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Micro coriolis flowmeters are extensively used in fluidic micro circuits and are of great interest to many researchers. Straight and curved coriolis flowmeters are common types of coriolis flowmeters. Therefore in the present work, the out-of- plane vibration and stability of curved micro tubes are investigated to study the dynamic behavior of curved coriolis flowmeters. The Hamilton principle is applied to derive a novel governing equation based on strain gradient theory for the curved micro tube conveying fluid. Lagrangian nonlinear strain is adopted to take into account the geometric nonlinearity and analyze hardening behavior as a result of the cubic nonlinear terms. Linear stability analysis is carried out to investigate the possibility of linear instabilities. Afterwards, the first nonlinear out-of-plane natural frequency is plotted versus fluid velocity to determine the influence of nonlinear terms and hardening behavior on stability of the system. The influence of the length scale parameter is studied by comparison of the results for classical, coupled stress and strain gradient theory. Finally the phase difference between two points at upstream and downstream is plotted versus fluid velocity. Linear relation between the phase difference and fluid velocity is noticed, thus the curved coriolis flowmeter can be calibrated to measure flow rate by measuring the phase difference between two points. [ABSTRACT FROM AUTHOR]

Abstract: In this paper a nonlinear model was developed for a drillstring system in deviated well with axially moving motion and axial loading, using the perturbation techniques. The drillstring was considered as a simply supported axially moving rotor. Governing equations of motion were obtained based on Hamilton''s principle and method of multiple scales was employed to solve the nonlinear motion equations in order to obtain the steady state response and stability region of the system. Then the effects of rotating speed, axial compression load, imbalance mass and nonlinear fluid force on the drillstring responses were investigated in detail and nonlinear natural frequencies and their corresponding mode shapes were presented. Analytical and numerical results reveal the rich and interesting nonlinear phenomena such as primary and parametric resonance that is being investigated for the first time in this study on the nonlinear vibration of the drillstring system. Finally in effort to validate the theoretical approach employed in this study, the numerical solutions obtained here were compared with a set of existing experimental data. [Copyright &y& Elsevier]