Quasi-2D finite element formulation of active–constrained layer beams

Abstract

The response of active–passive–constrained layer beams is examined via the use of quasi-two-dimensional finite element formulation. Passive damping in the system is provided by a viscoelastic layer, and a piezoelectric actuation layer is used to achieve active damping. The quasi-two-dimensional finite element formulation allows through-the-thickness representation of the field variables via polynomials and their interpolation along the span by Lagrange cubic elements. The formulation is compared with the conventional formulation via numerical simulations. The response magnitudes predicted using the conventional formulation are higher than those obtained using the present formulation for systems with high core thickness, while approximately identical magnitudes are predicted for systems with low core thickness. Specific to the present quasi-two-dimensional formulation, the application of a cantilevered boundary condition to the three layers yields the same response as would have been obtained by enforcing the clamped condition on just the top and bottom layers of the cantilevered end.

A Finite Element Formulation Of Active Constrained-Layer Functionally Graded Beam

“…The dynamic responses for Q2DE and Ref. [6] are identical while the Q2DT results in a slight phase shift from the two responses. All of the responses have the same amplitudes, but the conventional has an obvious phase shift from the three quasi-2D formulations.…”

“…In the past, research has been done on the vibration analysis of an ACLD beam where the structure consisted of an elastic host beam as the base, a viscoelastic damping layer as the core and piezoelectric layer on top [6,8]. A functionally graded (FG) host beam and a piezoelectric fiber reinforced composite (PFRC) top layer were adopted by Miroshnichenko [3].…”

“…It requires modifying the current formulation and comparing it to the study by Galucio et al [18] where the dynamic analysis of a sandwich beam with a viscoelastic core was investigated. Lastly, the dynamic analysis of a cantilever beam with a piezoelectric top layer from Bekuit et al [6] is considered. Note that Quasi-2D Euler-Bernoulli (Q2DE) denotes the ACLD beam formulation where both the top and bottom layers are modeled as Euler-Bernoulli beams and the core is modeled via a higher-order beam theory.…”

“…To further verify the accuracy of the present quasi-2D formulation, the work by Bekuit et al [6] is reproduced and compared. The model consists of an isotropic host beam, a viscoelastic core, and a piezoelectric constraining layer.…”

“…Figure 5.12 plots the response of the Q2DE, Q2DT, Ref. [6], and classical method for a core thickness of h c = 0.2 mm. The first subplot, (a), depicts the tip deflection of the passively damped beam.…”