Non-linear acoustic response of a spherical bubble - Texas A&M University (TAMU) Scholar

A NONLINEAR ANALYSIS IS PRESENTED FOR THE RADIAL OSCILLATIONS OF A SPHERICAL GAS BUBBLE IMMERSED IN AN INVISCID, SLIGHTLY COMPRESSIBLE FLUID.THE RESPONSE OF THE BUBBLE TO A PLANE, PRESSURE-WAVE TRAIN WHOSE WAVELENGTH IS LARGE COMPARED WITH THE RADIUS OF THE BUBBLE IS DETERMINED BY USING THE METHOD OF MULTIPLE SCALES WHEN THE FREQUENCY OF THE PRESSURE WAVE (EXCITATION FREQUENCY) IS NEAR THE LINEAR NATURAL FREQUENCY OF THE BUBBLE.THE STEADY-STATE AMPLITUDE EXHIBITS A JUMP PHENOMENON AS THE EXCITATION FREQUENCY IS SWEPT UP AND DOWN NEAR THE LINEAR NATURAL FREQUENCY.WHEN THE EXCITATION FREQUENCY IS APPROXIMATELY TWICE THE LINEAR NATURAL FREQUENCY, SUB-HARMONIC RESONANCES TAKE PLACE AND THE MOTION IS UNSTABLE IF THE EXCITATION AMPLITUDE EXCEEDS A CRITICAL VALUE.ON THE OTHER HAND, WHEN THE EXCITATION FREQUENCY IS APPROXIMATELY ONE HALF THE LINEAR NATURAL FREQUENCY, THE STEADY-STATE RESPONSE IS PERIODIC FOR ALL VALUES OF THE EXCITATION AMPLITUDE.(A)

Non-linear acoustic response of a spherical bubble Academic Article