Ovalling Mode Research Articles

Active control of acoustic scattering from a passively optimised spherical shell

At low frequencies, the sound power scattered from a spherical shell can be minimised by designing its material properties and thickness so that the mass and compressibility are the same as that of the displaced fluid. The scattered power is then dominated at higher frequencies by that due to the resonances of the structural modes of the shell, particularly the ovalling mode. The peaks in the scattered power due to structural resonances can be reduced somewhat by material damping but are more effectively attenuated with active control using structural actuators as secondary sources. Simulations are presented of the scattered sound power of such a shell when subject to feedforward control, which assumes knowledge of both the incident and scattered acoustic sound fields, and structural feedback control, which only assumes that the velocity on the surface of the sphere can be measured. The performance of the feedback controller is also examined if the structural actuators and sensors are distributed over the surface of the sphere, rather than just acting at single points.

On the collapse of thick-walled steel pipes under coupling initial geometric imperfection and corrosion defect

ABSTRACT Initial geometric imperfections and corrosion defects were considered as two of the most common imperfections for subsea pipes, which could lead to an inevitable reduction of collapse capacity. In this study, the coupling effect of both types of defects on the collapse performance was investigated numerically, with a particular focus on the relative corrosion position as described by defect location angle (DLA). A customised numerical framework was established to efficiently build FE models with various corrosion defects and imperfect geometry. Verification of the finite element (FE) model was performed using existing experiments in the open literature. In addition, extensive sensitivity studies were then conducted for several key problem parameters, including defect length, width, depth, initial ovality, and DLA. The variation of normalised collapse pressure with DLA exhibits two types of trajectories, namely ‘Minor Decrease’ and ‘Constant-Decrease-Constant’ responses. In the first, the normalised collapse pressure decreases slightly with increasing DLA. Among these cases, if the ratio stays above or close to 1.0, the collapse takes the form of classical ovalization mode. In contrast, for cases below 1.0, the collapse occurs in the corroded region. For the latter type of trajectory, the normalised collapse pressure follows a ‘Constant-Decrease-Constant’ path, and the collapse mode involves ovalization, anti-ovalization, non-symmetrical and U-shaped pattern. Subsequently, a series of empirical formulas were proposed upon extensive simulation results to predict the collapse pressure of non-symmetrical defect pipes.

Experimental Modal Analysis of a Palm Tree Log under Radial Vibrational Excitation

Trees may be subject to rot-inducing agents that degrade the strength of the material making their trunk, and decrease the quality of their crop. Several techniques, both non-destructive and destructive, are available for assessing the extent of damage caused by rot in a tree trunk. The present work presents the results of a preliminary study conducted on a palm tree trunk for isolating a specific mode from its response to a vibrational excitation, namely the so-called “ovalling” mode. This latter is cross-sectional and in a circular cylinder manifests itself relatively locally, i.e. has little dependence on the lateral extension of the cylinder. An experimental modal analysis is made on a piece of a date palm tree trunk when set into vibration through a radial mechanical excitation, and the response is collected at points along a circumference on the trunk. The value of the resonance frequency of the ovalling mode was found to be somehow variable, probably resulting from some coupling phenomena between various modes of vibration due to the inhomogeneity, anisotropy and fibre-like structure of the trunk wood. As rot usually affects markedly the strength of the trunk wood, the frequency of the ovalling mode, which depends on the strength of the material, can be used for estimating the severity of rot attack in the trunk. A numerical simulation is also made to a cylinder as a simplified representation of a tree trunk.

Monitoring of a Cross-Sectional Vibrational Mode in the Trunk of a Palm Tree

Palm trees, like all other tree species, are living entities that may be subject to the attack of several natural agents which affect the strength of the trunk. The most serious of these damaging agents are parasites and rot fungi, which proliferate in the substance of the stem, destroying its cells and fibers and weakening it. Consequently, this decay affects the physical characteristics of the modes of vibration in the tree trunk regarding resonance frequency, shape, and damping. Advanced stages of rot infection in a tree trunk may reach such an extreme level that substantial amounts of its solid mass are removed, ultimately leading to a hollow trunk rather than one of substance. In cases like these, the trunk presents less resistance to forced vibrations, and the active modes affecting the cross section of the trunk exhibit decreased resonance frequency values. This paper aims to present a method based on vibrations which might be employed for tracking a specific mode of radial vibrations known as the ovalling mode. To achieve this goal, the trunk of a palm tree was set into vibration via mechanical excitation in the radial direction and its response at some specific point on the trunk was examined. This method uses a single concentrated source of excitation and two vibration sensors, which are diametrically positioned and fastened to the surface of the tree trunk. The ovalling mode might be extracted from the frequency response by adding the signals recorded by the two sensors, which are in phase for a test specimen with a perfectly circular, cylindrical shape made of homogeneous, isotropic material. This study provides a preliminary investigation into the feasibility and reliability of this nondestructive method when applied for the identification of rot hosting by the trunks of standing trees, wooden poles, and logs, as well as the level of severity of rot attack.

Bridged Coupler and Oval Mode Converter Based Silicon Mode Division (De)Multiplexer and Terabit WDM-MDM System Demonstration

We propose a novel structure of a mode (de)multiplexer that realizes an on-chip (de)multiplexing function in a two-step process consisting of a bridged coupler and an oval mode converter. According to the two-step principle, we design and fabricate a three-mode (TE0, TE2, and TE4) (de)multiplexer with the standard silicon-on-isolator (SOI) technology. The measured crosstalk of the device is lower than −22.0 dB, −19.0 dB, and −16.0 dB for TE0, TE2, and TE4 modes, respectively, for wavelengths ranging from 1525 to 1585 nm. The device is tested in both single-wavelength and wavelength-division multiplexing (WDM) systems with 128 Gb/s (32 Gbaud) 16-ary quadrature amplitude modulation signals. We experimentally demonstrate 96-channel ( ${\text{32}}-{\text{wavelength}}\times {\text{3}}-{\text{mode}}$ ) on-chip WDM and mode-division multiplexing (MDM) transmission. Considering a single lane bit rate of 128 Gb/s, an on-chip data capacity of ∼10 Tb/s is achieved. To our best knowledge, this paper is the first demonstration of a Terabit on-chip WDM-MDM system that shows ultrahigh bandwidth communication on a single silicon chip.

Buckling phenomenon for imperfect pipe under pure bending

The buckling phenomenon for imperfect pipe under bending has been investigated by nonlinear FEA, considering the effect of a cross sectional oval deformation by changing the variables of pipes, that is, L/D varying from 2.5 to 20, D/t varying from 50 to 200, and imperfection (δ o/t) varying from 0.05 to 0.5. As well as the elastic buckling, the elasto-plastic buckling was investigated. From the calculation results, the followings were found. The reduction of buckling moment due to imperfection is larger in short pipe than in long pipe. The effect of imperfection for pipes with large values of D/t is larger than those with small values of D/t if L/D of both pipes is same. The effects of imperfection for elastic analysis are larger than elasto-plastic analysis. The buckling moment reduces more by the imperfection of buckling mode than by that of oval mode.

On the pressure response in the brain due to short duration blunt impacts.

When the head is subject to non-penetrating (blunt) impact, contusion-type injuries are commonly identified beneath the impact site (the coup) and, in some instances, at the opposite pole (the contre-coup). This pattern of injury has long eluded satisfactory explanation and blunt head injury mechanisms in general remain poorly understood. There are only a small number of studies in the open literature investigating the head's response to short duration impacts, which can occur in collisions with light projectiles. As such, the head impact literature to date has focussed almost exclusively on impact scenarios which lead to a quasi-static pressure response in the brain. In order to investigate the response of the head to a wide range of impact durations, parametric numerical studies were performed on a highly bio-fidelic finite element model of the human head created from in vivo magnetic resonance imaging (MRI) scan data with non-linear tissue material properties. We demonstrate that short duration head impacts can lead to potentially deleterious transients of positive and negative intra-cranial pressure over an order of magnitude larger than those observed in the quasi-static regime despite reduced impact force and energy. The onset of this phenomenon is shown to be effectively predicted by the ratio of impact duration to the period of oscillation of the first ovalling mode of the system. These findings point to dramatically different pressure distributions in the brain and hence different patterns of injury depending on projectile mass, and provide a potential explanation for dual coup/contre-coup injuries observed clinically.

Unsteady Reynolds averaged Navier–Stokes simulation of the post-critical flow around a closely spaced group of silos

During a storm in October 2002, wind induced ovalling vibrations were observed on several empty silos of a closely spaced group (pitch-to-diameter ratio of 1.05) consisting of 8 by 5 silos in the port of Antwerp (Belgium). Numerical simulations of the turbulent wind flow are performed to clarify the occurrence of the observed ovalling vibrations near the lee side corner of the group by studying the dynamic wind pressures on the silo surfaces and linking to the dynamic properties of the silo structures. As the orientation of the group largely affects the pressure distribution around the cylinders of the group, the influence of the angle of incidence of the wind flow on these ovalling vibrations is examined while other parameters, such as spacing ratio and Reynolds number are unchanged. To achieve results within a reasonable computation time, 2D unsteady Reynolds averaged Navier–Stokes (URANS) equations using Menter's shear stress transport turbulence model were performed. In order to elucidate the influence of the applied turbulence model and to qualitatively validate the spatial and temporal discretization of the 2D highly turbulent post-critical (Re=1.24×107) flow simulations for the silo group, single cylinder simulations were used. The geometric resemblance of the group arrangement with rectangular cylinders on the one hand and of the interstitial spaces with tube arrays (e.g. heat exchangers) on the other hand is used to qualitatively compare the observed flow phenomena. The simulations show that the silo group can be treated neither as a tube array nor as a solid bluff body. Subsequent linking of dynamic wind pressures to dynamic properties of the silo structures reveals strong narrow band frequency peaks in the turbulent pressure coefficient spectra of the silos near the lee side corners of the group that match the structural natural frequencies of the third and fourth ovalling mode shape of the silos. This match indicates a forced, resonant response which corresponds with the observed pattern of ovalling vibrations with three and four circumferential wavelengths. While the precise physical excitation mechanism is not yet fully understood, the simulations exclude discrete vortex shedding and since fluidelastic instability could not be considered, only turbulent buffeting remains which could very well give rise to the narrow band wake phenomena causing the ovalling silo wall vibrations.

Experimental and Numerical Investigations on Unstiffened Tubular T-Joints of Offshore Platforms

This paper presents the failure pattern, the ultimate strength, and the stress concentration factor of unstiffened T-joints obtained from experimental and numerical investigations conducted on them under axial brace compression loading. The numerical modeling was performed on the whole joint using ANSYS software package. This modeling has predicted the ultimate strength accurately when compared with that of the conventional modeling of only a portion of the joint. The nominal diameter and thickness of the chord of the unstiffened T-joints were 324 mm and 12 mm, respectively, and the corresponding values of the brace were 219 mm and 8 mm, respectively. The T-joint was approximately one-fourth the size of the largest joints in the platforms built in a shallow water depth of 80 m in the Bombay High field. The bending of the whole chord member combined with punching shear failure due to its ovalization was observed to be the predominant behavior of the unstiffened joint. The numerical analysis has simulated the behavior of the joint as was observed in the experiment and has also helped establish its correct failure pattern. It was also observed in these investigations that the unstiffened joint was stiffer in ovalization mode than in flexural deflection. The results obtained from the numerical modeling were observed, in general, to be in good agreement with that obtained from the testing. The stress concentration factor predicted by the numerical analysis is in close agreement with that measured in the experiment as well as that computed using well established parametric equations.

Collapse of partially corroded or worn pipe under external pressure

This paper is concerned with the effect of internal corrosion or erosion defects on the collapse of pipelines under external pressure. Experiments are conducted on SS-304 tubes with D/ t's of 21.0 and 18.7 with axially uniform grooves of several thicknesses and angular spans of 6–60°. All specimens exhibited the classical ovalization mode of collapse with the grooved side being more deformed. For groove angles between 6° and 20° the collapse pressure decreases as the angle increases but remains essentially constant for angles between 20° and 60°. The collapse pressure was found to decrease with groove depth, reducing by nearly 50% when the groove depth reached 50% of the pipe wall thickness. The experiments were simulated numerically using both the custom computer code BEPTICO as well as an axially uniform finite element model. The predictions were found to follow closely the trends of the experimental results. The three dimensionality of grooves was examined using appropriate finite element models. It was found that grooves shorter than about 8 D constitute local imperfections and accurate prediction of their effect on collapse pressure requires fully 3-D modeling. By contrast, grooves 10 D long or longer behave essentially as “long” grooves and can be analyzed using 2-D models.

Length dependence of critical measures in single-walled carbon nanotubes

This paper presents an investigation on the buckling behaviour of single-walled carbon nanotubes under various loading conditions (compression, bending and torsion) and unveils several aspects concerning the dependence of critical measures (axial strain, bending curvature and twisting angle) on the nanotube length. The buckling results are obtained by means of an atomistic-scale generalized beam theory (GBT) that incorporates local deformation of the nanotube cross-section by means of independent and orthogonal deformation modes. Moreover, some estimates are also obtained by means of non-linear shell finite element analyses using A baqus code. After classifying the buckling modes of thin-walled tubes (global, local and distortional), the paper addresses the importance of the two-wave distortional mode (flattening or ovalization mode) in their structural behaviour. Then, the well known expression to determine the critical strain of compressed nanotubes, which is based on Donnell theory for shallow shells, is shown to be inadequate for moderately long tubes due to warping displacements appearing in the distortional buckling modes. After that, an in-depth study on the buckling behaviour of nanotubes under compression, bending and torsion is presented. The variation of the critical kinematic measures (axial strain, bending curvature and twisting angle) with the tube length is thoroughly investigated. Concerning this dependence, some uncertainties that exist in the specific literature are meticulously explained, a few useful expressions to determine critical measures of nanotubes are proposed and the results are compared with available data collected from several published works (most of them, obtained from molecular dynamics simulations).

Analysis of the energy transmission in compound cylindrical shells with and without internal heavy fluid loading by boundary integral equations and by Floquet theory

This paper addresses three aspects of the steady-state free vibration of non-uniform (i.e., composed of alternating elements) elastic cylindrical shells with and without internal heavy fluid loading, which have not previously been studied in detailed form. Firstly, Floquet theory is applied to detect the location of frequency band gaps in an infinitely long periodic fluid-filled cylindrical shell vibrating in the ‘beam-type’ mode m = 1 and in the ovalling mode m = 2 in the framework of two simplified theories. As a prerequisite for this study, the validity range of these theories is estimated by comparison of the resulting dispersion curves with the exact solution. Secondly, the boundary equations are derived for a cylindrical shell with internal heavy fluid loading in the framework of the suggested theories. The methodology of boundary integral equations is used to obtain exact solutions for the problems of free vibrations of a finite shell and wave propagation in an infinitely long shell. Finally, the energy transmission in a semi-infinite non-uniform cylindrical shell with and without internal heavy fluid loading is addressed; predictions obtained by use of Floquet theory are compared with the exact solution obtained by the method of boundary integral equations.

Active control of the n = 2 axial propagating wave in an infinite in vacuo pipe

In pipe vibration the n = 2 (ovalling mode) axial propagating wave causes a large increase of strain in the pipe wall atfrequencies greater than its cut-on frequency (the frequency at which the wave starts topropagate axially). This wave readily propagates structure-borne noise and is difficult tocontrol by passive means. In this paper, the active control of this wave is investigated. Ann = 2 PVDF (polyvinylidene fluoride) modal sensor and PZT (lead zirconate titanate)modal actuator are used to selectively sense and control the wave. PVDFelements are shaped in the form of sine and cosine functions similar to then = 2 mode shape of the pipe to form the modal sensor and the modal actuator is constructedfrom a set of PZT elements bonded to the pipe. Using these transducers then = 2 wave can, in principle, be completely suppressed. Because this wave is dominant for a fewtens of hertz after cut-on, this control strategy is extremely effective over a limitedfrequency range. Theoretical models for the actuator and sensor are described andexperimental results demonstrating the effectiveness of the control system arepresented.

A PARAMETRIC STUDY ON THE AXISYMMETRIC MODES OF VIBRATION OF MULTI-LAYERED SPHERICAL SHELLS WITH LIQUID CORES OF RELEVANCE TO HEAD IMPACT MODELLING

The free vibration of spheres composed of inviscid compressible liquid cores surrounded by spherical layers of linear elastic, homogeneous and isotropic materials are studied using three-dimensional elasticity equations. The exact three-dimensional equations are first derived for an N -layered sphere with a liquid core and an extensive parametric study is then presented for the first few natural frequencies of the spheroidal modes of vibration. Non-dimensional frequency parameters are compared with values obtained using lower order membrane and shell theories. It is shown that for a remarkably wide range of geometric and material parameters, which encompasses values typical for the human head, the first ovalling mode of a fluid-filled shell behaves like a membrane filled with incompressible fluid and a simple closed-form expression is derived which closely approximates the natural frequencies obtained using the exact three-dimensional equations.

A MODEL FOR CALCULATING THE INSERTION LOSSES OF PIPE LAGGING

Lagging formed of jackets of porous materials such as glass wool and of impervious materials such as metal sheets are widely used to attenuate the sound radiated from pipes. A procedure is described for calculating the insertion losses produced by such lagging. The procedure yields the insertion losses corresponding to each of the low order mode types of the pipe. These are breathing, bending and ovalling mode types. Impedance and pressure transfer formulae for the various jacket types are given in terms of the fundamental properties of the jackets. The porous jacket, for example, is defined by its inner and outer diameters and the flow resistivity of the porous material. These formulae enable the frequency dependent insertion loss produced by an arbitrary pipe lagging to be determined. A comparison of the insertion losses predicted by this procedure with published results is given.

Vibration Analysis of Hyperbolic Cooling Towers due to Earthquake Excitations

The hyperbolidal shells of revolution supported on columns have been used effectively as natural draft cooling towers of reinforced concrete. The purpose of this paper is to analyze the dynamic response of hyperbolic cooling towers to earthquake excitations. Taking the propagating velocity of earthquake excitations into account, the author shows that hyperbolic cooling towers oscillate not only in beam vibration modes but also in such higher vibration modes as ovalization of their cross sections. When the value αR/V is considerably large, where α and V are circular frequency and propagating velocity of the earthquake excitation, respectively, and R is the radius of hyperbolic cooling towers on the foundation level, numerical example shows that owing to horizontal earthquake excitations an hyperbolic cooling tower oscillates mainly in an ovalization mode and that owing to vertical earthquake excitations it oscillates mainly in a rocking mode.

Nonlinear seismic response of a reinforced concrete nuclear reactor containment vessel

This paper examines the geometrically nonlinear, dynamic response of a reinforced concerte shell of revolution subjected to a horizontal acceleration at the base. The results from a numerical example indicate that the nonlinear effects are negligible and motion in the ovalling mode of the vessel is insignificant.

Vibration characteristics of a clamped-free and clamped-ring-stiffened circular cylindrical shell

A theoretical analysis for the free vibration of clamped-free and clamped-ring-stiffened cylindrical shells has been developed and programmed for digital computer solution. The analysis is capable of handling vibration characteristics of cylindrical shells in the swaying (cantilever mode, n = 1) as well as in the ovalling or breathing modes (n ≥ 2; n is circumferential wavenumber) with arbitrary length-to-radius ratio and radius-to-thickness ratio. In the case of a shell with an end ring, it also allows for variation in the non-dimensional ring characteristics (ring breadth-to-shell radius and ring depth-to-shell radius ratios).Three translational shell inertia components are included and the effect of ring eccentricity, mass and rotary inertia are examined.The problem is formulated using the Rayleigh-Ritz technique to obtain an approximate solution. Flügge's shell theory is used mainly but comparison is also made with the results from Timoshenko-Love theory. In both cases, special consideration is given to the results produced by assuming zero hoop and shear strain in the shell. Various choices of modal shapes are examined.Many numerical results are presented to illustrate the various aspects of the study, and it is concluded that (i) the assumption of zero hoop and shear strain produces negligible error (but considerable simplification) except for very short shells, (ii) the more exact Flügge shell theory adds little in accuracy to the simpler Timoshenko-Love theory, (iii) end-ring stiffening has little effect on swaying mode frequencies or on ovalling mode frequencies for very long shells but has a significant effect on ovalling mode frequencies for shorter shells, (iv) ring eccentricity can have significant effects on the ovalling mode frequencies.

Vibration studies of a ring-stiffened circular cylindrical shell

Studies are made into the free vibration characteristics of long circular cylindrical shells, typical of slender welded steel chimneys, with the lower edge fully restrained and the upper edge supported on a stiff reinforcing ring. The influence of edge boundary conditions is studied, particularly that of axial constraint, and also the influence of ring stiffness. It is concluded that axial constraint at the lower edge must be included if significant errors are to be eliminated in the prediction of the shell natural frequencies. For long shells oscillating in an ovalling mode the benefits of increased ring stiffness at the upper edge are limited.