Abstract

The geometrical nonlinear dynamic response of sandwich beams is studied using a dynamic high-order nonlinear model. The model is derived using the variational principle of virtual work and uses the Extended High-Order Sandwich Panel Theory approach with consideration of two interfaces between the three layers. A first-order shear deformation theory is adopted for the face sheets, while the kinematic assumption of high-order small deformations that account for out-of-plane compressibility are considered for the core layer. The nonlinearity of the dynamic model is introduced by considering geometrically nonlinear kinematic relations in the face sheets. The nonlinear kinematic relations and the dynamic modeling aim to evaluate the effects of the two features and their coupling on the response. The nonlinear dynamic response of sandwich beams is studied through two numerical cases and comparison of the nonlinear results with their linear counterparts. The first case looks into the coupling of the global geometrical nonlinear behavior with the dynamic behavior. The second case focuses on the local instability of the face sheets and its interaction with the compressibility of the core in the dynamic response of soft core sandwich beams. The comparison of linear and nonlinear dynamic response in the two cases sheds light on the coupling of the geometrical nonlinear and dynamic behaviors. Among other features, the latter is expressed by nonlinear attractors, higher modes response, nonlinear frequency response, and significant wrinkling response.

References

References
1.
Kardomateas
,
G.
,
Frostig
,
Y.
, and
Phan
,
C.
,
2012
, “
Dynamic Elasticity Solution for the Transient Blast Response of Sandwich Beams/Wide Plates
,”
AIAA J.
,
51
(
2
), pp.
485
491
. 10.2514/1.J051885
2.
Kardomateas
,
G. A.
,
Rodcheuy
,
N.
, and
Frostig
,
Y.
,
2015
, “
Transient Blast Response of Sandwich Plates by Dynamic Elasticity
,”
AIAA J.
,
53
(
6
), pp.
1424
1432
. 10.2514/1.J052865
3.
Loja
,
M.
,
Barbosa
,
J. I.
, and
Soares
,
C. M.
,
2015
, “
Dynamic Behaviour of Soft Core Sandwich Beam Structures Using Kriging-Based Layerwise Models
,”
Compos. Struct.
,
134
, pp.
883
894
. 10.1016/j.compstruct.2015.08.096
4.
Moreira
,
R.
, and
Rodrigues
,
J. D.
,
2010
, “
Static and Dynamic Analysis of Soft Core Sandwich Panels With Through-Thickness Deformation
,”
Compos. Struct.
,
92
(
2
), pp.
201
215
. 10.1016/j.compstruct.2009.07.015
5.
Ganapathi
,
M.
,
Patel
,
B.
, and
Makhecha
,
D.
,
2004
, “
Nonlinear Dynamic Analysis of Thick Composite/Sandwich Laminates Using an Accurate Higher-Order Theory
,”
Compos. Part B: Eng.
,
35
(
4
), pp.
345
355
. 10.1016/S1359-8368(02)00075-6
6.
Li
,
R.
,
Kardomateas
,
G. A.
, and
Simitses
,
G. J.
,
2009
, “
Point-Wise Impulse (Blast) Response of a Composite Sandwich Plate Including Core Compressibility Effects
,”
Int. J. Solids Struct.
,
46
(
10
), pp.
2216
2223
. 10.1016/j.ijsolstr.2009.01.036
7.
Yuan
,
Z.
, and
Kardomateas
,
G. A.
,
2018
, “
Nonlinear Dynamic Response of Sandwich Wide Panels
,”
Int. J. Solids Struct.
,
148
(
Special Issue Dedicated to the Memory of George Simitses
), pp.
110
121
. 10.1016/j.ijsolstr.2017.09.028
8.
Feldfogel
,
S.
, and
Rabinovitch
,
O.
,
2019
, “
Soft-Core Sandwich Plate Dynamics: Theory and Blast Analysis
,”
J. Sandwich Struct. Mater.
, p.
1099636219838968
.
9.
Katariya
,
P. V.
,
Panda
,
S. K.
, and
Mahapatra
,
T. R.
,
2017
, “
Prediction of Nonlinear Eigenfrequency of Laminated Curved Sandwich Structure Using Higher-Order Equivalent Single-Layer Theory
,”
J. Sandwich Struct. Mater.
,
21
(
8
), p.
1099636217728420
.
10.
Bilasse
,
M.
,
Azrar
,
L.
, and
Daya
,
E.
,
2011
, “
Complex Modes Based Numerical Analysis of Viscoelastic Sandwich Plates Vibrations
,”
Comput. Struct.
,
89
(
7–8
), pp.
539
555
. 10.1016/j.compstruc.2011.01.020
11.
Mahmoudkhani
,
S.
,
Haddadpour
,
H.
, and
Navazi
,
H.
,
2014
, “
The Effects of Nonlinearities on the Vibration of Viscoelastic Sandwich Plates
,”
Int. J. Non-Linear Mech.
,
62
, pp.
41
57
. 10.1016/j.ijnonlinmec.2014.01.002
12.
Schwarts-Givli
,
H.
,
Rabinovitch
,
O.
, and
Frostig
,
Y.
,
2007
, “
High-Order Nonlinear Contact Effects in the Dynamic Behavior of Delaminated Sandwich Panels With a Flexible Core
,”
Int. J. Solids Struct.
,
44
(
1
), pp.
77
99
. 10.1016/j.ijsolstr.2006.04.016
13.
Odessa
,
I.
,
Frostig
,
Y.
, and
Rabinovitch
,
O.
,
2020
, “
Dynamic Interfacial Debonding in Sandwich Panels
,”
Compos. Part B: Eng.
,
185
, p.
107733
. 10.1016/j.compositesb.2019.107733
14.
Burlayenko
,
V.
, and
Sadowski
,
T.
,
2014
, “
Nonlinear Dynamic Analysis of Harmonically Excited Debonded Sandwich Plates Using Finite Element Modelling
,”
Compos. Struct.
,
108
, pp.
354
366
. 10.1016/j.compstruct.2013.09.042
15.
Alijani
,
F.
, and
Amabili
,
M.
,
2013
, “
Nonlinear Vibrations of Laminated and Sandwich Rectangular Plates With Free Edges. Part 1: Theory and Numerical Simulations
,”
Compos. Struct.
,
105
, pp.
422
436
. 10.1016/j.compstruct.2013.05.034
16.
Alijani
,
F.
,
Amabili
,
M.
,
Ferrari
,
G.
, and
D’Alessandro
,
V.
,
2013
, “
Nonlinear Vibrations of Laminated and Sandwich Rectangular Plates With Free Edges. Part 2: Experiments & Comparisons
,”
Compos. Struct.
,
105
, pp.
437
445
. 10.1016/j.compstruct.2013.05.020
17.
Reddy
,
J. N.
,
2003
,
Mechanics of Laminated Composite Plates and Shells: Theory and Analysis
,
CRC Press
,
Boca Raton, FL
.
18.
Odessa
,
I.
,
Frostig
,
Y.
, and
Rabinovitch
,
O.
,
2018
, “
Modeling of Interfacial Debonding Propagation in Sandwich Panels
,”
Int. J. Solids Struct.
,
148
(
Special Issue Dedicated to the Memory of George Simitses
), pp.
67
78
. 10.1016/j.ijsolstr.2017.10.014
19.
Odessa
,
I.
,
Rabinovitch
,
O.
, and
Frostig
,
Y.
,
2019
, “
High-Order Crack Propagation in Compressed Sandwich Panels
,”
J. Sandwich Struct. Mater.
,
21
(
5
), pp.
1726
1750
. 10.1177/1099636218824873
20.
Phan
,
C. N.
,
Frostig
,
Y.
, and
Kardomateas
,
G. A.
,
2012
, “
Analysis of Sandwich Beams With a Compliant Core and With in-Plane Rigidity—Extended High-Order Sandwich Panel Theory Versus Elasticity
,”
ASME J. Appl. Mech.
,
79
(
4
), p.
041001
. 10.1115/1.4005550
21.
Rabinovitch
,
O.
,
2014
, “
An Extended High Order Cohesive Interface Approach to the Debonding Analysis of FRP Strengthened Beams
,”
Int. J. Mech. Sci.
,
81
, pp.
1
16
. 10.1016/j.ijmecsci.2014.01.013
22.
Rabinovitch
,
O.
,
2014
, “
Dynamic Edge Debonding in FRP Strengthened Beams
,”
Eur. J. Mech.-A/Solids
,
47
, pp.
309
326
. 10.1016/j.euromechsol.2014.04.008
23.
Char
,
B.
,
Geddes
,
K. O.
,
Gonnet
,
G. H.
,
Leong
,
B. L.
,
Monagan
,
M. B.
, and
Watt
,
S.
,
2013
,
Maple V Library Reference Manual
,
Springer Science & Business Media
,
New York
.
You do not currently have access to this content.