Besides, we would like to state that although Mr. Shahruz and Mr. Mahavamana’s paper about amplitude bounds for some nonclassically damped systems was published in December 1998 in the Journal of Sound and Vibration, their results were not known to the authors since our paper was received by the ASME Applied Mechanics Division on Aug. 24, 1998 and the final revision of the paper was received on Jan. 19, 1999. Therefore, a comparison with their results was not possible (and maybe not even reasonable since in our paper we discussed mainly response bounds with time evolution and not amplitude bounds).
In conclusion, we agree with Mr. Shahruz that no upper bound can be expected to be tight for all systems. In fact, in our paper we also stated that K. Yae and D. Inman’s response bounds given in paper (5) are in some cases better than ours. But in contrary to Mr. Shahruz we think that improvements on the response bounds are meaningful and do not consider only the amplitude bounds to be important. Mr. Shahruz stated that our response bounds are neither easily computable nor are tight. We hope that we have been able to contribute to this interesting field of research and that in the future more easily computable and tighter response bounds will be developed.