Abstract:A structural dynamics response optimization under bandwidth frequency excitation is considered. A differentiable -norm form of response function’s peak value is introduced according to properties of frequency response function. This equivalent aim function can be used in multiple-bandwidth situation. Sensitivities of equivalent aim function then can be derived from structure’s eigen-sensitivity. Besides,frequency constraints were introduced for prohibiting clustered or repeated frequencies during optimization. Illustrated examples of truss sizing and shape optimization are presented for verification and application for proposed method.