Vibration analysis of the active multi-layer beams by using spectrally formulated exact natural modes

Modal analysis method (MAM) is introduced for the fully coupled structural dynamic problems. in this paper, the beam with active constrained layered d amping (ACLD) treatment is considered as a representative problem. The ACLD beam consists of a viscoelastic layer that is sandwiched between the base beam structure and an active piezoelectric layer. The exact damped natural modes are spectrally formulated from a set of fully coupled dynamic equatio ns of motion. The orthogonality property of the exact damped natural modes is then derived in a closed form to complete the modal analysis method. The accuracy of the present MAM is evaluated through some illustrative example s: the dynamic characteristics obtained by the present MAM are compared wit h the results by spectral element method (SEM) and finite element method (F EM). It is numerically proved that MAM solutions become identical to the ac curate SEM solutions as the number of exact natural modes used in MAM is in creased.