Numerical-Integration of Forced-Vibration Equations

Modified forms of finite-difference equations for the numerical-integration of forced-vibration equations are presented. The numerical-integration method which consists of the application of a step-by-step procedure after having started by means of a special initial equation, does not necessitate the solution of a set of equations at each step, even in case of nonlinear damped vibrations of multidegree systems. The truncation errors involved are, in general, small compared with other well-known numerical-integration methods. For the special case of linear-elastic forced-vibrations of multidegree systems with viscous damping, a computer program, is developed through the use of the general matrix form of the modified finite-difference equations. A comparison of the method with other well-known numerical-integration methods is performed on a numerical example.