scholarly journals A Combined Energy Method for Flutter Instability Analysis of Weakly Damped Panels in Supersonic Airflow

Mathematics ◽  
2021 ◽  
Vol 9 (10) ◽  
pp. 1090
Author(s):  
Xiaochen Wang ◽  
Zhichun Yang ◽  
Guiwei Zhang ◽  
Xinwei Xu
Keyword(s):  
Energy Balance ◽  
Energy Method ◽  
Plate Theory ◽  
Dynamic Pressure ◽  
Physical Nature ◽  
Aeroelastic System ◽  
Dissipation Energy ◽  
Supersonic Airflow ◽  
Flutter Instability ◽  
Modal Damping

A combined energy method is proposed to investigate the flutter instability characteristics of weakly damped panels in the supersonic airflow. Based on the small damping assumption, the motion governing partial differential equation (PDE) of the panel aeroelastic system, is built by adopting the first-order piston theory and von Karman large deflection plate theory. Then by applying the Galerkin procedure, the PDE is discretized into a set of coupled ordinary differential equations, and the system reduced order model (ROM) with two degrees of freedom is obtained. Considering that the panel aeroelastic system is non-conservative in the physical nature, and assuming that the panel exhibits a single period oscillation on the flutter occurrence, the non-conservative energy balance principle is applied to the linearized ROM within one single oscillation period. The obtained result shows that the ROM modal coordinate amplitudes ratio is regulated by the modal damping coefficients ratio, though each modal damping coefficient is small. Furthermore, as the total damping dissipation energy can be eliminated due to its smallness, the He’s energy balance method is applied to the undamped ROM, therefore the critical non-dimensional dynamic pressure on the flutter instability occurrence, and the oscillation circular frequency amplitude relationship (linear and nonlinear form) are derived. In addition, the damping destabilization paradoxical influence on the system flutter instability is investigated. The accuracy and efficiency of the proposed method are validated by comparing the results with that obtained by using Routh Hurwitz criteria.

Calculation for Elastic Global Buckling of Sandwich Plates with Ribs

2012 ◽  
Vol 188 ◽  
pp. 25-30 ◽  
Author(s):  
Qi Chao Xue ◽  
Guang Ping Zou ◽  
Ye Wu ◽  
Hai Lin Xiong ◽  
Meng Chai
Keyword(s):  
Energy Method ◽  
Sandwich Plate ◽  
Plate Theory ◽  
Sandwich Plates ◽  
Buckling Stress ◽  
Global Buckling ◽  
Simple Support ◽  
Rectangular Sandwich Plate ◽  
Two Sides ◽  
Rectangular Sandwich Plates

Based on Reissner’s sandwich plate theory, the critical globlal buckling equation of sandwich plate with ribs is deduced by energy method under simple support boundary conditions. And the critical buckling solution is obtained and discussed here. Afterwards a rectangular sandwich plate with steel faceplate and polyurthane core is taken as an example. The influence on critical global buckling stress with different inertia moments in rectangular sandwich plates are discussed. simularly the effect of the lengh ratio of two sides and the thickness of rectangular sandwich plate are also studied.

The Effect of Structural Parameters on Response Characteristics of Aeroelastic System in the Presence of Dynamic Stall

2021 ◽  
Author(s):  
Zhan Qiu ◽  
Fuxin Wang
Keyword(s):  
Limit Cycle ◽  
Structural Parameters ◽  
Dynamic Pressure ◽  
Angle Of Attack ◽  
Dynamic Stall ◽  
System Response ◽  
Structural Stiffness ◽  
Aeroelastic System ◽  
Equilibrium Angle ◽  
Minimum Angle

Abstract The effect of structural paramters on the response and aerodynamic stiffness characteristics of the free aeroelastic system under the influence of dynamic stall is investigated adopting CFD (Computational Fluid Dynamics) method. The equilibrium angle of the spring and the structural stiffness are taken as parameters of interest. Systems with small equilibrium angles enter the symmetric limit-cycle state more quickly after a Hopf bifurcation and experience dynamic stall in both directions, rather than slowly decreasing in minimum angle of attack and remaining in the asymmetric limit-cycle state before dynamic stall in the opposite direction, as is the case with systems with large spring equilibrium angles. Thus, aerodynamic stiffness of system with large equilibrium angles can be more significantly influenced by the change in aerodynamic moment characteristics at the minimum angle of attack. Furthermore, by increasing the initial angular velocity, we find that the system response all becomes symmetric limit cycle and therefore the aerodynamic stiffness appears to have a monotonically increasing characteristic. As to the effect of structural stiffness, it is found that the limit cycle amplitude first increases with structural stiffness after bifurcation, then the amplitude is unchanged with varying structural stiffness at higher Mach number. Energy maps show that the parametric distribution of the energy transfer contributes to this phenomenon. Moreover, when entering the symmetric limit cycle state, the structural stiffness no longer has a significant effect on the aerodynamic stiffness of the system, as the increase in the aerodynamic stiffness is determined solely by the increase in dynamic pressure without the effect of changes in moment characteristics.

Existence and Energy Balance of the Solar Dynamo

1993 ◽  
Vol 157 ◽  
pp. 19-23
Author(s):  
J.H.G.M. van Geffen
Keyword(s):  
Magnetic Field ◽  
Energy Balance ◽  
Energy Method ◽  
Magnetic Energy ◽  
Mean Field ◽  
Solar Dynamo ◽  
Ensemble Averaging ◽  
Dynamo Theory ◽  
The Magnetic Field ◽  
Mean Field Dynamo

The idea behind the use of ensemble averaging and the finite magnetic energy method of van Geffen and Hoyng (1992) is briefly discussed. Applying this method to the solar dynamo shows that the turbulence — an essential ingredient of traditional mean field dynamo theory — poses grave problems: the turbulence makes the magnetic field so unstable that it becomes impossible to recognize any period.

Coupled Blade-Disk-Shroud Flutter Instabilities in Turbojet Engine Rotors

1967 ◽  
Vol 89 (3) ◽  
pp. 419-426 ◽  
Author(s):  
F. O. Carta
Keyword(s):  
Energy Method ◽  
Empirical Data ◽  
Parametric Study ◽  
Vibration Modes ◽  
Coupled Vibration ◽  
Flutter Instability ◽  
Rotating Blade ◽  
Turbojet Engine ◽  
High Incidence ◽  
Engine Rotors

An energy method is used to investigate a flutter instability of turbojet engine rotors which is caused by the interactions between unsteady air loading and the coupled vibration modes of the rotating blade-disk-shroud system. It is shown, analytically, in this parametric study that under certain circumstances the coupling between blade modes permits the transfer of energy from the air to the blade-disk-shroud system, giving rise to a self-excited instability. Both unsteady potential flow theory and empirical data for oscillating airfoils at high incidence are used.

Basic types of glazing with low-emissivity layers and their effects

2016 ◽  
Vol 7 (1) ◽  
pp. 45-50 ◽  
Author(s):  
R. Rabenseifer
Keyword(s):  
Energy Balance ◽  
High Performance ◽  
Physical Nature ◽  
Visual Comfort ◽  
Surface Emissivity ◽  
Advantages And Disadvantages

The article deals with the importance of low-emissivity glazing layers to improve energy balance and their significance in maintaining interior visual comfort. It describes the physical nature of radiation and the associated surface emissivity and the effects of changes in surface emissivity of glass, depending on the position of the low-emissivity layer. The paper also discusses principles, advantages and disadvantages of the most common combinations of glass and a low-emissivity layer the so-called “high performance” glass and the so-called “low-e” glass.

scholarly journals Study on Safety Control of Composite Roof in Deep Roadway Based on Energy Balance Theory

2019 ◽  
Vol 11 (13) ◽  
pp. 3688 ◽  
Author(s):  
Zhengzheng Xie ◽  
Nong Zhang ◽  
Yuxin Yuan ◽  
Guang Xu ◽  
Qun Wei
Keyword(s):  
Energy Balance ◽  
Energy Release ◽  
Coal Mine ◽  
Balance Theory ◽  
Dissipation Energy ◽  
Safety Control ◽  
Deformation Control ◽  
Low Dissipation ◽  
Coal Rock ◽  
Safety And Stability

Improving the safety and stability of composite roof in deep roadway is the strong guarantee for safe mining and sustainable development of coal mines. With three roadways of different composite roofs in Hulusu Coal Mine and Menkeqing Coal Mine as the research background, this paper explores the mechanical properties and energy dissipation law of coal-rock structures with different height ratios from the perspective of energy release and dissipation through lab experiments. The results indicate that the key to the stability of coal-rock structures lies in maintaining relatively low dissipation energy. Based on experimental results and the energy balance theory, two support principles were put forward and applied to experimental roadways. The field monitoring results show that the anchoring force on different composite roof displays different characteristics, proving that the work done by the support can adjust timely to the energy release and conversion so as to improve the safety and stability of roadways with different composite roofs. This study provides a reference for the deformation control in deep roadways with composite roofs under similar conditions.

Effects of Squeeze Film and Initial Deflection on the Resonance Frequencies and Modal Damping of Circular Microplates

2018 ◽  
Author(s):  
Aymen Jallouli ◽  
Najib Kacem ◽  
Fehmi Najar ◽  
Joseph Lardies
Keyword(s):  
Plate Theory ◽  
Differential Quadrature Method ◽  
Static Solution ◽  
Initial Deflection ◽  
Mode Shapes ◽  
Squeeze Film ◽  
Modal Damping ◽  
Resonance Frequencies ◽  
Grid Points ◽  
Air Film

We investigate the effects of squeeze air film and initial deflection on the resonance frequencies and modal damping of capacitive circular microplates. The equation of motion of a circular microplate, which are derived from the von kármán plate theory, coupled with the Reynolds equation are discretized using the Differential Quadrature Method (DQM). The eigenvalues and eigenvectors of the multiphysical problem are determined by perturbing the system of equations around a static solution. Therefore, the resonance frequencies, modal damping coefficients and mode shapes of the plate and the fluid can be determined. The advantage of using DQM is that the solution of the system can be obtained with only few grid points. The obtained numerical results are compared with the experimental data for the case of a capacitive circular microplates with an initial deflection. The increase of the static pressure leads to a shift in the resonance frequencies due to the increase in the stiffness of the plate. Also the initial deflection change the resonance frequencies due to the change in the effective gap distance. The developed model is an effective tool to predict the dynamic behavior of a microsystem under the effect of air film and with initial deflection.

On the Energetics of a Mechatronic Elevator System

2015 ◽  
Vol 137 (8) ◽  
Author(s):  
Kun-Yung Chen ◽  
Rong-Fong Fung
Keyword(s):  
Energy Balance ◽  
Balance Equation ◽  
Electrical Energy ◽  
Energy Balance Equation ◽  
Weighting Factor ◽  
Mechatronic System ◽  
Energy Control ◽  
Dissipation Energy ◽  
Calculus Of Variation ◽  
Total Input

The energy balance equation consisting of mechanical and electrical parts of a mechatronic elevator system is studied in this paper. The total input energy is equal to the mechanical and electrical energies, where a weighting factor should be added for the mechatronic system. The calculus of variation is implemented to find the minimum input electrical energy control (MIEEC) and minimum dissipation energy control (MDEC), which are compared and found to have the same results. From numerical simulations, it is confirmed to demonstrate that the energy balance equation must contain a weighting factor in a mechatronic system.

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