Elsevier

Thin-Walled Structures

Volume 112, March 2017, Pages 78-82
Thin-Walled Structures

Full length article
Buckling and vibrations of metal sandwich beams with trapezoidal corrugated cores – the lengthwise corrugated main core

https://doi.org/10.1016/j.tws.2016.12.013Get rights and content

Highlights

  • An original mathematical model of a multi-layered beam is proposed.

  • Buckling and vibration of presented structures is analysed.

  • The stiffness of the beam is very high in relation to its mass.

  • Mechanical properties of the beam can be easily modified by changing corrugations.

Abstract

The paper is devoted to the stability of an orthotropic multi-layered beam. This beam is an untypical sandwich structure the faces of which consist of three layers. The original mathematical model of the beam is formulated taking into account different properties of each layer. From the Hamilton's principle the system of equations of motion is derived which is the base for the analysis of buckling and vibration problems. As a result of the analysis the buckling load and natural frequencies of exemplary plates have been obtained. The results are compared with these given by the numerical solution realised with the use of the finite element method in the ANSYS and ABAQUS systems.

Introduction

The theory of sandwich structures is developed from the middle of 20th century, that is evidenced by the papers published in journals and at conferences. Basic facts on sandwich structures, their generalizations and applications, can be found in, e.g., Libove, Hubka [1], Allen [2] and Ventsel, Krauthammer [3]. Besides monographs there are also many papers on this subject. Computational models for sandwich plates and shells, predictor-corrector procedures, and the sensitivity of the sandwich response to variations in the different geometric and material parameters have been studied by Noor, Burton and Bert [4]. Carlsson, Nordstrand, Westerlind derived tension, shear, bending and twisting rigidities for sandwich structures with corrugated core. The paper [5] is devoted to the computation of the effective properties of corrugated core sandwich panels. Talbi, Batt, Ayad, Guo [6] presented an analytical homogenization model for corrugated cardboard and its numerical implementation in a shell element. In the paper [7] by Cheng, Le, Lu the finite element method (FEM) is used to derive equivalent stiffness properties of sandwich structures with various types of cores. Similar results can be found in [8], [9].

The present work is a continuation of the research on multi-layered structures with corrugated core conducted by the authors and co-authors. First works [10], [11] were derived to classical sandwich structures. Strength and stability of aluminium beams with lengthwise and crosswise corrugated core have been analysed. To increase the flexural stiffness of such beams the modification has been introduced presented in works [12,15]. In structures presented here the faces are composed of two elements: inside one which is a corrugated plate and outside one in the form of a flat sheet. The corrugations of the core and the faces are perpendicular to each other. The results of experiments on these five-layered beams presented in papers [16], [17] showed that although the stiffness of the beam is much higher when compare to the stiffness of a three-layered beam, the connection between two corrugated plates can be the weak point of the structure. Further modification has been made then by introducing a flat sheet between two corrugated plates. This way a seven-layered beam has been obtained – a sandwich beam with three-layered faces, as can be seen in Fig. 1.

The thin-walled beam presented in this paper is an innovatory orthotropic structure, not referred to in the literature. The main core is a lengthwise corrugated sheet. The two faces are three-layered structures the core of which, referred to as face core, is a crosswise corrugated sheet. The internal and external sheets of the faces are flat. All layers of the beam are made of the same material which is isotropic and homogeneous. A characteristic feature of the beam consists in differentiation of shear effects in particular layers, according to the core's corrugation direction. The deformation of the beam's cross section also depends on this direction. An original mathematical model of the structure will be formulated in the following sections. The model will include the hypothesis of deformation of the cross-section as well as rigidities of the layers in particular directions.

Section snippets

Mathematical model of the beam

The classical approach to modelling of sandwich structures is to assume a broken line hypothesis as to the field of displacements. For more than three layers the zig-zag hypotheses can be used formulated by Carrera [18]. In the proposed structure the stiffness of the core of the faces is considerably higher than the stiffness of the main core. For this reason it is assumed that the three-layered faces deforms according to Kirchhoff-Love hypothesis and the shear effect is present in the main

FE model of the plate

A family of beams of the width b=200 mm and the length L={1104,1288,1472,1656,1840,2024,2208,2392} mm has been considered in the analyses. The total thickness of the beam equals t=67 mm. The thickness of the sheets of all layers is equal to ts=0.8 mm. Dimensions of the corrugations are given in Fig. 4.

The beam has been considered as a thin-walled structure. For all seven layers linear shell elements have been used to prepare the finite element model (FE model). Number of finite elements has been

Summary and conclusions

Based on the results presented in the previous sections the properties of the seven layer beam can be easily determined. From the plot presented in Fig. 6 it is seen that the stiffness of the plate increase when its length decreases. It manifest itself in an increase of the value of both the critical load and natural frequency. The buckling mode and the mode of vibration is the same and has the form of one longitudinal half-wave. However, for beams shorter than 1200 mm, a local phenomenon

Acknowledgements

The project was funded by the National Science Centre allocated on the basis of the decision number DEC-2013/09/B/ST8/00170.

References (18)

There are more references available in the full text version of this article.

Cited by (29)

  • External mean flow effect on sound transmission through composite sandwich structures filled with porous materials

    2022, Applied Mathematical Modelling
    Citation Excerpt :

    Typical sandwich structures mainly include corrugated structure, honeycomb structure and truss structure. Magnucka-Blandzi et al. [18,19] focused on the stability and free vibration of sandwich beams with trapezoidal corrugated cores, their analytical models were verified using finite element method. Arunkumar et al. [20] applied the finite element method to study the vibro-acoustic characteristics of fiber-reinforced aluminum honeycomb sandwich panels.

  • The tolerance modelling of vibrations of periodic sandwich structures – Comparison of simple modelling approaches

    2021, Engineering Structures
    Citation Excerpt :

    The details of those hypotheses are described in literature, for example in work of Magnucki and Ostwald [6] or Carrera and Brischetto [7], while their application can be found for example in works of Grygorowicz et al. [8,9], Carrera et al. [10], Kumar et al. [11], Singha et al. [12], Yegao and Guang [13], Honda et al. [14], Iurlaro et al. [15–17], Kim [18], Monge et al. [19], Castañeda et al. [20], Paczos et al. [21] or Di Sciuva and Sorrenti [22,23]. The advanced hypotheses can be also adjusted to perform the analysis of complicated multi-layered structures, such as metal seven-layer sandwich beams with trapezoidal corrugated cores by Magnucka-Blandzi et al. [24,25] or to estimate strains in composite honeycomb sandwich panels basing only on the free vibration characteristic of the plate, cf. Kumar and Renji [26]. The same hypotheses can be also used to investigate the behaviour of the sandwich plates subjected to external electric and magnetic potentials, cf. Ghorbanpour-Arani et al. [27–29].

  • Investigation of mass distribution between core and face sheet on bending energy absorption of self-reinforced PP sandwich beams

    2021, Thin-Walled Structures
    Citation Excerpt :

    Still, very little work is available on the integrated investigation of material and structural properties of SRCs and other polymer composite based sandwich structures. Magnucka-Blandzi et al. [16–22] have developed advantageous mathematical models to predict corrugated structures' mechanical properties. Auclair et al. [2] fabricated timber-concrete beams and formulated a non-linear model for beams' bending behavior.

View all citing articles on Scopus
View full text