A numerical study on the effect of vibrator shape on the development of nonlinear standing waves in a 2-D acoustical resonator
The numerical analysis of the effects of different shape of the vibrator on the pressure and velocity profile in 2-D nonlinear standing wave resonator is studied. The wave equation for high-amplitude nonlinear acoustic waves in a thermo-viscous fluid is derived from the basic equations of fluid mechanics along with an appropriate state equation. Three different shapes are considered for the diaphragm which are, constant shape vibrating piston, circular shape and cosine shape, to investigate the effects of the diaphragm shape on the pressure and velocity waveforms of an acoustic resonator. It is observed that for the same maximum vibrational velocity of the diaphragm, the amplitudes of the pressure and velocity for constant shape vibrating piston are largest and for cosine shape are smallest.
Abstract By applying wrapping (Dattatreya Rao et al (2007)), offsetting (Girija et al (2013 and Radhika et al (2013)) and stereographic projection (Phani et al (2012)) have constructed circular models. Further the circular models based on the Rising Sun function are motivated by purely mathematical considerations as a smoothing function and possible application. This work takes a further step in this direction using several mathematical tools such as Real Analysis along with MATLAB and are applied to enlarge the horizon of Mathematical Statistics. Here an attempt is made to construct new circular models using the Rising Sun function and also the circular rising sun lemma is proposed