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Vibration analysis of multi-span lattice sandwich beams using the assumed
, Shurui Wen
, Fengming Li
College of Mechanical Engineering, Beijing University of Technology, Beijing 100124, China
College of Aerospace and Civil Engineering, Harbin Engineering University, Harbin 150001, China
Multi-span lattice sandwich beam
Free vibration analysis
Assumed mode method
So far, little attention has been paid to the vibration analysis of multi-span lattice sandwich beams, particularly
using the assumed mode method (AMM). In this paper, the mode shapes of multi-span sandwich beams are
assumed as those of uniform beams modiﬁed by the interpolation functions. The equation of motion of the beam
is established using Hamilton’s principle. The natural frequencies of multi-span pyramidal and Kagome sandwich
beams so calculated agree well with those determined using the ANSYS software, which indicates that the
present methodology is suitable for solving multi-span sandwich beams with lattice truss cores. The eﬀects of
Young's modulus, damping and geometric parameters of cores and sheets on the natural frequencies and time
domain responses of two kinds of multi-span sandwich beams are analyzed. When the truss radius and sheet
thickness are increased, the natural frequencies are increased initially and then decrease, while the vibration
amplitudes at the mid-points of both the multi-span pyramidal and Kagome sandwich beams decrease. With the
increase of the inclination angle of the truss α
, the natural frequencies of structures experience a slight decline.
In contrast, the amplitudes at the mid-points of the two diﬀerent three-span sandwich beams both rise.
Sandwich structures have attracted much attention because of their
particular properties of high speciﬁc strength, high speciﬁc stiﬀness,
energy absorbing capability and so on. In order to meet the requirement
of ultra-light structure and multifunctional properties for naval and
aeronautical applications, the multi-span lattice sandwich beams are
designed in these ﬁelds, such as maneuverable underwater vehicles,
submarines, satellites, aerospace industries, ﬂight structures and so on
[1–3]. In addition, multi-span sandwich beams are more ﬂexible and
stretchable than a single-span sandwich structure. Hence, multi-span
lattice beams are widely available in the practical engineering design.
The structures consist of many periodic unit-cells, which have two
surface plates and the core with diﬀerent kinds of trusses. Various types
of lattice truss structures such as the tetrahedral lattice truss, the pyr-
amidal lattice truss, the 3D-kagome and so on are available [4–10].
Wang et al. [11,12] experimentally investigated the mechanical
behaviors of sandwich structures. The results show that the relative
density of the core and the material properties of truss members have a
major impact. Wang et al.  studied the performance characteristics
of Kagome sandwich structures and found that they exhibit greater
resistance to plastic buckling than tetrahedron sandwich structures with
the same equivalent core density. Lim and Kang  analyzed the
mechanical behaviors of tetrahedral and Kagome sandwich panels using
the elementary beam theory and experiments. Deshpande and Fleck
 measured the collapse responses of sandwich beams with truss
cores in 3-point bending and concluded that sandwich beams with truss
cores are signiﬁcantly lighter than those with metallic foam cores.
Xiong et al. [16,17] studied the mechanical behavior and failure of
composite pyramidal truss core sandwich panels by applying analytical
and experimental methods. The post-failure responses of the sandwich
panels were explored in depth through experiments. The diﬀerent
failure modes and the mechanical properties of the panels under each
loading condition were also investigated. The researches yielded re-
ference value for the optimal design of sandwich panels.
The vibration of sandwich structures is an important area of concern
in practical engineering such as in aeronautic, astronautic, marine and
mechanical engineering ﬁelds. Lou et al.  investigated the free vi-
bration of the sandwich beams with pyramidal truss cores, and the
frequencies so calculated were veriﬁed by ABAQUS ﬁnite element
software. Li and Lyu  used Hamilton’s principle and the assumed
mode method (AMM) to construct the equation of motion of a lattice
sandwich beam equipped with piezoelectric actuator and sensor pairs,
and studied the active vibration control of the beam. Song and Li
Received 18 August 2017; Received in revised form 13 November 2017; Accepted 24 November 2017
Corresponding authors at: College of Mechanical Engineering, Beijing University of Technology, Beijing 100124, China (F. Li).
E-mail addresses: email@example.com (S. Wen), firstname.lastname@example.org (F. Li).
Composite Structures 185 (2018) 716–727
Available online 24 November 2017
0263-8223/ © 2017 Elsevier Ltd. All rights reserved.