Free Vibration of flexible soft-core sandwiches according to layerwise theories differently accounting for the transverse normal deformability

Abstract

This study aims to generalize a previously developed accurate and inexpensive 3-D zigzag theory up to an arbitrary representation form and to determine which simplifications are yet accurate in determining transverse shear and normal stress/deformation effects on vibrations of soft-core sandwiches with not moving middle/neutral plane (pumping). Natural frequencies are calculated using displacements assumed differently across the thickness, having fixed d.o.f., not yet explored forms of representation and zigzag functions differently accounting for the transverse normal deformability and that partially or fully fulfill physical constraints. Applications are presented for sandwich plates and beams with length-to-thickness ratios and material properties of faces and core varying within an industrial range, for which layerwise effects are very important and so suited to the evaluation of theories. Analytical solutions are found using the same trial functions and expansion order for all theories, so to evaluate their accuracy under the same conditions. The choice of the representation form and of zigzag functions is shown immaterial if displacement field coefficients are recomputed across the thickness by enforcing the fulfillment of all physical constraints (using symbolic calculus). Furthermore, it is shown that assigning a specific role to each coefficient is immaterial, as well as exchanging the order of representation of in-plane and transverse displacement components and even that zigzag functions could be omitted. This no longer occurs for lower-order theories with only a partial fulfillment of constraints. Pumping motions are highlighted as the first modes, which require the theories much accurately accounting for transverse normal deformability. Keywords Composite and sandwich plates and beams, interlaminar transverse shear and normal stress continuity, Navier's and 3D finite element analysis (FEA) solutions, free vibration behavior, different zigzag functions, various form of representation of variables 1 INTRODUCTION As it is well known, sandwiches find continuously increasing applications in aerospace, naval and terrestrial applications owing to superior specific strength and stiffness than traditional materials. Free Vibration of flexible soft-core sandwiches according to layerwise theories differently accounting for the transverse normal deformability Ugo Icardi et al.

An alternative finite strain elastoplastic model applied to soft core sandwich panels simulation

“…In order to find recent reviews readers are invited to consult, for example, the work of Abrate and Di Sciuva (2017) for general Equivalent-Single-Layer theories (ESL), Caliri et al (2016) for FEM shell theories, Garg et al(2021) to access theories including functionally graded materials, Nsengiyumva et al (2021) for a review associated with non-destructive experimental analysis and the work of Sayyad and Ghugal (2017) for vibrations and stability of laminated beams and plates. Some current works of great interest and related to the present study can be also cited, for example, the work of Icardi and Urraci (2019) regarding sandwich panels vibration, Chen et al (2016) related to impact analysis, Marques et al (2018) for structural health monitoring and Naik and Sayyad (2018) and Shekari et al (2017) for general plate theories.…”