In this paper, we examine and compare four different techniques for modal analysis of stepped piezoelectric
beams. The first technique is based on the solution of the exact transcendental eigenvalue problem, formulated
in terms of the dynamic stiffness matrix. The other three techniques are based on the Galerkin method for
obtaining a finite-dimensional version of the system. Besides the classical assumed modes method and finite-element
method, we propose a novel enhanced version of the assumed modes method, which introduces special
jump functions to enrich the standard basis functions.
We propose two identification techniques for estimating the piezoelectric couplings and the piezoelectric capacitances
of reduced order modal models of linear piezoelectric structures. The two methods are easily implementable
and demand few input data, which can be obtained both with experimental testing and numerical
models (e.g. finite elements). We apply these methods to a sample structure hosting multiple transducers.
We discuss in details the proper definition and identification of the inherent piezoelectric capacitances, whose
meaning is often misunderstood.
Several electric vibration absorbers based on distributed piezoelectric control of beam vibrations are studied. The damping devices are conceived by interconnecting with different modular electric networks an array of piezoelectric transducers uniformly distributed on a beam. Five different vibration absorbers made of five different network interconnecting topologies are considered and their damping performances are analyzed and compared. The analysis is based on homogenized models of modular piezo-electromechanical systems. The optimal parameters of these absorbers are found by adopting the criterion of critical damping of waves with a single wave number. We show that: i) there is an interconnecting network providing an optimal multimodal damping; ii) the performances required to the electr(on)ic components can be significantly decreased by increasing the number (and decreasing the dimensions) of the piezoelectric transducers.