽  
Elastic Coefficient ◽  
Pipe Section ◽  
Mode Function ◽  
Constrained Coefficients ◽  
Natural Characteristics

The natural characteristics of fluid conveying pipe with its ends under different supporting conditions were investigated. The expression of vertical vibration mode-function of pipe beam was derived from the boundary conditions of similarly supported beam. The effect of different supporting elastic coefficient, fluid pressure, flowrate, and axial force of pipe section on its natural characteristics was calculated and analyzed based on the eigenequation of motion. The numerical computation results showed that its natural frequency was proportional to elastic supporting coefficient and axially pressed force of pipe section, but was proportional conversely to fluid flowrate, fluid pressure and axially sectional drawn force of pipe. The natural frequency of different modes can be coupled with each other, the primarily mode and secondly mode would change either. In order to improve the natural frequency of fluid conveying pipe, the elastically constrained coefficients should be extended and the axially pressed force of pipe section should be avoided.

Sign in / Sign up

Export Citation Format

Share Document