Nonlinear Vibration of Beams Using a
Form-Function Approximation
Journal of Applied Mechanics, (1975)Abstract
The nonlinear response and stability of a vibrating, buckled beam is analyzed using a
form-function approximation. Such an approximation differs from the usual linear series
approximations in that the unknown parameter appears nonlinearly. This new approximation
has two major advantages. Since all harmonics (in both space and time) are
represented, the dominant harmonics are "singled out" in the solution, thus making it
very efficient. The form-function representation also permits an insight into system behavior
not found in other methods. Knowledge of the form parameter shows explicitly
how the form of the response changes with the system parameters, e.g., forcing function
magnitude and frequency, material constants, etc.
