Applied mathematics Seminar

Speaker: Richard Zalik

Title: On the Nonlinear Jeffcott Equations

Abstract: The Jeffcott equations are a system of coupled, nonlinear, ordinary differential equations. The primary application of their study is directed towards understanding the reasons for the excessive vibrations recorded in the cryogenic pumps of the second stage main engine of the Space Shuttle, during hot firing ground testing. In this talk we shall examine some properties of the solutions of the Jeffcott equations. In particular, we show how bounds for the solutions of these equations can be obtained from bounds of the solutions of the linearized equations. By studying the behavior of the Fourier transforms of the solutions, we are also able to predict the onset of destructive vibrations. These conclusions are verified by means of numerical solutions of the equations, and of power spectrum density plots.

This work shows how numerical simulations can be used to obtain an insight into the correct solution to a problem. Once this correct answer is known, it then becomes possible to give a rigorous proof.

Speaker: Richard Zalik

Title: On the Nonlinear Jeffcott Equations

Abstract: The Jeffcott equations are a system of coupled, nonlinear, ordinary differential equations. The primary application of their study is directed towards understanding the reasons for the excessive vibrations recorded in the cryogenic pumps of the second stage main engine of the Space Shuttle, during hot firing ground testing. In this talk we shall examine some properties of the solutions of the Jeffcott equations. In particular, we show how bounds for the solutions of these equations can be obtained from bounds of the solutions of the linearized equations. By studying the behavior of the Fourier transforms of the solutions, we are also able to predict the onset of destructive vibrations. These conclusions are verified by means of numerical solutions of the equations, and of power spectrum density plots.

This work shows how numerical simulations can be used to obtain an insight into the correct solution to a problem. Once this correct answer is known, it then becomes possible to give a rigorous proof.