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Dear Editor-in-Chief and the Associate Editor,
Thanks a lot for your helpful comments on our manuscript.
Now we are submitting this revised version after incorporating reviewer ’s comments and making
improvements.
Yours sincerely,
Kobe Bryant
Dear Reviewers,
We would like to express our sincere appreciation for your careful reading and invaluable
comments to improve this paper. We have addressed all issues raised be the reviewer. The
amendments made are mentioned below with reference to appropriate paragraphs and sections of
the revised manuscript.
Response to Reviewer #1
[Comment 1] Very Good efforts are done for experimental setup.
[Answer] Thank you for your encouragement of the research.
[Comment 2] How are the Theoretical modes shapes are calculated and presented in Fig. 2-4.
[Answer] We have added the theoretical transverse mode shape function of a free paraboloidal
membrane shell in Section 3.1 on page 8. This assumed mode shape function was obtained and
validated in our previous study and details could be found in ref.[27]. With this theoretical mode
shape function, one can achieve the theoretical mode shapes of the paraboloidal shell in Fig. 2-4.
In a previous study of a free paraboloidal shell, with experienced “trail-and-error” and verification,
a new transverse mode shape function of a paraboloidal membrane shell with free boundary
condition has been derived [27]
k
U A k 1 cos sin cos k (8)
3k k
where the mode number k=1,2,3…, Ak is the kth modal amplitude, ϕ is the meridional angle
measured from the pole, and ψis the circumferential angle.
[Comment 3] From Table 4, S
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