NONLINEAR DYNAMICS

In this study, multi-supported axially moving string is discussed. Supports located at the ends of the string are simple supports. A support located in the middle section owns the features of a spring. String speed is assumed to vary harmonically around an average rate. Hamilton's principle has been used to figure out the nonlinear equations of motion and boundary conditions. These equations and boundary conditions are dimensionless. Considering the nonlinear effects caused by the string extensions, nonlinear equations of motion are obtained. By using multi-timescaled method, which is one of the perturbation methods, approximate solutions have been found. The first term in the perturbation series causes the linear problem. With the solution of the linear problem, exact natural frequencies have been calculated for different locations of the supports on the middle, various spring coefficients and, with the spring support in the middle of the different location, different spring coefficient and axial speed values. Nonlinear terms on second order add correction terms to the linear problem. Effect of nonlinear terms on the natural frequency has been calculated for various parameters. The cases when the changing frequency of speed is equal to zero, close to zero and close to two times of the natural frequency have been analyzed separately. For each case, the stable and unstable areas in the solutions have been identified by stability analysis

Olfactory dysfunction and coronavirus disease 2019 severity: a prospective cohort study.

© 2021 Cambridge University Press. All rights reserved.Objective. The primary goal of this study was to evaluate the association between olfactory dysfunction or taste impairment olfactory dysfunction and disease severity and radiological findings in coronavirus disease-2019. The secondary goal was to assess the prevalence, severity and course of olfactory dysfunction or taste impairment in patients with coronavirus disease 2019. Method. This prospective observational cohort study evaluated patients hospitalised with coronavirus disease 2019 between April 1 and 1 May 2020. olfactory dysfunction and taste impairment were evaluated by two questionnaires. Chest computed tomography findings and coronavirus disease 2019 severity were assessed. Results. Among 133 patients, 23.3 per cent and 30.8 per cent experienced olfactory dysfunction and taste impairment, respectively, and 17.2 per cent experienced both. The mean age was 56.03 years, and 64.7 per cent were male and 35.3 per cent were female. No statistically significant association was found between olfactory dysfunction (p = 0.706) and taste impairment (p = 0.35) with either disease severity or chest computed tomography grading. Conclusion. Olfactory dysfunction or taste impairment does not have prognostic importance in patients with coronavirus disease 2019