"The application of the finite-difference technique, the Fourier transform, and the Laplace transform for the solution of a system governed by the one-dimensional wave equation is examined. A specific example consisting of a continuous shaft-flywheel system acted upon by an exciting torque applied at a specific section of the shaft is studied. The exact solution to this example is obtained using the classical method of superposition of modes, and is used as a reference to evaluate the accuracy (in terms of the rms error) and relative efficiency (based on computer time) of three approximate solution methods. A sinusoidal excitation was applied to study the steady state response whereas for the case of transient response, the aperiodic excitation applied was a half cycle sine pulse of the same amplitude and duration equal to half the period of the steady state excitation case. No damping in the system was considered. The natural frequencies of the system resulted in singularities of the system transfer function thus, making the integrand in the inverse Fourier integral non-analytic. Special considerations are required for the numerical quadrature of such an integral. The numerical evaluation of the inverse Fourier integral considered here was unsuccessful using Simpson's rule as an integral scheme. The finite-difference and the Laplace transform solutions were obtainable with rms errors less than 10⁻⁴ and 10⁻¹, respectively. Computing time for the finite-difference solution was found to be a function of the accuracy desired. For the Laplace transform solution, computing time remained constant for the solutions obtained over an interval of the same time values"--Abstract, pages ii-iii.
Barker, Clark R.
Rocke, R. D. (Richard Dale), 1938-
Keith, Harold D. (Harold Dean), 1941-
Mechanical and Aerospace Engineering
M.S. in Mechanical Engineering
University of Missouri--Rolla
xi, 75 pages
© 1970 Mahendrakumar Ramkrishna Patel, All rights reserved.
Thesis - Open Access
Oscillations -- Mathematical models
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Patel, Mahendrakumar Ramkrishna, "Numerical solutions of the torsional oscillations of a shaft-flywheel system" (1970). Masters Theses. 5497.