The Mathematica Journal


C. Christopher Reed, Alvar M. Kabe
Published April 19, 2019
A comprehensive discussion is presented of the closed-form solutions for the responses of single-degree-of-freedom systems subject to swept-frequency harmonic excitation. The closed-form solutions for linear and octave swept-frequency excitation are presented and these are compared to results obtained by direct numerical integration of the equations of motion. Included is an in-depth discussion of the numerical difficulties associated with the complex error functions and incomplete gamma functions, which are part of the closed-form solutions, and how these difficulties were overcome by employing exact arithmetic. The closed-form solutions allowed the in-depth study of several interesting phenomena. These include the scalloped behavior of the peak response (with multiple discontinuities in the derivative), the significant attenuation of the peak response if the sweep frequency is started at frequencies near or above the natural frequency, and the fact that the swept-excitation response could exceed the steady-state harmonic response. Read More »