Phase-Shift Determination in Coriolis Flowmeters With Added Masses

2010 ◽  
Author(s):  
Mergen H. Ghayesh ◽  
Marco Amabili ◽  
Michael P. Pai¨doussis
Keyword(s):  
Phase Shift ◽  
Equation Of Motion ◽  
Approximate Analytic Solution ◽  
Analytical Technique ◽  
Flow Prediction ◽  
At Resonance ◽  
Coriolis Flowmeter ◽  
Added Masses ◽  
Measuring Tube ◽  
Secular Terms

In this study, an approximate analytic solution for phase-shift (and thus mass flow) prediction along the length of the measuring tube of a Coriolis flowmeter is investigated. A single, straight measuring tube is considered; added masses at the sensor locations, are included in the model, and thus in the equation of motion. The method of multiple timescales, an approximate analytical technique, has been applied directly to the equation of motion, and the equations of order one and epsilon have been obtained analytically for the system at resonance. The solution of the equation of motion is obtained by satisfying the solvability condition (making the solution of order epsilon free of secular terms). The measuring tube is excited by the driver, and the phase-shift is measured at two symmetrically located points on either side of the mid-length of the tube. The effects of system parameters on the measured phase-shift are discussed.

Frequency Shifts of Micro and Nano Cantilever Beam Resonators Due to Added Masses

2016 ◽  
Vol 138 (9) ◽  
Author(s):  
Adam Bouchaala ◽  
Ali H. Nayfeh ◽  
Mohammad I. Younis
Keyword(s):  
Hybrid Approach ◽  
Specific Antigen ◽  
Galerkin Approximation ◽  
Higher Order ◽  
Mass Detection ◽  
Numerical Techniques ◽  
Frequency Shifts ◽  
Analytical Technique ◽  
Higher Order Modes ◽  
Added Masses

We present analytical and numerical techniques to accurately calculate the shifts in the natural frequencies of electrically actuated micro and nano (carbon nanotubes (CNTs)) cantilever beams implemented as resonant sensors for mass detection of biological entities, particularly Escherichia coli (E. coli) and prostate specific antigen (PSA) cells. The beams are modeled as Euler–Bernoulli beams, including the nonlinear electrostatic forces and the added biological cells, which are modeled as discrete point masses. The frequency shifts due to the added masses of the cells are calculated for the fundamental and higher-order modes of vibrations. Analytical expressions of the natural frequency shifts under a direct current (DC) voltage and an added mass have been developed using perturbation techniques and the Galerkin approximation. Numerical techniques are also used to calculate the frequency shifts and compared with the analytical technique. We found that a hybrid approach that relies on the analytical perturbation expression and the Galerkin procedure for calculating accurately the static behavior presents the most computationally efficient approach. We found that using higher-order modes of vibration of micro-electro-mechanical-system (MEMS) beams or miniaturizing the sizes of the beams to nanoscale leads to significant improved frequency shifts, and thus increased sensitivities.

Accelerated HPSTM: An efficient semi-analytical technique for the solution of nonlinear PDE’s

2020 ◽  
Vol 9 (1) ◽  
pp. 329-337
Author(s):  
Deepak Grover ◽  
Dinkar Sharma ◽  
Prince Singh
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Series Solution ◽  
Nonlinear Partial Differential Equation ◽  
Transformation Method ◽  
Proportional Delay ◽  
Approximate Analytic Solution ◽  
Partial Differential ◽  
Analytical Technique ◽  
Homotopy Perturbation

AbstractIn this paper a novel technique i.e. accelerated homotopy perturbation Sumudu transformation method (AHPSTM), which is a hybrid of accelerated homotopy perturbation method and Sumudu transformation to obtain an approximate analytic solution of nonlinear partial differential equation (PDE) with proportional delay, is used. This approach is based on the new form of calculating He’s polynomial, which accelerates the convergence of the series solution. The series solutions obtained from the proposed method are found to converge rapidly to exact solution. In order to affirm the effectiveness and legitimacy of proposed method, the proposed technique is implemented on nonlinear partial differential equation (PDE) with proportional delay. The condition of convergence of series solution is analyzed. Moreover, statistical analysis has been performed to analyze the outcome acquired by AHPSTM and other semi-analytic techniques.

Thermo-mechanical phase-shift determination in Coriolis mass-flowmeters with added masses

2012 ◽  
Vol 34 ◽  
pp. 1-13 ◽  
Author(s):  
Mergen H. Ghayesh ◽  
Marco Amabili ◽  
Michael P. Païdoussis
Keyword(s):  
Phase Shift ◽  
Added Masses

An Advanced Numerical Model for Single Straight Tube Coriolis Flowmeters

2006 ◽  
Vol 128 (6) ◽  
pp. 1346-1350 ◽  
Author(s):  
Tao Wang ◽  
Roger C. Baker ◽  
Yousif Hussain
Keyword(s):  
Finite Element Method ◽  
Numerical Model ◽  
Sensitivity Factor ◽  
Straight Tube ◽  
Modal Frequency ◽  
Shell Elements ◽  
Structure Interaction ◽  
Coriolis Flowmeter ◽  
Measuring Tube ◽  
Stiffness And Damping

A detailed numerical model has been developed to simulate the single straight tube Coriolis flowmeter, which includes all important practical features. The measuring tube is modeled as fluid-tube interaction elements characterized as mass, stiffness, and damping matrices based on the theories of fluid-structure interaction and finite element method. Other features, such as the inner and outer cases and the driver spring, are modeled as standard ANSYS beam and shell elements and coupled to the measuring tube. The modal frequency and sensitivity factor from experiments are used to validate the model. In particular, our results show that the modal behaviour of the meter can only be adequately modeled if these practical features are included.

scholarly journals Optimal Auxiliary Functions Method for a Pendulum Wrapping on Two Cylinders

Mathematics ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 1364 ◽  
Author(s):  
Vasile Marinca ◽  
Nicolae Herisanu
Keyword(s):  
Natural Frequency ◽  
Analytical Solutions ◽  
Nonlinear Oscillations ◽  
Equation Of Motion ◽  
Numerical Examples ◽  
Analytical Technique ◽  
Auxiliary Functions ◽  
Lagrange’S Equation ◽  
Good Agreement

In the present work, the nonlinear oscillations of a pendulum wrapping on two cylinders is studied by means of a new analytical technique, namely the Optimal Auxiliary Functions Method (OAFM). The equation of motion is derived from the Lagrange’s equation. Analytical solutions and natural frequency of the system are calculated. Our results obtained through this new procedure are compared with numerical ones and a very good agreement was found, which proves the accuracy of the method. The presented numerical examples show that the proposed approach is simple, easy to implement and very accurate.

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