Linear and nonlinear vibrations analysis of viscoelastic sandwich beams

Modeling of viscoelastic sandwich beams using solid–shell finite elements

“…Nevertheless, first of all and before we proceed further, the SHB8PS solid-shell finite element will be first validated on a simple cantilever beam and on the sandwich beam problem studied in [15,16].…”

“…() 12 (15) One can show that 34 B vanishes at all of the integration points of the SHB8PS element. Therefore, if theB operator is evaluated at this set of integration points, it reduces to 12 B .…”

“…Carrera [12,13] has provided a very comprehensive and well-documented historical review on zigzag theories for multilayered plates and shells as well as on modeling of multilayered and composite structures. In recent years, the zigzag approach has been applied in the context of vibration analysis (see, e.g., Boudaoud et al [14], Bilasse et al [15], Abdoun et al [16], as well as the more recent review and assessment of existing models by Hu et al [17]). Another noteworthy approach consists of Carrera's unified formulation (CUF) [18], in which several kinematic assumptions for the displacement fields can be included hierarchically in one single compact formulation.…”

Explicit solution for the natural frequency of structures with partial viscoelastic treatment

“…The concepts for numerical modeling of a flexible structure with viscoelastic treatment are numerous, and the inherent compromise between accuracy and computational effort has been a main aspect in the development of the various proposed solution strategies. The most common modeling approaches are assumed modal expansions [7][8][9][10][11] or discretization by finite elements [4,12,13]. Both modeling approaches lead to discretized equations of motion, where the complex-valued natural frequencies are determined by solving the full dimensional eigenvalue problem.…”

“…Both modeling approaches lead to discretized equations of motion, where the complex-valued natural frequencies are determined by solving the full dimensional eigenvalue problem. Concepts have recently been proposed to determine the complex-valued natural frequencies of dynamic systems with supplemental viscoelastic attachments [14] and structures with integrated viscoelastic parts [11,15]. A review of numerical solution strategies for solving the damped eigenvalue problem for viscoelastic plate structures is given in [16].…”