id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
aiti-7988	Mohmmed, Jabbar Hussein; Tawfik, Mauwafak Ali; Atiyah, Qasim Abbas 	Determination of Natural Frequency and Critical Velocity of Inclined Pipe Conveying Fluid under Thermal Effect by Using Integral Transform Technique	2021	15	.pdf	application/pdf	7662	375	61	′′Λ Γ − − − Λ Γ + Λ ⋅ Γ ′ ′+ Λ Γ + Λ Γ + Λ Γ = − ∫ ∫ ∫ ∫ ∫ ∫ ∫ (19) Γ(ζ) is beam Eigen function and varies according to boundary condition for the clamped supported case: ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )cosh L cos L cosh cos [ sinh sin ] sinh L sin L r r r r r r r r λ λ ζ λ ζ Keywords: pipe conveying fluid, natural frequency, critical flow velocity, finite Fourier sine transform, Laplace transform 1. Introduction Fluid-conveying pipes are very important parts in many engineering structures and have many potential applications in industry.	cache/aiti-7988.pdf	txt/aiti-7988.txt