Dynamics and Stability of Carbon Nanotubes

The low-frequency oscillations and energy localization of Single-Walled Carbon Nanotubes (SWNTs) are studied in the framework of the Sanders-Koiter shell theory. The circumferential flexure modes (CFMs) are analysed. Simply supported, clamped and free boundary conditions are considered. Two different approaches are proposed, based on numerical and analytical models. The numerical model uses in the linear analysis a double mixed series expansion for the displacement fields based on Chebyshev polynomials and harmonic functions. The Rayleigh-Ritz method is applied to obtain approximate natural frequencies and mode shapes. In the nonlinear analysis, the three displacement fields are re-expanded by using approximate eigenfunctions. An energy approach based on Lagrange equations is considered in order to obtain a set of nonlinear ordinary differential equations, which is solved by the Runge-Kutta numerical method. The analytical model considers a reduced version of the Sanders-Koiter shell theory obtained by assuming small circumferential and tangential shear deformations. These two assumptions allow to condense the longitudinal and circumferential displacement fields into the radial one. A nonlinear fourth-order partial differential equation for the radial displacement field is derived, which allows to calculate the natural frequencies and to estimate the nonlinearity effect. An analytical solution of this equation is obtained by the multiple scales method. The previous models are validated in linear field by means of comparisons with experiments, molecular dynamics simulations and finite element analyses retrieved from the literature. The concept of energy localization in SWNTs is introduced, which is a strongly nonlinear phenomenon. The low-frequency nonlinear oscillations of the SWNTs become localized ones if the intensity of the initial excitation exceeds some threshold which depends on the SWNTs length. This localization results from the resonant interaction of the zone-boundary and nearest nonlinear normal modes leading to the confinement of the vibration energy in one part of the system. The value of the initial excitation corresponding to this energy confinement is referred to as energy localization threshold. The effect of the aspect ratio on the analytical and numerical values of the energy localization threshold is investigated; different boundary conditions are considered

Nonlinear vibrations and energy conservation of Single-Walled Carbon Nanotubes

The nonlinear vibrations of Single-Walled Carbon Nanotubes are analysed. The Sanders-Koiter elastic shell theory is applied in order to obtain the elastic strain energy and kinetic energy. The carbon nanotube deformation is described in terms of longitudinal, circumferential and radial displacement fields. The theory considers geometric nonlinearities due to large amplitude of vibration. The displacement fields are expanded by means of a double series based on harmonic functions for the circumferential variable and Chebyshev polynomials for the longitudinal variable. The Rayleigh-Ritz method is applied in order to obtain approximate natural frequencies and mode shapes. Free boundary conditions are analysed. In the nonlinear analysis, the three displacement fields are re-expanded by using approximate eigenfunctions; an energy approach based on the Lagrange equations is considered in order to reduce the nonlinear partial differential equations to a set of nonlinear ordinary differential equations. Nondimensional parameters are considered. The total energy conservation of the system is verified by considering the combinations of different vibration modes. The effect of the companion mode participation on the nonlinear vibrations of the carbon nanotube is analysed

Linear and nonlinear dynamics of a circular cylindrical shell under static and periodic axial load

In this paper an experimental study on circular cylindrical shells subjected to axial compres- sive and periodic loads is presented. The setting of the experiment is explained and deeply described along with a complete analysis of the results. The linear and the nonlinear dynamic behaviour associated with a combined effect of compressive static and a periodic axial load has been considered and a chaotic response of the structure has been observed close to the resonance. The linear shell behaviour is also investigated by means of a theoretical and finite element model, in order to enhance the comprehension of experimental results, i.e. the natural frequencies of the system and their ratios

Beating phenomenon and energy localization in Single-Walled Carbon Nanotubes

In this paper, the low-frequency nonlinear oscillations and energy localization of Single-Walled Carbon Nanotubes (SWNTs) are analysed. The SWNTs dynamics is studied in the framework of the Sanders-Koiter nonlinear shell theory. The circumferential flexure vibration modes (CFMs) are considered. Simply supported, clamped and free boundary conditions are analysed. Two different approaches are compared, based on numerical and analytical models. The numerical model uses a double mixed series expansion for the displacement fields based on the Chebyshev polynomials and harmonic functions. The Lagrange equations are considered to obtain a set of nonlinear ordinary differential equations of motion which are solved using the implicit Runge-Kutta numerical method. The analytical model considers a reduced form of the shell theory assuming small circumferential and tangential shear deformations. The Galerkin procedure is used to get the nonlinear ordinary differential equations of motion, which are then solved using the multiple scales analytical method. The natural frequencies of SWNTs obtained by considering the analytical and numerical approaches are compared for different boundary conditions. A convergence analysis in the nonlinear field is carried out for the numerical method in order to select the correct number of the axisymmetric and asymmetric modes providing the actual localization threshold. The effect of the aspect ratio on the analytical and numerical values of the localization threshold for SWNTs with different boundary conditions is investigated in the nonlinear field

Insufficient birth weight: factors associated in two cohorts of newborns in Ribeirão Preto, São Paulo, Brazil

OBJETIVO: Avaliar fatores associados ao aumento das taxas de peso insuficiente (PI) em duas coortes de recém-nascidos (RN) vivos e de parto único de Ribeirão Preto, São Paulo, separadas por 15 anos (1978/79 e 1994). MÉTODOS: Foram estudados 6.223 partos em 1978/79 e 2.522 em 1994, excluindo-se os RN de baixo peso. Associação entre PI e variáveis independentes (idade, trabalho, escolaridade e tabagismo maternos, abortos e natimortos prévios, número de filhos, situação conjugal, visitas de pré-natal, tipo de parto e hospital, categoria de internação, renda familiar, idade gestacional e sexo do RN) foi analisada por cálculo da Odds Ratio (OR) bruto e intervalo de confiança 95%, seguida de regressão logística múltipla. RESULTADOS: Em 1978/79, na análise ajustada, idade materna <20 anos (p=0,014), renda familiar <5 salários-mínimos (p=0,030), menos de quatro consultas de pré-natais (p=0,003), parto vaginal (p<0,001), sexo feminino (p<0,001), tabagismo materno (p<0,001) e prematuridade (p<0,001) estiveram associados a PI. Em 1994, os fatores associados ao PI foram: trabalho materno fora do lar (p=0,020), sexo feminino (p<0,001), tabagismo materno (p<0,001) e prematuridade (p<0,001). CONCLUSÕES: Variáveis socioeconômicas que atuaram em 1978/79 desapareceram em 1994, restando o sexo do RN, o hábito de fumar e a prematuridade nos dois períodos. Como houve diminuição do tabagismo materno e não houve modificação na proporção de nascimentos do sexo feminino, uma explicação para o aumento do PI seria o aumento nos nascimentos pré-termo entre as duas coortes.OBJECTIVE: To evaluate factors associated to the increase in insufficient birth weight (IBW) rates in two population-based-cohorts of singletons born alive in Ribeirão Preto, São Paulo, Brazil, separated by 15 years (1978/79 and 1994). METHODS: The first cohort (1978/79) comprised 6,223 newborns and the second (1994), 2,522, excluding low birth weight newborns. Independent variables association with IBW (maternal age, work, schooling and smoking; previous abortion, previous stillbirth, number of live births, maternal marital status, family income, occupation group, type of hospital, mode of insurance, number of antenatal visits, type of delivery; newborn gender and gestational age) were analyzed. The Odds Ratio (OR) was determined using a logistic regression model and 95% confidence limits were calculated. RESULTS: In 1978/79, maternal age <20 years (p=0.014), family income <5 minimum Brazilian wages (p=0.030), <4 antenatal visits (p=0.003), vaginal delivery (p<0.001), female newborn gender (p<0.001), maternal smoking (p<0.001) and preterm birth (p<0.001) were associated with IBW. In 1994, maternal work outside home (p=0.020), female newborn gender (p<0.001), maternal smoking (p<0.001) and preterm births (p<0.001) were associated with IBW. CONCLUSIONS: Socioeconomics variables associated with IBW in 1978/79 were not determinants in 1994. Newborn gender, maternal smoking and preterm birth remained significant determinants of IBW in both moments. Considering the decrease in rate of maternal smoking and the maintenance of female births, the increase in IBW could be explained by increasing rates of preterm birth in this interval of 15 years.Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP

Diferença notável nas taxas de parto cesariano em hospital público e hospital privado no Brasil

This paper evaluates the association of maternal variables and of variables related to prenatal and delivery care with cesarean sections at a public and at a private maternity. A retrospective cross-sectional study was performed at a public maternity clinic (2,889 deliveries) and at a private maternity clinic (2,911 deliveries) in the city of Ribeirão Preto, São Paulo State, Brazil. The prevalence of cesarean sections was 18.9% at the public maternity clinic and 84.3% at the private one. The factors associated with cesarean sections at both hospitals were: mothers from other cities, aged > 25 years and with hypertension. Having more than one child was a protective factor. At the public hospital, cesarean sections were more frequent on Wednesdays and from 12:00 to 23:59 hours of any day of the week, whereas at the private hospital they occurred on any day, though were less common on Sundays, and at any time except in the early morning. At the private hospital, cesarean sections were more frequent when performed by the doctor who had provided the prenatal care. Non-medical factors were more associated with cesarean sections in the private maternity clinic than biological or clinical factors related to pregnancy.Este artigo avalia a associação de variáveis maternas e aquelas relacionadas ao cuidado pré-natal e ao parto com a ocorrência de cesáreas em um hospital público e em um hospital privado. Um estudo de corte transversal, retrospectivo, foi desenvolvido em uma maternidade pública (2.889 partos) e em uma maternidade privada (2.911 partos) em Ribeirão Preto, São Paulo, Brasil. A prevalência de cesárea foi 18,9% e 84,3%, respectivamente, na maternidade pública e na particular. Os fatores associados ao parto cesariano nos dois hospitais foram: mães procedentes de outras cidades, com idade > 25 anos e hipertensas. Ter mais de um filho foi fator protetor. No hospital público, a cesárea foi mais freqüente às quartas-feiras e das 12h00min às 23h59min de qualquer dia da semana, enquanto no hospital privado prevaleceram em qualquer dia, exceto aos domingos, e em qualquer horário, exceto de madrugada. Neste hospital, a cesárea foi mais freqüente quando realizada pelo médico que acompanhou o pré-natal. Fatores não médicos foram mais associados com os partos operatórios na maternidade privada do que fatores biológicos ou clínicos das gestantes

A New Tool for the Lamb Shift Calculation

We solve the Bethe-Salpeter equation for hydrogenic bound states by choosing an appropriate interaction kernel $K_c$. We want to use our solution to calculate up to a higher order the hydrogen Lamb-shift, and as a first application we present up to order \left(\aa / \pi\right)(\za)^7 the contribution of the lowest order self-energy graph, calculated {\it exactly}. The basic formalism is a natural extension to the hydrogenic bound states of the one previously presented by R. Barbieri and E. Remiddi and used in the case of positronium.Comment: 21 pages, Latex, Preprint DFUB-94-0

Vibration Localization of Imperfect Circular Cylindrical Shells

none4noThe goal of the present paper is the analysis of the effect of geometric imperfections in circular cylindrical shells. Perfect circular shells are characterized by the presence of double shell-like modes, i.e., modes having the same frequency with modal shape shifted of a quarter of wavelength in the circumferential direction. In presence of geometric imperfections, the double natural frequencies split into a pair of distinct frequencies, the splitting is proportional to the level of imperfection. In some cases, the imperfections cause an interesting phenomenon on the modal shapes, which present a strong localization in the circumferential direction. This study is carried out by means of a semi-analytical approach compared with standard finite element analyses.openPellicano, Francesco; Zippo, Antonio; Barbieri, Marco; Strozzi, MatteoPellicano, Francesco; Zippo, Antonio; Barbieri, Marco; Strozzi, Matte