Circular waveguide of moving boundary

Analytical Method for Solving the One-Dimensional Wave Equation with Moving Boundary

“…For solving this class of problems the method given in a previous paper [1] is expanded and used. Our approach, in this case, uses the analogy between Laplace's equation and the wave equation.…”

“…For a domain between a fixed boundary x = 0 and a moving boundary x = a(τ ) with a(τ ) = a 0 +βτ (linear boundary motion expanding β > 0 or shrinking β < 0 the x domain), the analytical function F (W ) permitting the conformal mapping, of the two regions is given by [1,20]:…”

“…Then, it is very difficult in this case to analyze and understand correctly the physical phenomena. For this reason, the analytical method given in a previous paper [1] is generalized and used in this work. It consists in transforming the wave equation for the domain with moving boundary into a form-invariant wave equation in a domain where the boundary is fixed.…”

Nature of Electromagnetic Field and Energy Behavior in a Plane Resonator with Moving Boundary

“…By means of the function U, the system of equations (4, 5) is reduced in an alone differential equation to the partial derivatives of hyperbolic type. Indeed, in combining the relations (8) and (9) we obtain:…”

“…Many studies have been made in this area employing, in general, approximate mathematical methods [1][2][3][4][5][6][7][8][9][10][11][12][13]. Our main in this work is to analyze the nature of electromagnetic field and the energy behavior in a plane resonator constituted by two parallel, perfectly conducting plates, one of which is moving normally to itself in arbitrary fashion.…”