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Nano/Micro tubes are extensively used in fluidic nano/micro circuits, biochemical industries and nano/micro electromechanical systems. In order to investigate the influence of length scale parameters, in the present work for the first time, the second strain gradient is applied along with Euler- Bernoulli beam theory to study the fluid-conveying nanotube. The hamilton principle is used to derive governing equation of the nano/micro tube conveying fluid. The partial governing equation of motion is discretized into ordinary differential equations by the Galerkin method. The possible instabilities are predicted by linear stability analysis. Onsets of the instabilities based on the second strain gradient theory are compared with those based on the classical and strain gradient theories. Afterwards, nonlinear stability analysis is performed by both Perturbation and numerical methods. The results obtained by numerical method are in good agreements with those achieved by perturbation approach. In nonlinear stability analysis, the onsets of instabilities are obtained more precisely considering the hardening effects. The resonance around the first nonlinear natural frequency and the influence of the fluid velocity on the resonance curve are investigated by the perturbation method. [ABSTRACT FROM AUTHOR]

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]

Abstract: An investigation of the possible performance improvements of thin walled composite beams through the use of the variable stiffness concept with curvilinear fiber is presented. The beams are constructed from a single-cell closed cross section and a number of non-classical effects such as material anisotropy, transverse shear, warping inhibition and nonuniform torsional model are considered in the beam model. The governing equations were derived by means of the extended Hamilton''s principle. Also the extended Galerkin''s method is used to solve governing equations. Composite beams subjected to different loading with given geometry and material properties are optimized for maximum failure load. Improvements of variable-stiffness beams over conventional, constant-stiffness beams are also demonstrated. [Copyright &y& Elsevier]

Abstract: This paper studies self-excited stick-slip oscillations of a rotary drillstring with a drag bit. In previous researches coupling between torsional and axial vibration was studied for a system with two degrees of freedom and without considering the effects of rotary table, damping of drilling mud and active damping system. In this research, for the first time a complete model is considered. This model is a discrete model with two degrees of torsional freedom and one degree of axial freedom. Both frictional contact and cutting process at bit-rock interface have been considered by bit-rock interaction law. There is a coupling between torsional mode and the axial mode through this law. In this paper, the effects of damping, active damping ratios and bit-rock interaction number have been studied on stick-slip motion. The equations of motion have been solved by numerical method. The technique of solution is Euler-forward finite difference technique. This research shows that by increasing the damping of drilling mud, bit parameter and by appropriate selection of active damping ratios, stick-slip oscillation of bit can be avoided and oscillation of rotary table be damped. [Copyright &y& Elsevier]