Passive radiator

Simple question:

Can a passive radiator incorporated into a subwoofer enclosure increase efficiency? Or is adding dynamic mass to the system, rather than just moving air, a reduction in efficiency but perhaps beneficial for directionality?

Is an "omnidirectional" passive enclosure -- for example, a 12" subwoofer mounted in a front baffle and housed in a framed "sealed" cubic enclosure with a compliant skin of some sort, e.g. latex or something with a relatively low modulus of elasticity, stretched taut across the five other sides worth experimenting with?
 
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My understandings of passive radiators while limited is somewhat similar to "ported" alignments...first off, yes, one will increase efficiency with a PR. I don't know of the formulas or simulation programs to engineer the PR system, I'm sure someone here has the formulas...I'd bet real monies the enclosure sizes will be immense, a cubic meters worth at least. Fabricating your own PR "membrane" will consume vast amounts of experimental time & effort.

-------------------------------------------------------------------------------------------------------------------------------------------------------------Rick...