A damping mechanics model and a beam finite element for the free-vibration of laminated composite strips under in-plane loading

Linearized Frequencies and Damping in Composite Laminated Beams Subject to Buckling

“…At composite ply level, a Kelvin viscoelastic strain model was considered, which provides the following stress-strain relationship [38]:…”

“…(7)) and collecting the terms based on their order of nonlinearity, the dissipated strain of the section has the following form: In the above, ½A d , ½B d , and ½D d are equivalent extensional-shear, coupling, and flexural damping matrices of the laminate, respectively, defined in Ref. [38]. The dissipated energy contains linear H ds0 , first-order H ds1 , and second-order nonlinear terms H ds2 included in the last three lines of Eq.…”

“…The first-order nonlinear damping matrix C ds1 ½ was first introduced by Chortis et al [38], and its effect was studied on prestressed composite beams in tension.…”

“…Lesieutre [34][35][36][37] reported an analytical solution based on classical laminate theory, which included the effect of membrane loads on the modal damping of composite structures. Chortis et al [38] presented a damping mechanics formulation and a beam finite element model for the prediction of nonlinear damping of laminated composite strips under large in-plane tension loads. This work set the basis of the theoretical formulation but was restricted to the case of prestressed composite beams, taking into account only first-order nonlinear stiffness and damping terms.…”

“…In the following sections, the theoretical framework and the beam finite element [38] are extended to include new second-order nonlinear damping and stiffness terms required to fully describe the buckling response of composite laminated beams. Kinematic equations based on first order shear deformation theory and Green-Lagrange strains are implied, and the effective and tangential (linearized) laminate stiffness and damping matrices are formulated assuming a Kelvin viscoelastic material.…”