A stochastic second-order and two-scale thermo-mechanical model for strength prediction of concrete materials

2016 ◽  
Vol 108 (8) ◽  
pp. 885-901 ◽  
Author(s):  
Xiaofei Guan ◽  
Haitao Yu ◽  
Xia Tian
Keyword(s):  
Mechanical Model ◽  
Second Order ◽  
Strength Prediction ◽  
Concrete Materials

scholarly journals The method of multiscale virtual power for the derivation of a second order mechanical model

2016 ◽  
Vol 99 ◽  
pp. 53-67 ◽  
Author(s):  
P.J. Blanco ◽  
P.J. Sánchez ◽  
E.A. de Souza Neto ◽  
R.A. Feijóo
Keyword(s):  
Mechanical Model ◽  
Second Order ◽  
Virtual Power

Influence of Blade Flexibility on the Dynamic Response Simulation of a Turbomolecular Pump on Magnetic Bearings

2020 ◽  
Vol 142 (4) ◽  
Author(s):  
Alysson Bruno Barbosa Moreira ◽  
Fabrice Thouverez
Keyword(s):  
Mechanical Model ◽  
Equations Of Motion ◽  
Low Frequency ◽  
Coupled System ◽  
Forced Response ◽  
Second Order ◽  
Magnetic Bearings ◽  
Flexible System ◽  
Turbomolecular Pump ◽  
Rigid Body Modes

Abstract This paper proposes the simulation of a complete mechanical model of a turbomolecular pump rotor, including rotor and blades flexibility, suspended by controlled active magnetic bearings. The mechanical model is composed of an eight stage blisk, attached to a shaft. Magnetic forces are linearized by the first-order Taylor expansion around a given point. Including blades and rotor flexibility makes the mechanical system asymmetric, so the equations of motion for the coupled system have periodic terms. A modal controller was designed to control rigid body modes, since the number of sensors is limited and no state observer is implemented. PID controllers are used for low frequency modes combined with the second order filters to damp high frequency modes. First of all, stability analysis was carried out for the axisymmetric case. Second, blades flexibility was included. Forced response of the whole system to an impulsive force was studied. Divergent responses for the system in rotation were obtained as a second order filter pole possibly interacting with blades modes. Taking the second order filters off the control loop allowed the system to be stable. These results show that the analysis method developed here is efficient to evaluate the performance of a controller in closed loop with the complete flexible system. This method may be used in industrial design processes as computation times for the complete system are very short.

Influence of Blade Flexibility on the Dynamic Response Simulation of a Turbomolecular Pump on Magnetic Bearings

2019 ◽  
Author(s):  
Alysson Bruno Barbosa Moreira ◽  
Fabrice Thouverez
Keyword(s):  
Mechanical Model ◽  
Equations Of Motion ◽  
Low Frequency ◽  
Coupled System ◽  
Forced Response ◽  
Second Order ◽  
Magnetic Bearings ◽  
Flexible System ◽  
Turbomolecular Pump ◽  
Rigid Body Modes

Abstract This paper proposes the simulation of a complete mechanical model of a turbomolecular pump rotor, including rotor and blades flexibility, suspended by controlled active magnetic bearings. The mechanical model is composed of an eight stage blisk, attached to a shaft. Magnetic forces are linearized by first order Taylor expansion around a given point. Including blades and rotor flexibility makes the mechanical system asymmetric, so the equations of motion for the coupled system have periodic terms. A modal controller was designed to control rigid body modes, since the number of sensors is limited and no state observer is implemented. PID controllers are used for low frequency modes combined with second order filters to damp high frequency modes. First of all, stability analysis was carried out for the axisymmetric case. Secondly, blades flexibility was included. Forced response of the whole system to an impulsive force was studied. Divergent responses for the system in rotation were obtained as a second order filter pole possibly interacts with blades modes. Taking second order filters off the control loop allowed the system to be stable. These results show that the analysis method developed here is efficient to evaluate the performance of a controller in closed loop with the complete flexible system. This method may be used in industrial design processes as computation times for the complete system are very short.

Disappearance Voltage Determinations Using a Convergent Beam

1971 ◽  
Vol 29 ◽  
pp. 184-185
Author(s):  
W. L. Bell
Keyword(s):  
Second Order ◽  
Objective Method ◽  
Uniform Thickness ◽  
Rocking Curve ◽  
Crystal Perfection ◽  
Kikuchi Line ◽  
Central Maximum ◽  
Diffraction Patterns ◽  
Convergent Beam ◽  
Beam Technique

Disappearance voltages for second order reflections can be determined experimentally in a variety of ways. The more subjective methods, such as Kikuchi line disappearance and bend contour imaging, involve comparing a series of diffraction patterns or micrographs taken at intervals throughout the disappearance range and selecting that voltage which gives the strongest disappearance effect. The estimated accuracies of these methods are both to within 10 kV, or about 2-4%, of the true disappearance voltage, which is quite sufficient for using these voltages in further calculations. However, it is the necessity of determining this information by comparisons of exposed plates rather than while operating the microscope that detracts from the immediate usefulness of these methods if there is reason to perform experiments at an unknown disappearance voltage.The convergent beam technique for determining the disappearance voltage has been found to be a highly objective method when it is applicable, i.e. when reasonable crystal perfection exists and an area of uniform thickness can be found. The criterion for determining this voltage is that the central maximum disappear from the rocking curve for the second order spot.

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