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

Demet Balkan; Zahit Mecitoǧlu

doi:10.1016/j.ijimpeng.2014.05.003

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

Demet Balkan^*
, Zahit Mecitoǧlu

^*Bu çalışma için yazışmadan sorumlu yazar

Uzay Mühendisliği Bölümü

Araştırma çıktısı: Dergi yayını › Makale › Hakem

38 Atıf (Scopus)

Özet

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.

Orijinal dil	İngilizce
Sayfa (başlangıç-bitiş)	85-104
Sayfa sayısı	20
Dergi	International Journal of Impact Engineering
Hacim	72
DOI'lar	https://doi.org/10.1016/j.ijimpeng.2014.05.003
Yayın durumu	Yayınlandı - Eki 2014

Finansman

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

Finansörler	Finansör numarası
The Scientific and Technological Research Council of Turkey	108M131

BM SKH

Bu sonuç, aşağıdaki Sürdürülebilir Kalkınma Hedefine/Hedeflerine katkıda bulunur

SKH 9 Sanayi, Yenilikçilik ve Altyapı

Belgeye Erişim

10.1016/j.ijimpeng.2014.05.003

Diğer Dosyalar ve Linkler

Link to publication in Scopus

Alıntı Yap

@article{27b292afea2647dca267c4dc4da19b9d,

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

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.",

keywords = "Galerkin's method, Kelvin-Voigt model, Manufacturing composite plates, Non-uniform blast load",

author = "Demet Balkan and Zahit Mecitoǧlu",

year = "2014",

month = oct,

doi = "10.1016/j.ijimpeng.2014.05.003",

language = "English",

volume = "72",

pages = "85--104",

journal = "International Journal of Impact Engineering",

issn = "0734-743X",

publisher = "Elsevier Ltd",

}

TY - JOUR

T1 - Nonlinear dynamic behavior of viscoelastic sandwich composite plates under non-uniform blast load

T2 - Theory and experiment

AU - Balkan, Demet

AU - Mecitoǧlu, Zahit

PY - 2014/10

Y1 - 2014/10

N2 - 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.

AB - 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.

KW - Galerkin's method

KW - Kelvin-Voigt model

KW - Manufacturing composite plates

KW - Non-uniform blast load

UR - https://www.scopus.com/pages/publications/84903184919

U2 - 10.1016/j.ijimpeng.2014.05.003

DO - 10.1016/j.ijimpeng.2014.05.003

M3 - Article

AN - SCOPUS:84903184919

SN - 0734-743X

VL - 72

SP - 85

EP - 104

JO - International Journal of Impact Engineering

JF - International Journal of Impact Engineering

ER -

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

Özet

Finansman

BM SKH

Belgeye Erişim

Diğer Dosyalar ve Linkler

Parmak izi

Alıntı Yap