scholarly journals Multiple-scales analysis on high speed and high frequency pressure waves induced by liquid compressibility in bubbly liquids

2018 ◽  
Author(s):  
Ryosuke Akutsu ◽  
Tetsuya Kanagawa ◽  
Yusuke Uchiyama
Keyword(s):  
High Frequency ◽  
High Speed ◽  
Multiple Scales ◽  
Pressure Waves ◽  
Bubbly Liquids ◽  
Liquid Compressibility ◽  
Multiple Scales Analysis

Weakly Nonlinear and High Speed Propagation of Quasi-Monochromatic High Frequency Waves in Compressible Bubbly Liquids

2019 ◽  
Author(s):  
Takanori Yoshimoto ◽  
Tetsuya Kanagawa
Keyword(s):  
High Speed ◽  
Bubble Dynamics ◽  
Multiple Scales ◽  
Compressible Liquid ◽  
Governing Equations ◽  
Nls Equation ◽  
Weakly Nonlinear ◽  
Bubbly Liquids ◽  
High Frequency Waves ◽  
Correction Terms

Abstract This study theoretically investigates plane progressive quasi-monochromatic waves in an initially quiescent compressible liquid containing many spherical gas bubbles, on the basis of the derivation of a nonlinear wave equation that represents waves propagating at a high phase velocity induced by taking the effect of liquid compressibility in consideration. The governing equations for bubbly flows are composed of the conservation equations of mass and momentum, the equation of bubble dynamics as radial oscillations, and so on. By using the method of multiple scales with an appropriate choice of set of scaling relations of nondimensional parameters, the nonlinear Schrödinger (NLS) equation with an attenuation term and some correction terms can be derived from the governing equations. The decrease in the group velocity in a far field is then clarified. The dependence of waveform on wavenumber is implied.

Bifurcations of a Planar Pendulum Driven at a Tilted Angle

2005 ◽  
Author(s):  
Mike A. Koplow ◽  
Brian P. Mann
Keyword(s):  
Approximate Solution ◽  
High Frequency ◽  
Multiple Scales ◽  
Experimental Tests ◽  
Free Oscillations ◽  
Pendulum System ◽  
Small Deviations ◽  
Tilted Angle ◽  
Multiple Scales Analysis ◽  
Bifurcation Behavior

This paper examines the bifurcation behavior of a planar pendulum subjected to high-frequency parametric excitation along a tilted angle. Analytical and numerical results show that small deviations from either a perfectly vertical or horizontal excitation will result in symmetry breaking bifurcations. This behavior is confirmed through a series of experimental tests. Additionally, a multiple scales analysis is used to obtain an approximate solution for the free oscillations of a viscously damped planar pendulum. System identification is performed by comparing the approximate solution to transient experimental data.

Sign in / Sign up

Export Citation Format

Share Document