This work deals with the theoretical developments required for the analysis of non-selfadjoint control of linearly elastic homogeneous thin plates in the presence of conventional in-plane loads. To represent the actual physical problem, the system is modelled as a distributed bi-parameter system with distributed rather than lumped masses. Using the Green function approach, the controlled response of the system is obtained as an integral solution with an unsymmetric kernel that is derived from an 'auxiliary' system rather than the 'fundamental' eigenvalue-generating-system. The theoretical treatment of the problem is discussed in this manuscript, while the corresponding simulations and parametric study will be presented in a forthcoming paper.

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Keywords Bi-parameter systems, Distributed systems, Non-selfadjoint control, Stability domain
Journal Archive of Applied Mechanics
Afagh, F, & Lin, B. (1998). Analysis of non-selfadjoint control of thin elastic plates in the presence of conservative in-plane forces. Archive of Applied Mechanics, 68(7-8), 501–512.