Finite Amplitude Dynamics of a Flexible Spinning Disc

1995 ◽  
Author(s):  
N. Malhotra ◽  
N. Sri Namachchivaya ◽  
T. Whalen
Keyword(s):  
High Speed ◽  
Equations Of Motion ◽  
Finite Amplitude ◽  
Dominant Mode ◽  
Transverse Motion ◽  
Power Series Solution ◽  
Time Varying ◽  
Bending Rigidity ◽  
Shape Functions ◽  
Spinning Disc

Abstract The transverse dynamics of a high speed spinning disc which is clamped at the inner radius and rotating with a time-varying spin rate is examined in a space fixed frame of reference. The general nonlinear equations of motion governing the disc dynamics are systematically derived using displacement as well as stress function formulations. These equations of motion include the effects due to inherent bending rigidity, membrane stresses arising from centrifugal forces, non-axisymmetry of the in-plane and transverse displacements, geometric nonlinearities, aerodynamic damping arising from air stationary and moving with respect to the disc, parametric excitation due to time varying spin rate, etc. For the constant rotation case, the linearized equations of motion are solved by taking both membrane as well as flexural stiffness effects into account. This leads to a power series solution for the radial shape functions and harmonic solutions for the circumferential shape functions. The two-dimensional eigen-functions thus obtained can describe a disc mode with any number of nodal diameters and nodal circles, and the resulting eigen-frequencies match very well with the numerical results. The nonlinear and non-axisymmetric in-plane response is also determined, and a 2-DOF system of ODEs is obtained which governs the dynamic variation of the amplitudes of traveling waves associated with the dominant mode of the transverse motion.

Dynamics of Spinning Disc Parametrically Excited by Noise

1999 ◽  
Author(s):  
Narayanan Ramakrishnan ◽  
N. Sri Namachchivaya
Keyword(s):  
Equations Of Motion ◽  
Planck Equation ◽  
Stochastic Averaging ◽  
Transverse Motion ◽  
Probability Density Distribution ◽  
Integral Of Motion ◽  
Parametrically Excited ◽  
One Dimensional ◽  
Small Intensity ◽  
Spinning Disc

Abstract The nonlinear dynamics of a circular spinning disc parametrically excited by noise of small intensity is investigated. The governing PDEs are reduced using a Galerkin reduction procedure to a two-DOF system of ODEs which, govern the transverse motion of the disc. The dynamics is simplified by exploiting the S1 invariance of the equations of motion of the reduced system and further, reduced by performing stochastic averaging. The resulting one-dimensional Markov diffusive process is studied in detail. The stationary probability density distribution is obtained by solving the Fokker-Planck equation along with the appropriate boundary conditions. The boundary behaviour is studied using an asymptotic approach. Some aspects of dynamical and phenomenological bifurcations of the stationary solution are also investigated. The scheme of things presented here can be applied in principle to a four-dimensional Hamiltonian system possessing one integral of motion in addition to the hamiltonian and having one fixed point.

scholarly journals The Impact of Participation in PPP Projects on Total Factor Productivity of Listed Companies in China

2021 ◽  
Vol 13 (14) ◽  
pp. 7603
Author(s):  
Xiangdong Liu ◽  
Guangxi Cao
Keyword(s):  
Total Factor Productivity ◽  
High Speed ◽  
Operation Mode ◽  
Listed Companies ◽  
Financing Constraints ◽  
Eastern Region ◽  
Time Varying ◽  
Factor Productivity ◽  
The Impact ◽  
China’S Economy

The key to transforming China’s economy from high-speed growth to high-quality development is to improve total factor productivity (TFP). Based on the panel data of China’s listed companies participating in PPP (Public–Private Partnerships) projects from 2010 to 2019, this paper constructs the time-varying DID method to test the impact of participation in PPP projects on the company’s TFP empirically, explore the mechanism of the effect of participation in PPP projects on the company’s TFP, and then conduct heterogeneous analysis from four perspectives: region, industry, ownership form, and operation mode. The empirical results show that participation in PPP projects can significantly promote the growth of the company’s TFP, which mainly comes from the promotion of the innovation level of listed companies and the alleviation of financing constraints by participating in PPP projects. In addition, participation in PPP projects has a significant impact on TFP of listed companies in the eastern region, listed companies in the secondary and tertiary industries, state-owned listed companies, and listed companies participating in PPP projects under the BOT mode.

scholarly journals Does the Opening of High-Speed Railway Lines Reduce the Carbon Intensity of China’s Resource-Based Cities?

Energies ◽  
2021 ◽  
Vol 14 (15) ◽  
pp. 4648
Author(s):  
Zhipeng Tang ◽  
Ziao Mei ◽  
Jialing Zou
Keyword(s):  
High Speed ◽  
National Average ◽  
Carbon Intensity ◽  
Time Varying ◽  
Low Carbon ◽  
High Speed Railway ◽  
Different Types ◽  
Endogenous Selection ◽  
Mode Of Development ◽  
The Impact

The carbon intensity of China’s resource-based cities (RBCs) is much higher than the national average due to their relatively intensive mode of development. Low carbon transformation of RBCs is an important way to achieve the goal of reaching the carbon emissions peak in 2030. Based on the panel data from 116 RBCs in China from 2003 to 2018, this study takes the opening of high-speed railway (HSR) lines as a quasi-experiment, using a time-varying difference-in-difference (DID) model to empirically evaluate the impact of an HSR line on reducing the carbon intensity of RBCs. The results show that the opening of an HSR line can reduce the carbon intensity of RBCs, and this was still true after considering the possibility of problems with endogenous selection bias and after applying the relevant robustness tests. The opening of an HSR line is found to have a significant reducing effect on the carbon intensity of different types of RBC, and the decline in the carbon intensity of coal-based cities is found to be the greatest. Promoting migration of RBCs with HSR lines is found to be an effective intermediary way of reducing their carbon intensity.

Behavior of Unsteady Turbulent Starting Round Jets

2012 ◽  
Vol 134 (6) ◽  
Author(s):  
Neerav Abani ◽  
Jaal B. Ghandhi
Keyword(s):  
High Speed ◽  
Penetration Rate ◽  
Injection Rate ◽  
Injection Velocity ◽  
Time Varying ◽  
Velocity Change ◽  
Rate Of Penetration ◽  
Round Jets ◽  
The Difference ◽  
Sudden Decrease

Turbulent starting jets with time-varying injection velocities were investigated using high-speed schlieren imaging. Two solenoid-controlled injectors fed a common plenum upstream of an orifice; using different upstream pressures and actuation times, injection-rate profiles with a step increase or decrease in injection velocity were tested. The behavior of the jet was found to be different depending on the direction of the injection-velocity change. A step increase in injection velocity resulted in an increased rate of penetration relative to the steady-injection case, and a larger increase in injection velocity resulted in an earlier change in the tip-penetration rate. The step-increase data were found to be collapsed by scaling the time by a convective time scale based on the tip location at the time of the injection-velocity change and the difference in the injection velocities. A sudden decrease in injection velocity to zero was found to cause a deviation from the corresponding steady-pressure case at a time that was independent of the initial jet velocity, i.e., it was independent of the magnitude of the injection-velocity change. Two models for unsteady injection from the literature were tested and some deficiencies in the models were identified.

On a sphere performing linear and torsional oscillations in a viscous fluid

1988 ◽  
Vol 66 (7) ◽  
pp. 576-579
Author(s):  
G. T. Karahalios ◽  
C. Sfetsos
Keyword(s):  
Boundary Layer ◽  
Viscous Fluid ◽  
Secondary Flow ◽  
Small Amplitude ◽  
Equations Of Motion ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Time Varying ◽  
Torsional Oscillations

A sphere executes small-amplitude linear and torsional oscillations in a fluid at rest. The equations of motion of the fluid are solved by the method of successive approximations. Outside the boundary layer, a steady secondary flow is induced in addition to the time-varying motion.

Optimal Control of a Flexible Mechanism Using a Combined Feedforward-Feedback Strategy: Simulation and Experiment

1999 ◽  
Author(s):  
Hubertus v. Stein ◽  
Heinz Ulbrich
Keyword(s):  
Optimal Control ◽  
Control Strategy ◽  
System Performance ◽  
High Speed ◽  
Time Varying ◽  
Linkage Mechanism ◽  
Additional Degree ◽  
Control Approach ◽  
Feedback Optimal Control ◽  
Four Bar Linkage

Abstract Due to the elasticity of the links in modern high speed mechanisms, increasing operating speeds often lead to undesirable vibrations, which may render a required accuracy unattainable or, even worse, lead to a failure of the whole process. The dynamic effects e.g. may lead to intolerable deviations from the reference path or even to the instability of the system. Instead of suppressing the vibration by a stiffer design, active control methods may greatly improve the system performance and lead the way to a reduction of the mechanism’s weight. We investigate a four-bar-linkage mechanism and show that by introducing an additional degree of freedom for a controlled actuator and providing a suitable control strategy, the dynamically induced inaccuracies can be substantially reduced. The modelling of the four-bar-linkage mechanism as a hybrid multi body system and the modelling of the complete system (including the actuator) is briefly explained. From the combined feedforward-feedback optimal control approach presented in (v. Stein, Ulbrich, 1998) a time-varying output control law is derived that leads to a very good system performance for this linear discrete time-varying system. The experimental results show the effectiveness of the applied control strategy.

scholarly journals Strong Azimuthal Combustion Instabilities in a Spray Annular Chamber With Intermittent Partial Blow-Off

2017 ◽  
Vol 140 (3) ◽  
Author(s):  
Kevin Prieur ◽  
Daniel Durox ◽  
Thierry Schuller ◽  
Sébastien Candel
Keyword(s):  
Light Intensity ◽  
High Speed ◽  
Transverse Velocity ◽  
Pressure Fluctuations ◽  
Pressure Sensors ◽  
Nodal Line ◽  
Operating Conditions ◽  
Acoustic Energy ◽  
Transverse Motion ◽  
Azimuthal Mode

This article reports experiments carried out in the MICCA-spray combustor developed at EM2C laboratory. This system comprises 16 swirl spray injectors. Liquid n-heptane is injected by simplex atomizers. The combustion chamber is formed by two cylindrical quartz tubes allowing full optical access to the flame region and it is equipped with 12 pressure sensors recording signals in the plenum and chamber. A high-speed camera provides images of the flames and photomultipliers record the light intensity from different flames. For certain operating conditions, the system exhibits well defined instabilities coupled by the first azimuthal mode of the chamber at a frequency of 750 Hz. These instabilities occur in the form of bursts. Examination of the pressure and the light intensity signals gives access to the acoustic energy source term. Analysis of the phase fluctuations between the two signals is carried out using cross-spectral analysis. At limit cycle, large pressure fluctuations of 5000 Pa are reached, and these levels persist over a finite period of time. Analysis of the signals using the spin ratio indicates that the standing mode is predominant. Flame dynamics at the pressure antinodal line reveals a strong longitudinal pulsation with heat release rate oscillations in phase and increasing linearly with the acoustic pressure for every oscillation levels. At the pressure nodal line, the flames are subjected to large transverse velocity fluctuations leading to a transverse motion of the flames and partial blow-off. Scenarios and modeling elements are developed to interpret these features.

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