We consider damped second order in time systems such as those arising in structures with piezoceramic actuators and sensors. These systems are naturally formulated as abstract second order systems with unbounded nonhomogeneous term. Existence, uniqueness and continuous dependence of solutions in a weak or variational setting are given. A semigroup formulation is presented and conditions under which the variational solutions and semigroup solutions are the same are discussed.
H. T. Banks. K. Ito. Y. Wang. "Well posedness for damped second-order systems with unbounded input operators." Differential Integral Equations 8 (3) 587 - 606, 1995. https://doi.org/10.57262/die/1369316508