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bouncy existing floor joists

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HI
 
I have A problem A custom home built in 1980's with 2x10 floor joist  at 12" on center
it spans 18 feet long the floor has 1 1/2" light weight concrete
the owner try to remodel and want to stiffen  the floor system because is very bouncy
and vibrating even it has dry wall at bottom
so the dry wall pulled off and just added 1 3/4 x 91/4 PSL 2.0 E. at 12' on center .
no dry wall added yet and the floor still bouncy and vibrating
1- is it possible after adding the dry wall will be ok
2- what other solution can be done without adding beams or increase the depth of floor joists
    because adding a beam will be deeper and too big due to long span where possible to
    add post.
3- is it adding steel tube joist at 24" will solve the problem
 
thank in advance for any advice
Dave A. P.E.