Significance Statement
FRP materials have gained ground in pipeline applications due to their mechanical and chemical properties. Pressure wave propagation in liquid–filled pipes correlates to industrial problems of water hammer and other types of oscillating pressure. Both flow characteristics and anisotropic material properties of laminated wall of FRP pipes are controlling the dynamic displacement derivation of an accurate model for dynamic response simulation which should consider both elastic and dynamic properties.
Numerical studies regarding dynamic flow, flow-pipe interactions and wave propagation in isotropic pipes have been researched extensively but damping characteristics and unsteady pressure oscillations have been neglected. The proposed solution takes into account the elastic and damping characteristics of FRP materials layout by using Fourier sine as Laplace integral transforms and generalized functions properties to derive Partial Differential Equation (PDE) of dynamic radial displacement w(x,t) which is then transformed into an algebraic one containing integral transformation of the variable.
From the experiment set-up, material damping effect was accounted for in simulation of cylindrical shells under axisymmetric loading due to its effect on vibration response. Rate of free vibrations reduction due to energy dissipation caused by damping effect is estimated by logarithmic decrement of factor on corresponding relative energy dissipation factor (ψ).
The effect of fibre orientation and damping parameter on dynamic response of the wall of multi-layered cylindrical shells with length L=1000m, diameter D=0.1m composed from N=10 E-Glass/Epoxy layers with thickness of 0.15mm and density ρ= 1000kg/m3 coupled with dynamic properties of E1=39× 109 N/m2, E2= 8.6× 109N/m2 and G12= 3.8×109N/m2 and ν12=0.28 and damping factors of ψT=0.0501, ψL= 0.087 and ψLT= 0.069 was taken into consideration and accounted for.
Effect of fibre orientation dynamic response with winding angle of ϑ= ±300, ±450 and ±600 showed results for the area at -4≤s≤4 indicating that radial displacement decreases when fibre orientation tends to reach circumferential direction.
Effect of damping parameter on dynamic response of FRP cylindrical shell indicated that there is a critical value of velocity of pressure travel lying between the values of 1.0<a<1.5 showing that small values of damping parameter yields a rapid increase of normalized radial reflection.
Pavlou (2016), also considered the effect of filament wound FRP pipeline in fluid-hammer conditions which demonstrated that an increase in diameter results to decrease of wave propagation, velocity and pressure amplitude.
Comparing the results with the transverse vibration when damping is not considered at the three fibre orientation angle of ±30o, ±450, ±600, Pavlou (2016) indicated that there is an excellent agreement for peak value of deflection and deviations far from vicinity of the location of the loading action.
Journal Reference
Pavlou D.G. Dynamic Response of a Multi-Layered FRP Cylindrical Shell under Unsteady Loading Conditions. Engineering Structures, Volume 112, 2016, Pages 256–264.
Department of Mechanical & Structural Engineering and Materials Science, University of Stavanger, 4036 Stavanger, Norway
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