Dynamic behaviour of soft core sandwich beam structures using kriging-based layerwise models

A static analysis of three-dimensional sandwich beam structures using one-dimensional modelling approach is presented within this paper. A family of several one-dimensional beam elements is obtained by hierarchically expanding the displacements over the cross-section and letting the expansion order a free parameter. The finite element approximation order over the beam axis is also a formulation free parameter (linear, quadratic and cubic elements are considered). The principle of virtual displacements is used to obtain the problem weak form and derive the beam stiffness matrix and equivalent load vectors in a nuclear, generic form. Displacements and stresses are presented for different load and constraint configurations. Results are validated towards three-dimensional finite element solutions and experimental results. Sandwich beams present a three-dimensional stress state and higher-order models are necessary for an accurate description. Numerical investigations show that fairly good results with reduced computational costs can be obtained by the proposed finite element formulation.

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Transverse Vibrations and Stability of Axially Traveling Sandwich Beam With Soft Core

Journal of Vibration and Acoustics ◽

10.1115/1.4023951 ◽

2013 ◽

Vol 135 (5) ◽

Cited By ~ 7

Author(s):

Xiao-Dong Yang ◽

Wei Zhang ◽

Li-Qun Chen

Keyword(s):

Critical Speed ◽

Natural Frequencies ◽

Sandwich Beam ◽

Axial Loading ◽

Core Layer ◽

Soft Core ◽

Axially Moving Beam ◽

Transverse Vibrations ◽

Axially Moving ◽

The Galerkin Method

The transverse vibrations and stability of an axially moving sandwich beam are studied in this investigation. The face layers are assumed to be in the membrane state, which bears only axial loading but no bending. Only shear deformation is considered for the soft core layer. The governing partial equation is derived using Newton's second law and then transferred into a dimensionless form. The Galerkin method and the complex mode method are employed to study the natural frequencies. In comparison with the classical homogenous axially moving beam, the gyroscopic matrix is no longer skew-symmetric because of the introduction of the soft core. The critical speed for the divergence of the axially moving sandwich beam is analytically obtained. The contribution of the core layer shear modulus to the natural frequencies and critical speed is discussed.

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Dynamic Characteristic of Axially Moving Soft Sandwich Beam

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.702.275 ◽

2013 ◽

Vol 702 ◽

pp. 275-279

Author(s):

Hai Wei Lv ◽

Ying Hui Li ◽

Liang Li

Keyword(s):

Governing Equation ◽

Sandwich Beam ◽

Beam Theory ◽

Soft Core ◽

Independent Variables ◽

The Third ◽

Second Mode ◽

Galerkin Truncation ◽

Axially Moving ◽

State Of Tension

A new sandwich beam theory is proposed by introducing independent variables of the displacements of face sheets, middle plane of soft core according to the incompression in transverse direction of traditional sandwich beam theory. Based on Hamilton principal, the governing equation of the system is established. Galerkin truncation method was used to solve the governing equation. It was found that (1) the first mode of the system displays that it is consistent with the traditional sandwich beam theory; (2) the second mode of the system shows that the soft core is in the state of tension or in compression; (3) the third mode of the system displays that the upper part and lower part of soft core are in different state (tension or compression); (4) The incompressible model of sandwich beam is the special form of soft sandwich beam we establish in this paper.

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