Nonlinear secondary whirl of an overhung rotor

Gravity critical speeds of rotors have hitherto been studied using linear analysis, and ascribed to rotor stiffness asymmetry. Here, we study an idealized asymmetric nonlinear overhung rotor model of Crandall and Brosens, spinning close to its gravity critical speed.Nonlinearities arise from finite displacements, and the rotor's staticlateral deflection under gravity is taken as small. Assuming small asymmetry and damping, slow modulations of whirl amplitudes are studied using the method of multiple scales. Inertia asymmetry appears only at second order. More interestingly, even without stiffness asymmetry, the gravity-induced resonance survives through geometric nonlinearities. The gravity resonant forcing does not influence the resonant mode at leading order, unlike the typical resonant oscillations. Nevertheless,the usual phenomena of resonances, namely saddle-node bifurcations, jump phenomena and hysteresis, are all observed. An unanticipated periodic solution branch is found. In the three-dimensional space oftwo modal coefficients and a detuning parameter, the full set of periodic solutions is found to be an imperfect version of three mutually intersecting curves: a straight line,a parabola and an ellipse.

Semi-active vibration isolation using a near-zero-spring-rate device:steady state analysis of a single-degree-of-freedom model

A vibration isolator is described which incorporates a near-zero-spring-rate device within its operating range. The device is an assembly of a vertical spring in parallel with two inclined springs. A low spring rate is achieved by combining the equivalent stiffness in the vertical direction of the inclined springs with the stiffness of the vertical central spring. It is shown that there is a relation between the geometry and the stiffness of the individual springs that results in a low spring rate. Computer simulation studies of a single-degree-of-freedom model for harmonic base input show that the performance of the proposed scheme is superior to that of the passive schemes with linear springs and skyhook damping configuration. The response curves show that, for small to large amplitudes of base disturbance, the system goes into resonance at low frequencies of excitation. Thus, it is possible to achieve very good isolation over a wide low-frequency band. Also, the damper force requirements for the proposed scheme are much lower than for the damper force of a skyhook configuration or a conventional linear spring with a semi-active damper.

Field Emission Properties of Carbon Nanotube Arrays with Defects and Impurities

It has been found experimentally that the results related to the collective field emission performance of carbon nanotube (CNT) arrays show variability. The emission performance depends on the electronic structure of CNTs (especially their tips). Due to limitations in the synthesis process, production of highly pure and defect free CNTs is very difficult. The presence of defects and impurities affects the electronic structure of CNTs. Therefore, it is essential to analyze the effect of defects on the electronic structure, and hence, the field emission current. In this paper, we develop a modeling approach for evaluating the effect of defects and impurities on the overall field emission performance of a CNT array. We employ a concept of effective stiffness degradation for segments of CNTs, which is due to structural defects. Then, we incorporate the vacancy defects and charge impurity effects in our Green's function based approach. Simulation results indicate decrease in average current due to the presence of such defects and impurities.

A constraint Jacobian based approach for static analysis of pantograph masts

This paper presents a constraint Jacobian matrix based approach to obtain the stiffness matrix of widely used deployable pantograph masts with scissor-like elements (SLE). The stiffness matrix is obtained in symbolic form and the results obtained agree with those obtained with the force and displacement methods available in literature. Additional advantages of this approach are that the mobility of a mast can be evaluated, redundant links and joints in the mast can be identified and practical masts with revolute joints can be analysed. Simulations for a hexagonal mast and an assembly with four hexagonal masts is presented as illustrations.

A Kalman filter based strategy for linear structural system identification based on multiple static and dynamic test data

The problem of identification of stiffness, mass and damping properties of linear structural systems, based on multiple sets of measurement data originating from static and dynamic tests is considered. A strategy, within the framework of Kalman filter based dynamic state estimation, is proposed to tackle this problem. The static tests consists of measurement of response of the structure to slowly moving loads, and to static loads whose magnitude are varied incrementally; the dynamic tests involve measurement of a few elements of the frequency response function (FRF) matrix. These measurements are taken to be contaminated by additive Gaussian noise. An artificial independent variable τ, that simultaneously parameterizes the point of application of the moving load, the magnitude of the incrementally varied static load and the driving frequency in the FRFs, is introduced. The state vector is taken to consist of system parameters to be identified. The fact that these parameters are independent of the variable τ is taken to constitute the set of ‘process’ equations. The measurement equations are derived based on the mechanics of the problem and, quantities, such as displacements and/or strains, are taken to be measured. A recursive algorithm that employs a linearization strategy based on Neumann’s expansion of structural static and dynamic stiffness matrices, and, which provides posterior estimates of the mean and covariance of the unknown system parameters, is developed. The satisfactory performance of the proposed approach is illustrated by considering the problem of the identification of the dynamic properties of an inhomogeneous beam and the axial rigidities of members of a truss structure.

A multistep transversal linearization (MTL) method in non-linear dynamics through a Magnus characterization

A new form of a multi-step transversal linearization (MTL) method is developed and numerically explored in this study for a numeric-analytical integration of non-linear dynamical systems under deterministic excitations. As with other transversal linearization methods, the present version also requires that the linearized solution manifold transversally intersects the non-linear solution manifold at a chosen set of points or cross-section in the state space. However, a major point of departure of the present method is that it has the flexibility of treating non-linear damping and stiffness terms of the original system as damping and stiffness terms in the transversally linearized system, even though these linearized terms become explicit functions of time. From this perspective, the present development is closely related to the popular practice of tangent-space linearization adopted in finite element (FE) based solutions of non-linear problems in structural dynamics. The only difference is that the MTL method would require construction of transversal system matrices in lieu of the tangent system matrices needed within an FE framework. The resulting time-varying linearized system matrix is then treated as a Lie element using Magnus’ characterization [W. Magnus, On the exponential solution of differential equations for a linear operator, Commun. Pure Appl. Math., VII (1954) 649–673] and the associated fundamental solution matrix (FSM) is obtained through repeated Lie-bracket operations (or nested commutators). An advantage of this approach is that the underlying exponential transformation could preserve certain intrinsic structural properties of the solution of the non-linear problem. Yet another advantage of the transversal linearization lies in the non-unique representation of the linearized vector field – an aspect that has been specifically exploited in this study to enhance the spectral stability of the proposed family of methods and thus contain the temporal propagation of local errors. A simple analysis of the formal orders of accuracy is provided within a finite dimensional framework. Only a limited numerical exploration of the method is presently provided for a couple of popularly known non-linear oscillators, viz. a hardening Duffing oscillator, which has a non-linear stiffness term, and the van der Pol oscillator, which is self-excited and has a non-linear damping term.

Seismic damage estimation through measurable dynamic characteristics

Ductility based design of reinforced concrete structures implicitly assumes certain damage under the action of a design basis earthquake. The damage undergone by a structure needs to be quantified, so as to assess the post-seismic reparability and functionality of the structure. The paper presents an analytical method of quantification and location of seismic damage, through system identification methods. It may be noted that soft ground storied buildings are the major casualties in any earthquake and hence the example structure is a soft or weak first storied one, whose seismic response and temporal variation of damage are computed using a non-linear dynamic analysis program (IDARC) and compared with a normal structure. Time period based damage identification model is used and suitably calibrated with classic damage models. Regenerated stiffness of the three degrees of freedom model (for the three storied frame) is used to locate the damage, both on-line as well as after the seismic event. Multi resolution analysis using wavelets is also used for localized damage identification for soft storey columns.

Effect of indium doping on the electrical switching behaviour of Ge-Te glasses

Bulk Ge15Te85-xInx (1 <= x <= 11) series of glasses have been found to exhibit a threshold switching behaviour for an input current of 2 mA. An initial decrease is seen in the switching voltages (V-T) with the addition of indium, which is due to the higher metallicity of indium. An increase is seen in V-T above 3 at.% of indium, which proceeds until 8 at.%, with a change in slope (lower to higher) seen around 7 at.%. Beyond x = 8, a reversal in trend is exhibited in the variation of V-T, with a well-defined minimum around x = 9 at.%. Based on the composition dependence of V-T, it is proposed that Ge15Te85-xInx glasses exhibit an extended rigidity percolation threshold. The composition, x = 3, at which the V-T starts to increase and the composition, x = 7, at which a slope change is exhibited correspond to the onset and completion, respectively, of the extended stiffness transition. Thermal studies and photoconductivity e85-xInx glasses. In addition, the minimum seen in V-T at x = 9 is associated with the chemical threshold (CT) of this glassy system.

Free vibration and wave propagation analysis of uniform and tapered rotating beams using spectrally formulated finite elements

This paper presents a formulation of an approximate spectral element for uniform and tapered rotating Euler-Bernoulli beams. The formulation takes into account the varying centrifugal force, mass and bending stiffness. The dynamic stiffness matrix is constructed using the weak form of the governing differential equation in the frequency domain, where two different interpolating functions for the transverse displacement are used for the element formulation. Both free vibration and wave propagation analysis is performed using the formulated elements. The studies show that the formulated element predicts results, that compare well with the solution available in the literature, at a fraction of the computational effort. In addition, for wave propagation analysis, the element shows superior convergence. (C) 2007 Elsevier Ltd. All rights reserved.

Fuzzy-logic-based health monitoring and residual-life prediction for composite helicopter rotor

A health-monitoring and life-estimation strategy for composite rotor blades is developed in this work. The cross-sectional stiffness reduction obtained by physics-based models is expressed as a function of the life of the structure using a recent phenomenological damage model. This stiffness reduction is further used to study the behavior of measurable system parameters such as blade deflections, loads, and strains of a composite rotor blade in static analysis and forward flight. The simulated measurements are obtained using an aeroelastic analysis of the composite rotor blade based on the finite element in space and time with physics-based damage modes that are then linked to the life consumption of the blade. The model-based measurements are contaminated with noise to simulate real data. Genetic fuzzy systems are developed for global online prediction of physical damage and life consumption using displacement- and force-based measurement deviations between damaged and undamaged conditions. Furthermore, local online prediction of physical damage and life consumption is done using strains measured along the blade length. It is observed that the life consumption in the matrix-cracking zone is about 12-15% and life consumption in debonding/delamination zone is about 45-55% of the total life of the blade. It is also observed that the success rate of the genetic fuzzy systems depends upon the number of measurements, type of measurements and training, and the testing noise level. The genetic fuzzy systems work quite well with noisy data and are recommended for online structural health monitoring of composite helicopter rotor blades.

Genetic programming metamodel for rotating beams

This paper investigates the use of Genetic Programming (GP) to create an approximate model for the non-linear relationship between flexural stiffness, length, mass per unit length and rotation speed associated with rotating beams and their natural frequencies. GP, a relatively new form of artificial intelligence, is derived from the Darwinian concept of evolution and genetics and it creates computer programs to solve problems by manipulating their tree structures. GP predicts the size and structural complexity of the empirical model by minimizing the mean square error at the specified points of input-output relationship dataset. This dataset is generated using a finite element model. The validity of the GP-generated model is tested by comparing the natural frequencies at training and at additional input data points. It is found that by using a non-dimensional stiffness, it is possible to get simple and accurate function approximation for the natural frequency. This function approximation model is then used to study the relationships between natural frequency and various influencing parameters for uniform and tapered beams. The relations obtained with GP model agree well with FEM results and can be used for preliminary design and structural optimization studies.

Vave propagation and bandgaps in a parametrically modulated composite laminate

Wave propagation and its frequency bandgaps in a parametrically modulated composite laminate are reported in this paper. The modulated properties under considerations are due to periodic microstructure, for example honeycomb core sandwich composite, which can be parameterized and homogenized in a suitable scale. Wave equations are derived by assuming a third-order shear deformation theory. Homogenization of the wave equations is carried out in the scale of wavelength. In-plane wave and flexural-shear wave dispersions are obtained for a range of values of a stiffness modulation coefficient (alpha). A clear pattern of stop-bands is observed for alpha >= 4. To validate the band-gap phenomena, we take recourse to time domain response obtained from finite element simulation. As predicted by the proposed analytical technique, a distinct correlation between the chosen frequency band and the simulated wave arrival time and amplitude reduction is found. This promises practical applications of the proposed analytical technique to designing parametrically modulated composite laminate for wave suppression. (C) 2009 Elsevier B.V. All rights reserved.

A Legendre spectral element model for sloshing and acoustic analysis in nearly incompressible fluids

A new spectral finite element formulation is presented for modeling the sloshing and the acoustic waves in nearly incompressible fluids. The formulation makes use of the Legendre polynomials in deriving the finite element interpolation shape functions in the Lagrangian frame of reference. The formulated element uses Gauss-Lobatto-Legendre quadrature scheme for integrating the volumetric stiffness and the mass matrices while the conventional Gauss-Legendre quadrature scheme is used on the rotational stiffness matrix to completely eliminate the zero energy modes, which are normally associated with the Lagrangian FE formulation. The numerical performance of the spectral element formulated here is examined by doing the inf-sup test oil a standard rectangular rigid tank partially filled with liquid The eigenvalues obtained from the formulated spectral element are compared with the conventional equally spaced node locations of the h-type Lagrangian finite element and the predicted results show that these spectral elements are more accurate and give superior convergence The efficiency and robustness of the formulated elements are demonstrated by solving few standard problems involving free vibration and dynamic response analysis with undistorted and distorted spectral elements. and the obtained results are compared with available results in the published literature (C) 2009 Elsevier Inc All rights reserved

Evidence for a thermally reversing window in bulk Ge-Te-Si glasses revealed by alternating differential scanning calorimetry

Experiments on Ge15Tc85-xSix glasses (2 <= x <= 12) using alternating differential scanning calorimetry (ADSC) indicate that these glasses exhibit one glass transition and two crystallization reactions upon heating. The glass transition temperature has been found to increase almost linearly with silicon content, in the entire composition tie-line. The first crystallization temperature (T-cl) exhibits an increase with silicon content for x<5; T-cl remains almost a constant in the composition range 5 < x <= 10 and it increases comparatively more sharply with silicon content thereafter. The specific heat change (Delta C-p) is found to decrease with an increase in silicon content, exhibiting a minimum at x=5 (average coordination number, (r) = 2.4); a continuous increase is seen in Delta C-p with silicon concentration above x = 5. The effects seen in the variation with composition of T-cl and Delta C-p at x=5, are the specific signatures of the mean-field stiffness threshold at (r) = 2.4. Furthermore, a broad trough is seen in the enthalpy change (Delta H-NR), which is indicative of a thermally reversing window in Ge15Te85-xSix glasses in the composition range 2 <= x <= 6 (2.34 <= (r) <= 2.42).

Development of a new flexor tendon repair technique performed with bioabsorbable poly-L/D-lactide (PLDLA) suture

Sormen koukistajajännevamman korjauksen jälkeisen aktiivisen mobilisaation on todettu johtavan parempaan toiminnalliseen lopputulokseen kuin nykyisin yleisesti käytetyn dynaamisen mobilisaation. Aktiivisen mobilisaation ongelma on jännekorjauksen pettämisriskin lisääntyminen nykyisten ommeltekniikoiden riittämättömän vahvuuden vuoksi. Jännekorjauksen lujuutta on parannettu kehittämällä monisäieommeltekniikoita, joissa jänteeseen tehdään useita rinnakkaisia ydinompeleita. Niiden kliinistä käyttöä rajoittaa kuitenkin monimutkainen ja aikaa vievä tekninen suoritus. Käden koukistajajännekorjauksessa käytetään yleisesti sulamattomia ommelmateriaaleja. Nykyiset käytössä olevat biohajoavat langat heikkenevät liian nopeasti jänteen paranemiseen nähden. Biohajoavan laktidistereokopolymeeri (PLDLA) 96/4 – langan vetolujuuden puoliintumisajan sekä kudosominaisuuksien on aiemmin todettu soveltuvan koukistajajännekorjaukseen. Tutkimuksen tavoitteena oli kehittää välittömän aktiivisen mobilisaation kestävä ja toteutukseltaan yksinkertainen käden koukistajajännekorjausmenetelmä biohajoavaa PLDLA 96/4 –materiaalia käyttäen. Tutkimuksessa analysoitiin viiden eri yleisesti käytetyn koukistajajänneompeleen biomekaanisia ominaisuuksia staattisessa vetolujuustestauksessa ydinompeleen rakenteellisten ominaisuuksien – 1) säikeiden (lankojen) lukumäärän, 2) langan paksuuden ja 3) ompeleen konfiguraation – vaikutuksen selvittämiseksi jännekorjauksen pettämiseen ja vahvuuteen. Jännekorjausten näkyvän avautumisen todettiin alkavan perifeerisen ompeleen pettäessä voima-venymäkäyrän myötöpisteessä. Ydinompeleen lankojen lukumäärän lisääminen paransi ompeleen pitokykyä jänteessä ja suurensi korjauksen myötövoimaa. Sen sijaan paksumman (vahvemman) langan käyttäminen tai ompeleen konfiguraatio eivät vaikuttaneet myötövoimaan. Tulosten perusteella tutkittiin mahdollisuuksia lisätä ompeleen pitokykyä jänteestä yksinkertaisella monisäieompeleella, jossa ydinommel tehtiin kolmen säikeen polyesterilangalla tai nauhamaisen rakenteen omaavalla kolmen säikeen polyesterilangalla. Nauhamainen rakenne lisäsi merkitsevästi ompeleen pitokykyä jänteessä parantaen myötövoimaa sekä maksimivoimaa. Korjauksen vahvuus ylitti aktiivisen mobilisaation jännekorjaukseen kohdistaman kuormitustason. PLDLA 96/4 –langan soveltuvuutta koukistajajännekorjaukseen selvitettiin tutkimalla langan biomekaanisia ominaisuuksia ja solmujen pito-ominaisuuksia staattisessa vetolujuustestauksessa verrattuna yleisimmin jännekorjauksessa käytettävään punottuun polyesterilankaan (Ticron®). PLDLA –langan todettiin soveltuvan hyvin koukistajajännekorjaukseen, sillä se on polyesterilankaa venymättömämpi ja solmujen pitävyys on parempi. Viimeisessä vaiheessa tutkittiin PLDLA 96/4 –langasta valmistetulla kolmisäikeisellä, nauhamaisella jännekorjausvälineellä tehdyn jännekorjauksen kestävyyttä staattisessa vetolujuustestauksessa sekä syklisessä kuormituksessa, joka simuloi staattista testausta paremmin mobilisaation toistuvaa kuormitusta. PLDLA-korjauksen vahvuus ylitti sekä staattisessa että syklisessä kuormituksessa aktiivisen mobilisaation edellyttämän vahvuuden. Nauhamaista litteää ommelmateriaalia ei aiemmin ole tutkittu tai käytetty käden koukistajajännekorjauksessa. Tässä tutkimuksessa ommelmateriaalin nauhamainen rakenne paransi merkitsevästi jännekorjauksen vahvuutta, minkä arvioidaan johtuvan lisääntyneestä kontaktipinnasta jänteen ja ommelmateriaalin välillä estäen ompeleen läpileikkautumista jänteessä. Tutkimuksessa biohajoavasta PLDLA –materiaalista valmistetulla rakenteeltaan nauhamaisella kolmisäikeisellä langalla tehdyn jännekorjauksen vahvuus saavutti aktiivisen mobilisaation edellyttämän tason. Lisäksi uusi menetelmä on helppokäyttöinen ja sillä vältetään perinteisten monisäieompeleiden tekniseen suoritukseen liittyvät ongelmat.