RESUMO
In the present paper, a comparison is conducted between three classical shell theories as applied to the linear vibrations of single-walled carbon nanotubes (SWCNTs); specifically, the evaluation of the natural frequencies is conducted via Donnell, Sanders, and Flügge shell theories. The actual discrete SWCNT is modelled by means of a continuous homogeneous cylindrical shell considering equivalent thickness and surface density. In order to take into account the intrinsic chirality of carbon nanotubes (CNTs), a molecular based anisotropic elastic shell model is considered. Simply supported boundary conditions are imposed and a complex method is applied to solve the equations of motion and to obtain the natural frequencies. Comparisons with the results of molecular dynamics simulations available in literature are performed to check the accuracy of the three different shell theories, where the Flügge shell theory is found to be the most accurate. Then, a parametric analysis evaluating the effect of diameter, aspect ratio, and number of waves along the longitudinal and circumferential directions on the natural frequencies of SWCNTs is performed in the framework of the three different shell theories. Assuming the results of the Flügge shell theory as reference, it is obtained that the Donnell shell theory is not accurate for relatively low longitudinal and circumferential wavenumbers, for relatively low diameters, and for relatively high aspect ratios. On the other hand, it is found that the Sanders shell theory is very accurate for all the considered geometries and wavenumbers, and therefore, it can be correctly adopted instead of the more complex Flügge shell theory for the vibration modelling of SWCNTs.
RESUMO
BACKGROUND AND PURPOSE: Lumbar stenosis and instability frequently coexist. Spinal canal decompression is often combined with fixation of the relevant vertebral segment and can be performed using different techniques and devices, including pedicle screws and interspinous devices and facet screws. The present study evaluates the clinical outcome of laminectomy and single-level fusion using a minimally invasive technique for rigid posterior spinal column fixation with two cross-linked lag screws. METHODS: The records of patients operated from 2012 to 2016 were retrieved from the computerised medical record database system. Data on age, sex, surgical level, type of deficit and disease were collected. The Oswestry Disability Index (ODI) and Short Form-36 (SF-36) questionnaires were administered pre-operatively and at 1, 6, 12 and 24 months after surgery. MAIN FINDINGS: A total of 46 consecutive patients were operated between January 2012 to October 2016. One intraoperative complication was reported, and 4 patients experienced radiographic pseudarthrosis postoperatively. Five patients underwent additional surgery. The lumbar and lower limb VAS score, ODI and SF-36 scores showed statistically significant improvement for each score at the first and last follow-up (p < 0.01). CONCLUSION: Percutaneous lumbar transfacet screw placement with the Facet-Link ® system is feasible and safe but with a relatively high rate of poor articular fusion. This technique can reduce the morbidity of single-level lumbar spinal stenosis and mild instability and improve patient outcome scores. Comparative studies, including randomised controlled trials, are needed to confirm these findings.
