<title>Predicting actuation efficiency of structurally integrated active materials</title>

Design of a piezoelectric actuator and compliant mechanism combination for maximum energy efficiency

“…The energy conversion efficiency of the system is then defined as the ratio of output mechanical energy, equation ( 16), to the input electric energy, equation (17). That is,…”

“…Solving equations ( 2), (10), and ( 15), for the displacements, forces, and electric charge, and substituting into equations ( 16) and (17), and after algebraic simplification, the energy conversion efficiency of the system, equation (18), is given by η…”

“…They found that the stiffness matching concept, in which the stiffness of the stack actuator is matched to the stiffness of the structure, is still applicable, but the optimal impedance ratio is different from unity. Davis et al [17] derived energy efficiency relations of a stack actuator coupled to a structure modeled as a linear spring, and developed the equations in the frequency domain to include dynamic effects. Lutz and Hagood [18] presented a general formulation for determining the energy (actuation) efficiency of a smart material system, allowing for nonlinearity.…”