The chief tool for design of viscoelastic-based damping treatments over the
past 20 years has been the modal strain energy (MSS) approach. This approa
ch to damping design traditionally has involved a practitioner to vary plac
ement and stiffness of add-on elements using experience and trial and error
so as to maximize the add-on element share of system MSE in modes of inter
est. Ira this paper we develop a new technique for maximizing strain energy
as a function of stiffness for add-on structural elements modeled as rank
r perturbations to the original stiffness matrix. The technique is based on
a constrained substructure approach allowing us to parameterize strain ene
rgy in terms of the eigenvalues of the perturbed structure. An optimality c
ondition is derived that relates the input-output response at the attachmen
t location of the add-on elements to the maximum achievable strain energy.
A realizability, condition is also derived which indicates whether or not t
he optimal solution is achievable with passive structural elements. This me
thod has applications in the design of structural treatments for controllin
g sound and vibration and promises an efficient means of determining the li
mits of performance of passive structural treatments. An advantage of our a
pproach over existing methods is that the maximum achievable strain energy
fraction in the add-on elements is directly computable with the realizabili
ty condition then indicating whether the optimal solution is achievable.