New upper bounds for excited vibration systems with applications of the differential calculus of norms

Abstract

In an earlier paper, the author introduced new upper bounds for free linear and nonlinear vibration systems; to compute the best upper bounds, the differential calculus of norms was applied. In the present paper, this work is continued for the corresponding excited systems. Some new techniques and ideas are involved. The results in the applications cannot be obtained by the methods used so far.

Keywords:

• Nonlinear dynamical system
• Excited system
• Vibration model
• Upper bound
• Differential calculus of norms