NETWORK REPRESENTATION FOR PIEZOELECTRIC BIMORPHS

The exact electrical network representation for rectangular cantilevered bimorphs is developed from the constituent equations for the bimorph. These equations are written in terms of redefined extensive and intensive variables that makes it possible to write the bimorph matrix in numerical form. This numerical matrix is diagonalized to give the eigenvalues of bimorphs. The modal matrix is used to find the corresponding eigenstates. A physical interpretation of bimorph eigenstates is proposed. Two realizations of network representation are given for the admittance matrix. The eigenvalue matrix is inverted to give the impedance matrix. The bimorph matrix is also diagonalized with congruent transformations which give a transformation matrix which is upper triangular. This way two goals are met: to diagonalize the matrix, and to have a transformation matrix with the least number of elements, which can be used to create a network with the least number of elements. The network representation of the impedance matrix is given. The network representation is exact, it contains no approximations. The network permits faithful models of actuators using software CAD programs, such as Spice.