Longitudinal–Flexural–Torsional Dynamic Behavior of Liquid-Filled Pipelines: An Analytic Solution

The 14 partial differential equation system describing the longitudinal–flexural–torsional dynamic behavior of liquid-filled pipelines contains coupled equations due to mutual boundary conditions and Poisson contraction ratio terms. Solutions of the above system are available in the frequency-domain or in the time-domain (method of characteristics (MOC)). In this paper, an analytic solution in the domain of time and space is achieved. Double integral transform, namely, finite sine Fourier transform (FSFT) and Laplace transform, is applied to the derived system of the 14 fourth-order partial differential equations, yielding an algebraic system in terms of the transformed variables. The inversion of the FSFT is an easy task, but the analytic inversion of the Laplace transforms is very challenging. Both integral transform inversions of the 14 transformed variables are successfully performed, and an analytic matrix formula in the domain of time and space along with numerical results is obtained.

Random Fiber Networks With Superior Properties Through Network Topology Control

In this work, we study the effect of network architecture on the nonlinear elastic behavior and strength of athermal random fiber networks of cellular type. We introduce a topology modification of Poisson–Voronoi (PV) networks with convex cells, leading to networks with stochastic nonconvex cells. Geometric measures are developed to characterize this new class of nonconvex Voronoi (NCV) networks. These are softer than the reference PV networks at the same nominal network parameters such as density, cross-link density, fiber diameter, and connectivity number. Their response is linear elastic over a broad range of strains, unlike PV networks that exhibit a gradual increase of the tangent stiffness starting from small strains. NCV networks exhibit much smaller Poisson contraction than any network of same nominal parameters. Interestingly, the strength of NCV networks increases continuously with an increasing degree of nonconvexity of the cells. These exceptional properties render this class of networks of interest in a variety of applications, such as tissue scaffolds, nonwovens, and protective clothing.

Application of the Transfer Matrix Method to the Analysis of Hydro-Mechanical Vibration of NPP Piping

The transfer matrix method (TMM) was used for description of harmonic vibrations of piping with transported medium. Apart from 12 well-known mechanical parameters which characterize the state of piping system in each cross section two additional parameters that characterize the vibration of the medium, namely its translation and pressure pulsations were considered. The solution of these equations, which take into account the Poisson contraction of the pipe wall, in the form suitable for the transfer matrix method application was derived. The biggest uncertainty in the analytical modeling is to adopt the boundary conditions for above mentioned 2 parameters for the considered piping section. To solve this problem of identification of the most probable induced frequency we developed the technique of choosing such boundary conditions at which the maximum of energy is confined within the considered piping section. The validity of the approach was tested on some analytical examples. This method was used to analyze the forced vibration of the second circuit loop of unit 1 Zaporizhia Nuclear Power Plant (ZNPP) with VVER-1000 (from Russian: Vodo-Vodyanoi Energetichesky Reactor; Water-Water Power Reactor) arising from turbulent eddies in the flow of steam. Natural frequencies and forms of mechanical, hydrodynamic, and related hydro-mechanical vibration were found, a number of recommendations were given to reduce the vibration levels.

Application and interpretation of zero and short-span testing on nanofibre sheet materials

This paper investigates the use of zerospan testing to measure the tensile strength of cellulose nanofibre sheets. The mechanical strength of cellulose nanofibre paper is a key property but tensile strength measurement requires a substantial amount test material, whereas a zero/short span test needs much less material. Sheets made from cellulose nanofibres, microfibrillated cellulose (MFC) and northern bleached softwood fibres were tested at spans ranging from 0 to 0.6 mm and tensile strength spans of 50 and 100 mm. For the cellulose nanofibres or the MFC sheets, strength was constant with span from 0 to 0.6 mm when tested dry and negligible when tested wet, except at zero span. The sheets made from the softwood fibres showed significant strength when tested wet at all spans from 0 to 0.6 mm. The results showed that for nanofibre materials, the zero or short span strength is measuring sheet tensile strength at a smaller sample length. The strength of the nanofibre sheets at 50 or 100 mm was smaller than at zero/short span due to sample size effects and Poisson contraction. The effects of starch and grammage on strength were also studied.

Exact Computation of the Axial Vibration of Two Coupled Liquid-Filled Pipes

A simple recursion is presented that finds exact solutions to the problem of two coupled axially-vibrating liquid-filled pipes. Fluid-structure interaction at pipe ends and junction, and along the pipe because of axial-radial Poisson contraction, is taken into account. The solutions obtained for a waterhammer problem show unprecedented details that resemble noise.

The Fiber Composite With Nonlinear Interface—Part I: Axial Tension

This paper treats the effective axial tension response of a composite consisting of fibers that debond from the matrix according to nonlinear Needleman-type cohesive zones. A second, related paper (Part II) treats effective antiplane shear response. The composite cylinders representation of a representative volume element (RVE) is employed throughout. For axial tension loading a simple rotationally symmetric boundary value problem for a single composite cylinder is solved. Bounds on the total potential energy and the total complementary energy are shown to coincide and an exact solution for axial extension and Poisson contraction of an RVE of the composite is obtained. Nonlinear interfacial debonding, however, is shown to have a negligible effect on extensional response and only a small, though potentially destabilizing, effect on Poisson contraction response. [S0021-8936(00)02004-3]

Analysis of Pulsations and Vibrations in Fluid-Filled Pipe Systems

Pressure pulsations and mechanical vibrations in pipe systems may cause excessive noise and may even lead to damage of piping or machinery. In fluid-filled pipe systems pulsations and vibrations will be strongly coupled. A calculation method has been developed for the simulation of coupled pulsations and vibrations in pipe systems. The analytical method is based upon the transfer matrix method. It describes plane pressure waves in the fluid and extensional, bending and torsional waves in the pipe wall. Fluid pulsations and pipe wall vibrations are coupled at discontinuities (e.g. elbows and T-junctions) and via Poisson contraction of the pipe wall. For a given source description, the model calculates levels of vibration, mode shapes, vibro-acoustic energy flow, etc. The method has been validated experimentally on a test rig consisting of two straight pipes and an elbow. The predicted pulsation and vibration levels agree reasonably well with the measurements.