Nabeel

This is Nabeel Ahmad, a post-graduate in applied mathematics who has worked as a teacher for six years at a reputable university and colleges. A seasoned teacher who is willing to clarify topics in accordance with the needs of the students. Moreover, for the past few years, I have been a math specialist and coaching students on various online platforms. Committed to establish a long-lasting relationship with students. My MS research work was on mathematical modeling and analysis of bifurcated/trifurcated planar and nonplanar waveguide structures. These waveguides have been studied in the literature with planar surfaces without step discontinuities. However, the present study focuses on considering non-planar surfaces along with vertical discontinuities which may ease the propagation of waves. The mathematical procedure considered herein uses mode matching method based on generalized orthogonality relations and non-linear dispersion relations. The mode-matching scheme with the use of appropriate matching conditions enables to describe the form of the velocity potentials and identify the associated wavenumbers for each region of waveguide. The flexural nature of the waveguide requires to use the appropriate physical edge conditions for uniqueness of the solution. These edge conditions are required to determine unknown dependent sums that arise after employing the generalized orthogonality relations. The energy equations are formulated from the equation of motions thereby presenting energy distribution in different sections of ducts against different parameters of interest. Through mathematical and graphical illustration, the obtained solution is verified satisfying all geometrical conditions as well as law of conservation of energy