Nonlinear dynamic behavior of viscoelastic sandwich composite plates under non-uniform blast load: Theory and experiment

Demet Balkan*, Zahit Mecitoǧlu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

35 Citations (Scopus)

Abstract

In this paper, the dynamic behavior of a viscoelastic sandwich composite plate subjected to the non-uniform blast load is investigated. The theoretical and experimental study is carried out. The plate examined has carbon/epoxy face sheets and an aramid honeycomb core. In the theoretical study, the sandwich plate is modeled using first order shear deformation theory. Because of the large deformations which occurred after the blast load in some tests, geometrical nonlinearities are considered in the derivations. The shear and large deflection effects are considered. The equations of motion are derived by the use of virtual work principle for the sandwich plate. The clamped boundary conditions are considered for all edges of the plate. The viscoelastic properties of carbon/epoxy coupons and sandwich coupons are determined using Dynamic Mechanical Analyzer. The viscoelastic behavior is modeled by using the Kelvin-Voigt linear viscoelastic theory. The equations of motion are obtained in the time domain using Galerkin's method. The nonlinear coupled equation system is solved by Mathematica Software. A special experimental setup is used to obtain the blast pressure for the blast test. The experimental, theoretical and finite element analysis results are compared and the vibration characteristics, peak points, vibration frequencies are found to be in an agreement.

Original languageEnglish
Pages (from-to)85-104
Number of pages20
JournalInternational Journal of Impact Engineering
Volume72
DOIs
Publication statusPublished - Oct 2014

Funding

This research is supported by The Scientific and Technological Research Council of Turkey under Project No. 108M131 . Appendix A (1) a 0 = − π 2 2 a b ( − 1 + ν + 2 ν 2 ) ( a 2 ( − 1 + 2 ν ) ( E 0 ( h − 4 h f ) + 8 h f Q ¯ 66 ( 1 + ν ) ) + 6 b 2 ( E 0 ( h − 4 h f ) ( − 1 + ν ) + 4 h f Q ¯ 11 ( − 1 + ν + 2 ν 2 ) ) ) a 1 = − π 2 2 ( − 1 + ν + 2 ν 2 ) ( − E 0 h + 4 E 0 h f + 8 h f ( Q ¯ 12 + Q ¯ 66 ) ( − 1 + ν + 2 ν 2 ) ) a 2 = − 1 4 a b ( − 1 + ν + 2 ν 2 ) ( − 4 a E 0 h π 3 + 16 a E 0 h f π 3 + 32 a h f π 3 Q ¯ 12 − 32 a h f π 3 Q ¯ 66 + 16 a E 0 h π 3 ν − 64 a E 0 h f π 3 ν − 32 a h f π 3 Q ¯ 12 ν + 32 a h f π 3 Q ¯ 66 ν − 64 a h f π 3 Q ¯ 12 ν 2 + 64 a h f π 3 Q ¯ 66 ν 2 ) a 3 = 1 4 a b ( − 1 + ν + 2 ν 2 ) ( − 2 a 2 E 1 h π 2 − 12 b 2 E 1 h π 2 + 8 a 2 E 1 h f π 2 + 48 b 2 E 1 h f π 2 + 4 a 2 E 1 h π 2 ν + 12 b 2 E 1 h π 2 ν − 16 a 2 E 1 h f π 2 ν − 48 b 2 E 1 h f π 2 ν ) a 4 = − 1 4 a b ( − 1 + ν + 2 ν 2 ) ( − 2 a b E 1 h π 2 + 8 a b E 1 h f π 2 ) a 5 = − 1 4 a b ( − 1 + ν + 2 ν 2 ) ( − 8 a E 1 h π 3 + 32 a E 1 h f π 3 + 32 a E 1 h π 3 ν − 128 a E 1 h f π 3 ν ) a 6 = − 1 4 a b ( − 1 + ν + 2 ν 2 ) ( − 3 a 2 b 2 I 0 + 3 a 2 b 2 I 0 ν + 6 a 2 b 2 I 0 ν 2 ) a 7 = − 3 4 a b I 1 (2) b 0 = − π 2 2 ( − 1 + ν + 2 ν 2 ) ( − E 0 h + 4 E 0 h f + 8 h f ( Q ¯ 12 + Q ¯ 66 ) ( − 1 + ν + 2 ν 2 ) ) b 1 = − π 2 2 a b ( − 1 + ν + 2 ν 2 ) ( b 2 ( − 1 + 2 ν ) ( E 0 ( h − 4 h f ) + 8 h f Q ¯ 66 ( 1 + ν ) ) + 6 a 2 ( E 0 ( h − 4 h f ) ( − 1 + ν ) + 4 h f Q ¯ 22 ( − 1 + ν + 2 ν 2 ) ) ) b 2 = 1 4 a b ( − 1 + ν + 2 ν 2 ) ( − 4 b E 0 h π 3 + 16 b E 0 h f π 3 + 32 b h f π 3 Q ¯ 12 − 32 b h f π 3 Q ¯ 66 + 16 b E 0 h π 3 ν − 64 b E 0 h f π 3 ν − 32 b h f π 3 Q ¯ 12 ν + 32 b h f π 3 Q ¯ 66 ν − 64 b h f π 3 Q ¯ 12 ν 2 + 64 b h f π 3 Q ¯ 66 ν 2 ) b 3 = 1 4 a b ( − 1 + ν + 2 ν 2 ) ( − 2 a b E 1 h π 2 + 8 a b E 1 h f π 2 ) b 4 = 1 4 a b ( − 1 + ν + 2 ν 2 ) ( − 12 a 2 E 1 h π 2 − 2 b 2 E 1 h π 2 + 48 a 2 E 1 h f π 2 + 8 b 2 E 1 h f π 2 + 12 a 2 E 1 h π 2 ν + 4 b 2 E 1 h π 2 ν − 48 a 2 E 1 h f π 2 ν − 16 b 2 E 1 h f π 2 ν ) b 5 = 1 4 a b ( − 1 + ν + 2 ν 2 ) ( − 8 b E 1 h π 3 + 32 b E 1 h f π 3 + 32 b E 1 h π 3 ν − 128 b E 1 h f π 3 ν ) b 6 = 1 4 a b ( − 1 + ν + 2 ν 2 ) ( − 3 a 2 b 2 I 0 + 3 a 2 b 2 I 0 ν + 6 a 2 b 2 I 0 ν 2 ) b 7 = 3 4 a b I 1 (3) c 0 = − 2 π 3 b ( − 1 + ν + 2 ν 2 ) ( E 0 ( h − 4 h f ) ( − 1 + 4 ν ) − 8 h f ( Q ¯ 12 − Q ¯ 66 ) ( − 1 + ν + 2 ν 2 ) ) c 1 = − 2 π 3 a ( − 1 + ν + 2 ν 2 ) ( E 0 ( h − 4 h f ) ( − 1 + 4 ν ) − 8 h f ( Q ¯ 12 − Q ¯ 66 ) ( − 1 + ν + 2 ν 2 ) ) c 2 = − 5 π 4 8 a 3 b 3 ( − 1 + ν + 2 ν 2 ) ( 21 b 4 ( E 0 ( h − 4 h f ) ( − 1 + ν ) + 4 h f Q ¯ 11 ( − 1 + ν + 2 ν 2 ) ) + 21 a 4 ( E 0 ( h − 4 h f ) ( − 1 + ν ) + 4 h f Q ¯ 22 ( − 1 + ν + 2 ν 2 ) ) + 10 a 2 b 2 ( E 0 ( h − 4 h f ) ( − 1 + ν ) + 4 h f ( Q ¯ 12 + 2 Q ¯ 66 ) ( − 1 + ν + 2 ν 2 ) ) ) c 3 = − 3 b E 0 π κ 4 ( − 1 + ν + 2 ν 2 ) ( h − 4 h f ) ( − 1 + 2 ν ) c 4 = − 3 a E 0 π κ 4 ( − 1 + ν + 2 ν 2 ) ( h − 4 h f ) ( − 1 + 2 ν ) c 5 = − 3 ( a 2 + b 2 ) E 0 π 2 κ 2 a b ( − 1 + ν + 2 ν 2 ) ( h − 4 h f ) ( − 1 + 2 ν ) c 6 = − 2 E 1 π 3 b ( − 1 + ν + 2 ν 2 ) ( h − 4 h f ) ( − 1 + 4 ν ) c 7 = − 2 E 1 π 3 a ( − 1 + ν + 2 ν 2 ) ( h − 4 h f ) ( − 1 + 4 ν ) c 8 = − 3 ( a 2 + b 2 ) E 1 π 2 κ 2 a b ( − 1 + ν + 2 ν 2 ) ( h − 4 h f ) ( − 1 + 2 ν ) c 9 = − 5 E 1 π 4 ( − 1 + ν ) 4 a 3 b 3 ( − 1 + ν + 2 ν 2 ) ( 21 a 4 + 10 a 2 b 2 + 21 b 4 ) ( h − 4 h f ) c 10 = − 3 b E 1 π κ 4 ( − 1 + ν + 2 ν 2 ) ( h − 4 h f ) ( − 1 + 2 ν ) c 11 = − 3 a E 1 π κ 4 ( − 1 + ν + 2 ν 2 ) ( h − 4 h f ) ( − 1 + 2 ν ) c 12 = − 9 a b I 0 4 ( − 1 + ν + 2 ν 2 ) ( 1 + ν ) ( − 1 + 2 ν ) (4) d 0 = − 3 b E 0 π κ 4 ( − 1 + ν + 2 ν 2 ) ( h − 4 h f ) ( − 1 + 2 ν ) d 1 = 1 24 a b ( − 1 + ν + 2 ν 2 ) ( ( − a 2 ( − 1 + 2 ν ) E 0 ( h − 4 h f ) 3 π 2 + 9 b 2 E 0 ( h − 4 h f ) κ + 8 h f ( 3 h 2 − 12 h h f + 16 h f 2 ) π 2 Q ¯ 66 ( 1 + ν ) ) − 6 b 2 π 2 ( E 0 ( h − 4 h f ) 3 ( − 1 + ν ) + 4 h f ( 3 h 2 − 12 h h f + 16 h f 2 ) Q ¯ 11 ( − 1 + ν + 2 ν 2 ) ) ) d 2 = 1 24 a b ( − 1 + ν + 2 ν 2 ) ( a b E 0 h 3 π 2 − 12 a b E 0 h 2 h f π 2 + 48 a b E 0 h h f 2 π 2 − 64 a b E 0 h f 3 π 2 + 24 a b h 2 h f π 2 Q ¯ 12 − 96 a b h h f 2 π 2 Q ¯ 12 + 128 a b h f 3 π 2 Q ¯ 12 + 24 a b h 2 h f π 2 Q ¯ 66 − 96 a b h h f 2 π 2 Q ¯ 66 + 128 a b h f 3 π 2 Q ¯ 66 − 24 a b h 2 h f π 2 Q ¯ 12 ν + 96 a b h h f 2 π 2 Q ¯ 12 ν − 128 a b h f 3 π 2 Q ¯ 12 ν − 24 a b h 2 h f π 2 Q ¯ 66 ν + 96 a b h h f 2 π 2 Q ¯ 66 ν − 128 a b h f 3 π 2 Q ¯ 66 ν − 48 a b h 2 h f π 2 Q ¯ 12 ν 2 + 192 a b h h f 2 π 2 Q ¯ 12 ν 2 − 256 a b h f 3 π 2 Q ¯ 12 ν 2 − 48 a b h 2 h f π 2 Q ¯ 66 ν 2 + 192 a b h h f 2 π 2 Q ¯ 66 ν 2 − 256 a b h f 3 π 2 Q ¯ 66 ν 2 ) d 3 = 1 24 a b ( − 1 + ν + 2 ν 2 ) ( 18 a b 2 E 1 h π κ − 72 a b 2 E 1 h f π κ − 36 a b 2 E 1 h π κ ν + 144 a b 2 E 1 h f π κ ν ) d 4 = 1 24 a b ( − 1 + ν + 2 ν 2 ) ( a 2 E 1 h 3 π 2 + 6 b 2 E 1 h 3 π 2 − 12 a 2 E 1 h 2 h f π 2 − 72 b 2 E 1 h 2 h f π 2 + 48 a 2 E 1 h h f 2 π 2 + 288 b 2 E 1 h h f 2 π 2 − 64 a 2 E 1 h f 3 π 2 − 384 b 2 E 1 h f 3 π 2 + 9 a 2 b 2 E 1 h κ − 36 a 2 b 2 E 1 h f κ − 2 a 2 E 1 h 3 π 2 ν − 6 b 2 E 1 h 3 π 2 ν + 24 a 2 E 1 h 2 h f π 2 ν + 72 b 2 E 1 h 2 h f π 2 ν − 96 a 2 E 1 h h f 2 π 2 ν − 288 b 2 E 1 h h f 2 π 2 ν + 128 a 2 E 1 h f 3 π 2 ν + 384 b 2 E 1 h f 3 π 2 ν − 18 a 2 b 2 E 1 h κ ν + 72 a 2 b 2 E 1 h f κ ν ) d 5 = 1 24 a b ( − 1 + ν + 2 ν 2 ) ( a b E 1 h 3 π 2 − 12 a b E 1 h 2 h f π 2 + 48 a b E 1 h h f 2 π 2 − 64 a b E 1 h f 3 π 2 ) d 6 = 1 24 a b ( − 1 + ν + 2 ν 2 ) ( 18 a 2 b 2 I 1 − 18 a 2 b 2 I 1 ν − 36 a 2 b 2 I 1 ν 2 ) d 7 = − 3 4 a b I 2 (5) e 0 = − 3 a E 0 π κ 4 ( − 1 + ν + 2 ν 2 ) ( h − 4 h f ) ( − 1 + 2 ν ) e 1 = π 2 24 ( − 1 + ν + 2 ν 2 ) ( E 0 ( h − 4 h f ) 3 − 8 h f ( 3 h 2 − 12 h h f + 16 h f 2 ) ( Q ¯ 12 + Q ¯ 66 ) ( − 1 + ν + 2 ν 2 ) ) e 2 = 1 24 a b ( − 1 + ν + 2 ν 2 ) ( 6 a 2 E 0 h 3 π 2 + b 2 E 0 h 3 π 2 − 72 a 2 E 0 h 2 h f π 2 − 12 b 2 E 0 h 2 h f π 2 + 288 a 2 E 0 h h f 2 π 2 + 48 b 2 E 0 h h f 2 π 2 − 384 a 2 E 0 h f 3 π 2 − 64 b 2 E 0 h f 3 π 2 + 72 a 2 h 2 h f π 2 Q ¯ 22 − 288 a 2 h h f 3 π 2 Q ¯ 22 + 384 a 2 h f 3 π 2 Q ¯ 22 + 24 b 2 h 2 h f π 2 Q ¯ 66 − 96 b 2 h h f 2 π 2 Q ¯ 66 + 128 b 2 h f 3 π 2 Q ¯ 66 + 9 a 2 b 2 E 0 h κ − 36 a 2 b 2 E 0 h f κ − 6 a 2 E 0 h 3 π 2 ν − 2 b 2 E 0 h 3 π 2 ν + 72 a 2 E 0 h 2 h f π 2 ν + 24 b 2 E 0 h 2 h f π 2 ν − 288 a 2 E 0 h h f 2 π 2 ν − 96 b 2 E 0 h h f 2 π 2 ν + 384 a 2 E 0 h f 3 π 2 ν + 128 b 2 E 0 h f 3 π 2 ν − 72 a 2 h 2 h f π 2 Q ¯ 22 ν + 288 a 2 h h f 2 π 2 Q ¯ 22 ν − 384 a 2 h f 3 π 2 Q ¯ 22 ν − 24 b 2 h 2 h f π 2 Q ¯ 66 ν + 96 b 2 h h f 2 π 2 Q ¯ 66 ν − 128 b 2 h f 3 π 2 Q ¯ 66 ν − 18 a 2 b 2 E 0 h κ ν + 72 a 2 b 2 E 0 h f κ ν − 144 a 2 h 2 h f π 2 Q ¯ 22 ν 2 + 576 a 2 h h f 2 π 2 Q ¯ 22 ν 2 − 768 a 2 h f 3 π 2 Q ¯ 22 ν 2 − 48 b 2 h 2 h f π 2 Q ¯ 66 ν 2 + 192 b 2 h h f 2 π 2 Q ¯ 66 ν 2 − 256 b 2 h f 3 π 2 Q ¯ 66 ν 2 ) e 3 = 1 24 a b ( − 1 + ν + 2 ν 2 ) ( 18 a 2 b E 1 h π κ − 72 a 2 b E 1 h f π κ − 36 a 2 b E 1 h π κ ν + 144 a 2 b E 1 h f π κ ν ) e 4 = 1 24 a b ( − 1 + ν + 2 ν 2 ) ( a b E 1 h 3 π 2 − 12 a b E 1 h 2 h f π 2 + 48 a b E 1 h h f 2 π 2 − 64 a b E 1 h f 3 π 2 ) e 5 = 1 24 a b ( − 1 + ν + 2 ν 2 ) ( 6 a 2 E 1 h 3 π 2 + b 2 E 1 h 3 π 2 − 72 a 2 E 1 h 2 h f π 2 − 12 b 2 E 1 h 2 h f π 2 + 288 a 2 E 1 h h f 2 π 2 + 48 b 2 E 1 h h f 2 π 2 − 384 a 2 E 1 h f 3 π 2 − 64 b 2 E 1 h f 3 π 2 + 9 a 2 b 2 E 1 h κ − 36 a 2 b 2 E 1 h f κ − 6 a 2 E 1 h 3 π 2 ν − 2 b 2 E 1 h 3 π 2 ν + 72 a 2 E 1 h 2 h f π 2 ν + 24 b 2 E 1 h 2 h f π 2 ν − 288 a 2 E 1 h h f 2 π 2 ν − 96 b 2 E 1 h h f 2 π 2 ν + 384 a 2 E 1 h f 3 π 2 ν + 128 b 2 E 1 h f 3 π 2 ν − 18 a 2 b 2 E 1 h κ ν + 72 a 2 b 2 E 1 h f κ ν ) e 6 = 1 24 a b ( − 1 + ν + 2 ν 2 ) ( 18 a 2 b 2 I 1 − 18 a 2 b 2 I 1 ν − 36 a 2 b 2 I 1 ν 2 ) e 7 = − 3 4 a b I 2

FundersFunder number
The Scientific and Technological Research Council of Turkey108M131

    Keywords

    • Galerkin's method
    • Kelvin-Voigt model
    • Manufacturing composite plates
    • Non-uniform blast load

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