ارتعاشات و آناليز احتمال انديشانه پايداري لوله هاي حامل سيال با پارامترهاي تصادفي

چكيده انگليسي :

83Vibrations and probabilistic stability analysis of pipes conveying fluid with stochastic parameters Ali Asghar Alizadeh as alizadeh@me iut ac ir Date of Submission 2015 1 17 Department of Mechanical Engineering Isfahan University of Technology Isfahan 84156 83111 Iran Degree M Sc Language FarsiSupervisor Hamidreza Mirdamadi hrmirdamadi @cc iut ac irAbstractIn this thesis the Monte Carlo simulation method MCSM is used in conjunction with finite elements FEs forprobabilistic analysis of both self excited vibration and dynamic stability of pipes conveying fluid For fluid structure interaction the Euler Bernoulli beam kinematic model is used for analyzing pipe structure and plugflow model for representing internal fluid flow through the pipe Moreover due to the inherent uncertainty inthe system parameters and for determining the problem more precisely parameters such as masses per unitlength of structure and fluid bending stiffness of structure and fluid flow velocity are modeled as randomfields By considering the structural and fluid parameters of system as random fields the deterministicgoverning partial differential equation PDE of continuous system is transformed into a stochastic PDE Thecontinuous random fields are discretized by mid point and local average discretization methods In other words at the beginning covariance matrix is generated for each of the random fields by discretization methods Then each of those random fields is converted into a random vector by generating an independent Gaussian randomvector and using the Cholesky decomposition of covariance matrix On the other hand a certain value isassigned to each of the random fields in every finite element due to assuming that the number of FEs is the sameas the number of elements required for the discretized random fields Then by using the Monte Carlosimulations in each iteration loop every distributed parameter PDE having stochastic lumped parameters istransformed into a deterministic distributed parameter PDE Each PDE is transformed into a system ofdeterministic ordinary differential equations ODEs by using FEs Accordingly all of the deterministic andstochastic parameters of the system are discretized For self excited vibration analysis the eigenvalue problemis solved for investigating the complex valued eigenvalues and critical eigenfrequencies Consequently havingcomplex eigenfrequencies and divergence velocities the statistical responses of stochastic problem are obtainedlike expected values standard deviations probability density functions and the probability of occurrence fordivergence instabilities As expected the standard deviation values for mid point discretization method arelarger than those for local average As a result the mid point discretization method seems to show the upperbound while the local average demonstrates to be a lower bound for the standard deviations of the systemresponses Furthermore the probability density function of imaginary part of the eigenfrequency in the firstmode appears to consist of two distinct parts the first part is similar to a Dirac delta function and the second partis similar to a continuous density function Actually the former represents the unstable region while the latterrepresents the stable part of the system On the other hand it has been shown that the randomness effects of thefluid parameters on the system are much more pronounced than those of structural parameters Consequently randomness in the structural parameters could be ignored compared to that in the fluid parameters Keywords Random vibration Random fields Monte Carlo simulation Fluid structure interaction Stochastic stability analysis Pipes conveying fluid

عليزاده، علي اصغر

ارتعاشات و آناليز احتمال انديشانه پايداري لوله هاي حامل سيال با پارامترهاي تصادفي

ارتعاشات اتفاقي , ميدان هاي تصادفي , شبيه سازي مونت كارلو , اندركنش سيال سازه , آناليز پايداري تصادفي