scholarly journals Post-buckling dynamics of spherical shells

2021 ◽  
Vol 477 (2253) ◽  
pp. 20210378 ◽  
Author(s):  
Marcel Mokbel ◽  
Adel Djellouli ◽  
Catherine Quilliet ◽  
Sebastian Aland ◽  
Gwennou Coupier
Keyword(s):  
Theoretical Model ◽  
Acoustic Waves ◽  
Three Dimensional ◽  
Spherical Shells ◽  
Dissipation Mechanism ◽  
Post Buckling ◽  
Buckled State

We explore the intrinsic dynamics of spherical shells immersed in a fluid in the vicinity of their buckled state, through experiments and three-dimensional axisymmetric simulations. The results are supported by a theoretical model that accurately describes the buckled shell as a two-variable-only oscillator. We quantify the effective ‘softening’ of shells above the buckling threshold, as observed in recent experiments on interactions between encapsulated microbubbles and acoustic waves. The main dissipation mechanism in the neighbouring fluid is also evidenced.

Stability and instability of some nonlinear dispersive solitary waves in higher dimension

1996 ◽  
Vol 126 (1) ◽  
pp. 89-112 ◽  
Author(s):  
Anne de Bouard
Keyword(s):  
Solitary Waves ◽  
Acoustic Waves ◽  
Vries Equation ◽  
Three Dimensional ◽  
Higher Dimension ◽  
Ion Acoustic Waves ◽  
Stability And Instability ◽  
Ion Acoustic ◽  
De Vries ◽  
The Stability

We study the stability of positive radially symmetric solitary waves for a three dimensional generalisation of the Korteweg de Vries equation, which describes nonlinear ion-acoustic waves in a magnetised plasma, and for a generalisation in dimension two of the Benjamin–Bona–Mahony equation.

Non-Linear Dynamic Stability of Shallow Reticulated Spherical Shells

2011 ◽  
Vol 142 ◽  
pp. 107-110
Author(s):  
Ming Jun Han ◽  
You Tang Li ◽  
Ping Qiu ◽  
Xin Zhi Wang
Keyword(s):  
Three Dimensional ◽  
Dynamical Equations ◽  
Third Order ◽  
Spherical Shells ◽  
Nonlinear Dynamical ◽  
Linear Dynamic ◽  
The Third ◽  
Displacement Mode ◽  
Nonlinear Forced Vibration ◽  
The Stability

The nonlinear dynamical equations are established by using the method of quasi-shells for three-dimensional shallow spherical shells with circular bottom. Displacement mode that meets the boundary conditions of fixed edges is given by using the method of the separate variable, A nonlinear forced vibration equation containing the second and the third order is derived by using the method of Galerkin. The stability of the equilibrium point is studied by using the Floquet exponent.

Three-Dimensional Analysis of Closed-Die Forging Processes: Part 1: Formulation

1989 ◽  
Vol 203 (1) ◽  
pp. 33-37 ◽  
Author(s):  
C F Lugora ◽  
A N Bramley
Keyword(s):  
Theoretical Model ◽  
Energy Dissipation ◽  
Metal Flow ◽  
Three Dimensional ◽  
Total Rate ◽  
Die Forging ◽  
Closed Die Forging ◽  
Proposed Model ◽  
Optimum Velocity ◽  
Forging Load

In this series of papers, a theoretical model based on the upper bound elemental technique is presented for prediction of forging load and metal flow in three-dimensional closed-die forging processes. Three basic elements are introduced in order to partition a forging into simple elementary regions. An optimum velocity distribution within the forging is obtained by minimizing the total rate of energy dissipation using a simplex optimizing procedure. Applications of the proposed model are discussed in Part 2.

A Pulsed Wire Probe for the Measurement of Velocity and Flow Direction in Slowly Moving Air

1984 ◽  
Vol 106 (1) ◽  
pp. 72-78 ◽  
Author(s):  
D. E. Olson ◽  
K. H. Parker ◽  
B. Snyder
Keyword(s):  
Heat Transfer ◽  
Theoretical Model ◽  
Spatial Resolution ◽  
Flow Direction ◽  
Three Dimensional ◽  
Velocity Fields ◽  
Transport Time ◽  
Wire Probe ◽  
Circular Pipes ◽  
Measured Flow

This report describes the theory and operation of a pulsed-probe anemometer designed to measure steady three-dimensional velocity fields typical of pulmonary tracheo-bronchial airflows. Local velocities are determined by measuring the transport time and orientation of a thermal pulse initiated at an upstream wire and sensed at a downstream wire. The transport time is a reproducible function of velocity and the probe wire spacing, as verified by a theoretical model of convective heat transfer. When calibrated the anemometer yields measurements of velocity accurate to ±5 percent and resolves flow direction to within 1 deg at airspeeds ≥10 cm/s. Spatial resolution is ±0.5 mm. Measured flow patterns typical of curved circular pipes are included as examples of its application.

scholarly journals New Explicit Solutions to the Fractional-Order Burgers’ Equation

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
M. Hafiz Uddin ◽  
Mohammad Asif Arefin ◽  
M. Ali Akbar ◽  
Mustafa Inc
Keyword(s):  
Differential Equations ◽  
Rational Function ◽  
Acoustic Waves ◽  
Burgers Equation ◽  
Three Dimensional ◽  
Wall Friction ◽  
Weakly Nonlinear ◽  
Bubbly Liquids ◽  
Fractional Differential ◽  
Accuracy Of Results

The closed-form wave solutions to the time-fractional Burgers’ equation have been investigated by the use of the two variables G ′ / G , 1 / G -expansion, the extended tanh function, and the exp-function methods translating the nonlinear fractional differential equations (NLFDEs) into ordinary differential equations. In this article, we ascertain the solutions in terms of tanh , sech , sinh , rational function, hyperbolic rational function, exponential function, and their integration with parameters. Advanced and standard solutions can be found by setting definite values of the parameters in the general solutions. Mathematical analysis of the solutions confirms the existence of different soliton forms, namely, kink, single soliton, periodic soliton, singular kink soliton, and some other types of solitons which are shown in three-dimensional plots. The attained solutions may be functional to examine unidirectional propagation of weakly nonlinear acoustic waves, the memory effect of the wall friction through the boundary layer, bubbly liquids, etc. The methods suggested are direct, compatible, and speedy to simulate using algebraic computation schemes, such as Maple, and can be used to verify the accuracy of results.

Numerical and theoretical analyses of the dynamics of droplets driven by electrowetting on dielectric in a Hele-Shaw cell

2018 ◽  
Vol 839 ◽  
pp. 468-488 ◽  
Author(s):  
Yasufumi Yamamoto ◽  
Takahiro Ito ◽  
Tatsuro Wakimoto ◽  
Kenji Katoh
Keyword(s):  
Theoretical Model ◽  
Contact Line ◽  
Three Dimensional ◽  
Simulation Method ◽  
Movement Speed ◽  
Electrowetting On Dielectric ◽  
Moving Contact Line ◽  
Moving Contact ◽  
Droplet Movement ◽  
Hele Shaw Cell

Droplet movement by electrowetting on dielectric (EWOD) in a Hele-Shaw cell is analysed theoretically and numerically. We propose a simple theoretical model for the motion, which describes well the voltage dependency of droplet speed below the saturation voltage as measured experimentally. The simulation method for numerical analyses is constructed by using the Young–Lippmann equation to represent EWOD and the generalised Navier boundary condition to represent the moving contact line in the context of the front-tracking method. With an adjusted slip parameter, the present full three-dimensional numerical simulation reproduces well the shape evolution and movement speed of droplets as observed experimentally. We verify the proposed theoretical model in numerical experiments with various shapes and voltages. Furthermore, we analyse theoretically the behaviour of the contact line at the onset of droplet motion as observed in the simulation and experiment, and we are able to estimate very well the time scale on which the contact angle changes.

Role of Freestream Slow Acoustic Waves in a Hypersonic Three-Dimensional Boundary Layer

AIAA Journal ◽  
2018 ◽  
Vol 56 (9) ◽  
pp. 3570-3584 ◽  
Author(s):  
Guoliang Xu ◽  
Gang Liu ◽  
Jianqiang Chen ◽  
Song Fu
Keyword(s):  
Boundary Layer ◽  
Acoustic Waves ◽  
Three Dimensional ◽  
Dimensional Boundary

Numerical Simulation of a Particle in Air Flow Around a Turbine Blade

2020 ◽  
Author(s):  
Ippei Oshima ◽  
Mikito Furuichi
Keyword(s):  
Numerical Simulation ◽  
Theoretical Model ◽  
Turbine Blade ◽  
Gas Flow ◽  
Three Dimensional ◽  
Prediction Method ◽  
Stokes Number ◽  
Lagrangian Simulation ◽  
Background Gas ◽  
Liquid Mass Flow Rate

Abstract The Steam turbine is widely used for generating electricity, in the thermal, nuclear and geothermal power generation systems. A wet loss is known as one of the degrading factors of the performance. To reduce the amount of liquid phase generated by condensation and atomization from nozzles, the prediction of the distribution of liquid mass flow rate inside the turbine is important. However, the quantitative understanding and the prediction method of the liquid flow inside the turbine remain unclear because physics inside a turbine is consisting of complex multiscale and multiphase events. In the present study, we proposed a theoretical model predicting the motion of droplet particles in gas flow based on Stokes number whose model does not require numerical simulation. We also conducted the numerical validation test using three-dimensional Eulerian-Lagrangian simulation for the problem with turbine blade T106. The numerical simulation shows that the particle motion is characterized by the Stokes number, that is consistent with the assumption of the theoretical model and previous studies. When Stokes number is smaller than one, the particle trajectory just follows the gas flow streamline and avoids the impacts on the surface of T106. With increasing Stokes number, the particles begin to deviate from the gas flow. As a result, many particles collide with the surface of T106 when the Stokes number is approximately one. When the Stokes number is extremely larger than one, particles move straight regardless of the background gas flow. The good agreements between the theoretical predictions and numerical experiment results justify the use of our proposed theoretical model for the prediction of the particle flow around the turbine blade.

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