Spectral finite element-based Hamiltonian semi-analytic approach for vibration analysis of layered composite-piezoelectric smart structures

Abstract The present work proposes an original spectral finite element (SFE)-based Hamiltonian semi-analytic approach for vibration analyses of layered composite-piezoelectric (PE) smart structures . For this, a Legendre Transform is first performed to recast the classical Lagrangian functional into a Hamiltonian one so that the resulting partial-mixed variational formulation can be expressed in terms of the translational displacements, electric potential and their duals , the transverse stresses and electric displacement as primary variables. Within this Hamiltonian formalism , the layered composite-PE smart structure in plane is discretized into two-dimensional p-type high-order SFE, while the resulting first-order one-dimensional differential system is solved analytically by enforcing the electromechanical interface continuity constraints . The layered composite-PE smart structure dynamic stiffness matrix is then built and its eigenvalues computed using Wittrick-Williams algorithm . A detailed discussion is provided on the proposed approach implementation aspects and, for the assessment of the latter’s robustness, accuracy and effectiveness, few literature smart structures benchmarks are analysed in free-vibration under electrical short-circuit and mechanical non-classical (cantilever and fully-clamped) boundary conditions. It is found that the SFE-based Hamiltonian semi-analytic approach is fastly and accurately converging to the reference experimental and numerical results. Hence, the presented tabulated results can be used safely for benchmarking other methodologies for solving similar problems.