Startseite Technik Improving the dynamic behavior of the plate under supersonic air flow by using nonlinear energy sink
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Improving the dynamic behavior of the plate under supersonic air flow by using nonlinear energy sink

  • Hassan Asadigorji und Ardeshir Karami Mohammadi ORCID logo EMAIL logo
Veröffentlicht/Copyright: 3. September 2021
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International Journal of Nonlinear Sciences and Numerical Simulation
Aus der Zeitschrift International Journal of Nonlinear Sciences and Numerical Simulation Band 24 Heft 6

Abstract

In this paper, a nonlinear energy sink is used to improve the dynamic behavior of a square plate in supersonic flow. The plate is examined with different boundary conditions. The effect of changing the parameters and installation location of nonlinear energy sink on improving the dynamic behavior of the plate has been studied. The governing equations are first obtained using Von Kármán’s plate theory and piston theory, and then discretized using the Rayleigh–Ritz process. These equations are then solved using the fourth-order Runge–Kutta method. Time history curves, phase portraits, Poincaré maps, and bifurcation diagrams were used to investigate the dynamic behavior and impact of nonlinear energy sink. The results show that the dynamic behavior of the plate is very complex in some cases, but with proper use of nonlinear energy sinks, this behavior can be improved.

Keywords: bifurcation diagram; nonlinear energy sink; plate; Poincarémap; Rayleigh–Ritz method; supersonic flow
Corresponding author: Ardeshir Karami Mohammadi, Department of Mechanical Engineering, Shahrood University of Technology, P.O. Box 3619995161, Shahrood, Iran, E-mail:

  1. Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.

  2. Research funding: No funds received.

  3. Conflict of interest statement: The authors declare no conflicts of interest regarding this article.

Appendix A

The equation of motions

a ρ m h ∑ g = 1 G ∑ h = 1 H a ̈ g h t ∫ 0 a u i u g d x ∫ 0 b v j v h d y + E h 1 − ν 2 × ∑ g = 1 G ∑ h = 1 H a g h t ∫ 0 a u i ′ u g ′ d x ∫ 0 b v j v h d y   + 1 2 ∑ o = 1 O ∑ p = 1 P q o p t ∑ o 1 = 1 O 1 ∑ p 1 = 1 P 1 q o 1 p 1 t ∫ 0 a u i ′ ϕ o ′ ϕ o 1 ′ d x ∫ 0 b v j ψ p ψ p 1 d y   + ν ∑ f = 1 F ∑ d = 1 D b f d t ∫ 0 a u i ′ u f d x ∫ 0 b v j v d ′ d y + 1 2 ∑ o = 1 O ∑ p = 1 P q o p t ∑ o 1 = 1 O 1 ∑ p 1 = 1 P 1 q o 1 p 1 t ∫ 0 a u i ′ ϕ o ϕ o 1 d x ∫ 0 b v j ψ p ′ ψ p 1 ′ d y   + 1 − ν 2 ∑ f = 1 F ∑ d = 1 D b f d t ∫ 0 a u i u f ′ d x ∫ 0 b v j ′ v d d y + ∑ g = 1 G ∑ h = 1 H a g h t ∫ 0 a u i u g d x ∫ 0 b v j ′ v h ′ d y   + ∑ o = 1 O ∑ p = 1 P q o p t ∑ o 1 = 1 O 1 ∑ p 1 = 1 P 1 q o 1 p 1 t ∫ 0 a u i ϕ o ′ ϕ o 1 d x ∫ 0 b v j ′ ψ p ψ p 1 ′ d y = 0

b ρ m h ∑ f = 1 F ∑ d = 1 D b ̈ f d τ ∫ 0 a u r u f d x ∫ 0 b v s v d d y + E h 1 − ν 2 × ∑ f = 1 F ∑ d = 1 D b f d τ ∫ 0 a u r u f d x ∫ 0 b v s ′ v d ′ d y   + 1 2 ∑ o = 1 O ∑ p = 1 P q o p τ ∑ o 1 = 1 O 1 ∑ p 1 = 1 P 1 q o 1 p 1 τ ∫ 0 a u r ϕ o ϕ o 1 d x ∫ 0 b v s ′ ψ p ′ ψ p 1 ′ d y   + ν ∫ 0 a u r u g ′ d x ∫ 0 b v s ′ v h d y ∑ g = 1 G ∑ h = 1 H a g h τ   + 1 2 ∑ o = 1 O ∑ p = 1 P q o p τ ∑ o 1 = 1 O 1 ∑ p 1 = 1 P 1 q o 1 p 1 τ ∫ 0 a u r ϕ o ′ ϕ o 1 ′ d x ∫ 0 b v s ′ ψ p ψ p 1 d y   + 1 − ν 2 ∑ f = 1 F ∑ d = 1 D b f d τ ∫ 0 a u r ′ u f ′ d x ∫ 0 b v s v d d y + ∑ g = 1 G ∑ h = 1 H a g h τ ∫ 0 a u r ′ u g d x ∫ 0 b v s v h ′ d y   + ∑ o = 1 O ∑ p = 1 P q o p τ ∑ o 1 = 1 O 1 ∑ p 1 = 1 P 1 q o 1 p 1 τ ∫ 0 a u r ′ ϕ o ′ ϕ o 1 d x ∫ 0 b v s ψ p ψ p 1 ′ d y = 0

c ρ m h ∑ o = 1 O ∑ p = 1 P q ̈ o p t ∫ 0 a ϕ m ϕ o d x ∫ 0 b ψ n ψ p d y + D × ∑ o = 1 O ∑ p = 1 P q o p τ ∫ 0 a ϕ m ″ ϕ o ″ d x ∫ 0 b ψ n ψ p d y + ∑ o = 1 O ∑ p = 1 P q o p τ ∫ 0 a ϕ m ″ ϕ o d x ∫ 0 b ψ n ψ p ″ d y   + ∑ o = 1 O ∑ p = 1 P q o p τ ∫ 0 a ϕ m ϕ o ″ d x ∫ 0 b ψ n ″ ψ p d y + ∑ o = 1 O ∑ p = 1 P q o p τ ∫ 0 a ϕ m ϕ o d x ∫ 0 b ψ n ″ ψ p ″ d y   − 1 − ν ∑ o = 1 O ∑ p = 1 P q o p τ ∫ 0 a ϕ m ″ ϕ o d x ∫ 0 b ψ n ψ p ″ d y + ∑ o = 1 O ∑ p = 1 P q o p τ ∫ 0 a ϕ m ϕ o ″ d x ∫ 0 b ψ n ″ ψ p d y   − 2 ∑ o = 1 O ∑ p = 1 P q o p τ ∫ 0 a ϕ m ′ ϕ o ′ d x ∫ 0 b ψ n ′ ψ p ′ d y

+ E h 1 − ν 2 ∑ o = 1 O ∑ p = 1 P q o p t ∑ g = 1 G ∑ h = 1 H a g h t ∫ 0 a ϕ m ′ ϕ o ′ u g ′ d x ∫ 0 b ψ n ψ p v h d y   + 1 2 ∑ o = 1 O ∑ p = 1 P q o p t ∑ o 1 = 1 O 1 ∑ p 1 = 1 P 1 q o 1 p 1 t ∑ o 2 = 1 O 2 ∑ p 2 = 1 P 2 q o 2 p 2 t ∫ 0 a ϕ m ′ ϕ o ′ ϕ o 1 ′ ϕ o 2 ′ d x ∫ 0 b ψ n ψ p ψ p 1 ψ p 2 d y   + ∑ o = 1 O ∑ p = 1 P q o p t ∑ f = 1 F ∑ d = 1 D b f d t ∫ 0 a ϕ m ϕ o u f d x ∫ 0 b ψ n ′ ψ p ′ v d ′ d y + ν ∑ o = 1 O ∑ p = 1 P q o p t ∑ f = 1 F ∑ d = 1 D b f d t ∫ 0 a ϕ m ′ ϕ o ′ u f d x ∫ 0 b ψ n ψ p v d ′ d y   + ∑ o 2 = 1 O 2 ∑ p 2 = 1 P 2 q o 2 p 2 t ∑ g = 1 G ∑ h = 1 H a g h t ∫ 0 a ϕ m ϕ o 2 u g ′ d x ∫ 0 b ψ n ′ ψ p 2 ′ v h d y   + 1 2 ∑ o 2 = 1 O 2 ∑ p 2 = 1 P 2 q o 2 p 2 t ∑ o = 1 O ∑ p = 1 P q o p t ∑ o 1 = 1 O 1 ∑ p 1 = 1 P 1 q o 1 p 1 t ∫ 0 a ϕ m ϕ o 2 ϕ o ′ ϕ o 1 ′ d x ∫ 0 b ψ n ′ ψ p 2 ′ ψ p ψ p 1 d y   + 1 2 ∑ o = 1 O ∑ p = 1 P q o p t ∑ o 1 = 1 O 1 ∑ p 1 = 1 P 1 q o 1 p 1 t ∑ o 2 = 1 O 2 ∑ p 2 = 1 P 2 q o 2 p 2 t ∫ 0 a ϕ m ′ ϕ o ′ ϕ o 1 ϕ o 2 d x ∫ 0 b ψ n ψ p ψ p 1 ′ ψ p 2 ′ d y

+ E h 1 − ν 2 + 1 − ν 2 ∑ o = 1 O ∑ p = 1 P q o p t ∑ f = 1 F ∑ d = 1 D b f d t ∫ 0 a ϕ m ′ ϕ o u f ′ d x ∫ 0 b ψ n ψ p ′ v d d y   + ∑ o = 1 O ∑ p = 1 P q o p t ∑ f = 1 F ∑ d = 1 D b f d t ∫ 0 a ϕ m ϕ o ′ u f ′ d x ∫ 0 b ψ n ′ ψ p v d d y   + ∑ o = 1 O ∑ p = 1 P q o p t ∑ g = 1 G ∑ h = 1 H a g h t ∫ 0 a ϕ m ′ ϕ o u g d x ∫ 0 b ψ n ψ p ′ v h ′ d y   + ∑ o = 1 O ∑ p = 1 P q o p t ∑ g = 1 G ∑ h = 1 H a g h t ∫ 0 a ϕ m ϕ o ′ u g d x ∫ 0 b ψ n ′ ψ p v h ′ d y   + ∑ o = 1 O ∑ p = 1 P q o p t ∑ o 1 = 1 O 1 ∑ p 1 = 1 P 1 q o 1 p 1 t ∑ o 2 = 1 O 2 ∑ p 2 = 1 P 2 q o 2 p 2 t ∫ 0 a ϕ m ′ ϕ o ϕ o 1 ′ ϕ o 2 d x ∫ 0 b ψ n ψ p ′ ψ p 1 ψ p 2 ′ d y   + ∑ o = 1 O ∑ p = 1 P q o p t ∑ o 1 = 1 O 1 ∑ p 1 = 1 P 1 q o 1 p 1 t ∑ o 2 = 1 O 2 ∑ p 2 = 1 P 2 q o 2 p 2 t ∫ 0 a ϕ m ϕ o ′ ϕ o 1 ′ ϕ o 2 d x ∫ 0 b ψ n ′ ψ p ψ p 1 ψ p 2 ′ d y

+ 2 q β ∑ o = 1 O ∑ p = 1 P q o p τ ∫ 0 a ϕ m ϕ o ′ d x ∫ 0 b ψ n ψ p d y + M a 2 − 2 M a 2 − 1 1 V ∞ ∑ o = 1 O ∑ p = 1 P q ̇ o p τ ∫ 0 a ϕ m ϕ o d x ∫ 0 b ψ n ψ p d y

+ K 1 ∂ w x e , y e , t ∂ q m n w x e , y e , t − q s t + K 3 ∂ w x e , y e , t ∂ q m n w x e , y e , t − q s t 3 + C ∂ w ̇ x e , y e , t ∂ q ̇ m n w ̇ x e , y e , t − q ̇ s t = 0

d m q ̈ s − K 1 ∑ m = 1 M ∑ n = 1 N q m n t ϕ m x e ψ n y e + K 1 q s t

− K 3 ∑ m = 1 M ∑ n = 1 N q m n t ϕ m x e ψ n y e ∑ m 1 = 1 M ∑ n 1 = 1 N q m 1 n 1 t ϕ m 1 x e ψ n 1 y e   × ∑ m 2 = 1 M ∑ n 2 = 1 N q m 2 n 2 t ϕ m 2 x e ψ n 2 y e − 3 ∑ m = 1 M ∑ n = 1 N q m n t ϕ m x e ψ n y e   × ∑ m 1 = 1 M ∑ n 1 = 1 N q m 1 n 1 t ϕ m 1 x e ψ n 1 y e q s t + 3 ∑ m = 1 M ∑ n = 1 N q m n t ϕ m x e ψ n y e q s 2 t − q s 3 t − C ∑ m = 1 M ∑ n = 1 N q ̇ m n t ϕ m x e ψ n ( y e ) + C q ̇ s t = 0

Appendix B

M u = ∑ g = 1 G ∑ h = 1 H a ̈ g h τ ∫ 0 1 u i u g d ξ ∫ 0 1 v j v h d η

N L u w 1 = ∑ o = 1 O ∑ p = 1 P q o p τ ∑ o 1 = 1 O 1 ∑ p 1 = 1 P 1 q o 1 p 1 τ ∫ 0 1 u i ′ ϕ o ′ ϕ o 1 ′ d ξ ∫ 0 1 v j ψ p ψ p 1 d η

N L u w 2 = ∑ o = 1 O ∑ p = 1 P q o p τ ∑ o 1 = 1 O 1 ∑ p 1 = 1 P 1 q o 1 p 1 τ ∫ 0 1 u i ′ ϕ o ϕ o 1 d ξ ∫ 0 1 v j ψ p ′ ψ p 1 ′ d η

N L u w 3 = ∑ o = 1 O ∑ p = 1 P q o p τ ∑ o 1 = 1 O 1 ∑ p 1 = 1 P 1 q o 1 p 1 τ ∫ 0 1 u i ϕ o ′ ϕ o 1 d ξ ∫ 0 1 v j ′ ψ p ψ p 1 ′ d η

M v = ∑ f = 1 F ∑ d = 1 D b ̈ f d τ ∫ 0 1 u r u f d ξ ∫ 0 1 v s v d d η

K v v 12 = ∑ f = 1 F ∑ d = 1 D b f d τ ∫ 0 1 u r u f d ξ ∫ 0 1 v s ′ v d ′ d η

K v v 34 = ∑ f = 1 F ∑ d = 1 D b f d τ ∫ 0 1 u r ′ u f ′ d ξ ∫ 0 1 v s v d d η

K v u 12 = ∑ g = 1 G ∑ h = 1 H a g h τ ∫ 0 1 u g ′ u r d ξ ∫ 0 1 v h v s ′ d η

K v u 34 = ∑ g = 1 G ∑ h = 1 H a g h τ ∫ 0 1 u r ′ u g d ξ ∫ 0 1 v s v h ′ d η

N L v w 1 = ∑ o = 1 O ∑ p = 1 P q o p τ ∑ o 1 = 1 O 1 ∑ p 1 = 1 P 1 q o 1 p 1 τ ∫ 0 1 u r ϕ o ϕ o 1 d ξ ∫ 0 1 v s ′ ψ p ′ ψ p 1 ′ d η

N L v w 2 = ∑ o = 1 O ∑ p = 1 P q o p τ ∑ o 1 = 1 O 1 ∑ p 1 = 1 P 1 q o 1 p 1 τ ∫ 0 1 ϕ o ′ ϕ o 1 ′ u r d ξ ∫ 0 1 ψ p ψ p 1 v s ′ d η

N L v w 3 = ∑ o = 1 O ∑ p = 1 P q o p τ ∑ o 1 = 1 O 1 ∑ p 1 = 1 P 1 q o 1 p 1 τ ∫ 0 1 u r ′ ϕ o ′ ϕ o 1 d ξ ∫ 0 1 v s ψ p ψ p 1 ′ d η

K u v 34 = ∑ f = 1 F ∑ d = 1 D b f d τ ∫ 0 1 u i u f ′ d ξ ∫ 0 1 v j ′ v d d η

M w w 1 = ∑ o = 1 O ∑ p = 1 P q ̈ o p τ ∫ 0 1 ϕ m ϕ o d ξ ∫ 0 1 ψ n ψ p d η

K w w 1 = ∑ o = 1 O ∑ p = 1 P q o p τ ∫ 0 1 ϕ m ϕ o d ξ ∫ 0 1 ψ n ″ ψ p ″ d η

K w w 2 = ∑ o = 1 O ∑ p = 1 P q o p τ ∫ 0 1 ϕ m ″ ϕ o ″ d ξ ∫ 0 1 ψ n ψ p d η

K w w 3 = ∑ o = 1 O ∑ p = 1 P q o p τ ∫ 0 1 ϕ m ″ ϕ o d ξ ∫ 0 1 ψ n ψ p ″ d η

K w w 4 = ∑ o = 1 O ∑ p = 1 P q o p τ ∫ 0 1 ϕ m ϕ o ″ d ξ ∫ 0 1 ψ n ″ ψ p d η

K w w 5 = ∑ o = 1 O ∑ p = 1 P q o p τ ∫ 0 1 ϕ m ′ ϕ o ′ d ξ ∫ 0 1 ψ n ′ ψ p ′ d η

N L w u 1 = ∑ o = 1 O ∑ p = 1 P q o p τ ∑ g = 1 G ∑ h = 1 H a g h τ ∫ 0 1 ϕ m ′ ϕ o ′ u g ′ d ξ ∫ 0 1 ψ n ψ p v h d η

N L w u 2 = ∑ g = 1 G ∑ h = 1 H a g h τ ∑ o 2 = 1 O 2 ∑ p 2 = 1 P 2 q o 2 p 2 τ ∫ 0 1 u g ′ ϕ m ϕ o 2 d ξ ∫ 0 1 v h ψ n ′ ψ p 2 ′ d η

N L w u 3 = ∑ o = 1 O ∑ p = 1 P q o p τ ∑ g = 1 G ∑ h = 1 H a g h τ ∫ 0 1 ϕ m ′ ϕ o u g d ξ ∫ 0 1 ψ n ψ p ′ v h ′ d η

N L w v 1 = ∑ o = 1 O ∑ p = 1 P q o p τ ∑ f = 1 F ∑ d = 1 D b f d τ ∫ 0 1 ϕ m ϕ o u f d ξ ∫ 0 1 ψ n ′ ψ p ′ v d ′ d η

N L w v 2 = ∑ o = 1 O ∑ p = 1 P q o p τ ∑ f = 1 F ∑ d = 1 D b f d τ ∫ 0 1 ϕ m ′ ϕ o ′ u f d ξ ∫ 0 1 ψ n ψ p v d ′ d η

N L w v 3 = ∑ o = 1 O ∑ p = 1 P q o p τ ∑ f = 1 F ∑ d = 1 D b f d τ ∫ 0 1 ϕ m ′ ϕ o u f ′ d ξ ∫ 0 1 ψ n ψ p ′ v d d η

N L w w 1 = ∑ o = 1 O ∑ p = 1 P q o p τ ∑ o 1 = 1 O 1 ∑ p 1 = 1 P 1 q o 1 p 1 τ ∑ o 2 = 1 O 2 ∑ p 2 = 1 P 2 q o 2 p 2 τ ∫ 0 1 ϕ m ′ ϕ o ′ ϕ o 1 ′ ϕ o 2 ′ d ξ ∫ 0 1 ψ n ψ p ψ p 1 ψ p 2 d η

K u u 12 = ∑ g = 1 G ∑ h = 1 H a g h τ ∫ 0 1 u i ′ u g ′ d ξ ∫ 0 1 v j v h d η

K u u 34 = ∑ g = 1 G ∑ h = 1 H a g h τ ∫ 0 1 u i u g d ξ ∫ 0 1 v j ′ v h ′ d η

N L w w 2 = ∑ o = 1 O ∑ p = 1 P q o p τ ∑ o 1 = 1 O 1 ∑ p 1 = 1 P 1 q o 1 p 1 τ ∑ o 2 = 1 O 2 ∑ p 2 = 1 P 2 q o 2 p 2 τ ∫ 0 1 ϕ m ϕ o ϕ o 1 ϕ o 2 d ξ ∫ 0 1 ψ n ′ ψ p ′ ψ p 1 ′ ψ p 2 ′ d η ,

N L w w 3 = ∑ o = 1 O ∑ p = 1 P q o p τ ∑ o 1 = 1 O 1 ∑ p 1 = 1 P 1 q o 1 p 1 τ ∑ o 2 = 1 O 2 ∑ p 2 = 1 P 2 q o 2 p 2 τ ∫ 0 1 ϕ o ′ ϕ o 1 ′ ϕ m ϕ o 2 d ξ ∫ 0 1 ψ p ψ p 1 ψ n ′ ψ p 2 ′ d η ,

K u v 12 = ∑ f = 1 F ∑ d = 1 D b f d τ ∫ 0 1 u i ′ u f d ξ ∫ 0 1 v j v d ′ d η

N L w w 6 = ∑ o = 1 O ∑ p = 1 P q o p τ ∑ o 1 = 1 O 1 ∑ p 1 = 1 P 1 q o 1 p 1 τ ∑ o 2 = 1 O 2 ∑ p 2 = 1 P 2 q o 2 p 2 τ ∫ 0 1 ϕ m ′ ϕ o ϕ o 1 ′ ϕ o 2 d ξ ∫ 0 1 ψ n ψ p ′ ψ p 1 ψ p 2 ′ d η ,

F w = ∑ o = 1 O ∑ p = 1 P q o p τ ∫ 0 1 ϕ m ϕ o ′ d ξ ∫ 0 1 ψ n ψ p d η ,

C w = ∑ o = 1 O ∑ p = 1 P q ̇ o p τ ∫ 0 1 ϕ m ϕ o d ξ ∫ 0 1 ψ n ψ p d η

K s w = ∑ m = 1 M ∑ n = 1 N q m n τ ϕ m ξ e ψ n ( η e )

N L s w w w = ∑ m = 1 M ∑ n = 1 N ∑ m 1 = 1 M ∑ n 1 = 1 N ∑ m 2 = 1 M ∑ n 2 = 1 N q m n τ q m 1 n 1 τ q m 2 n 2 τ ϕ m × ξ e ϕ m 1 ξ e ϕ m 2 ξ e ψ n η e ψ n 1 η e ψ n 2 η e

N L s w w q = ∑ m = 1 M ∑ n = 1 N ∑ m 1 = 1 M ∑ n 1 = 1 N q m n τ q m 1 n 1 τ q s τ ϕ m ξ e ϕ m 1 ξ e ψ n η e ψ n 1 η e ,

N L s w q q = ∑ m = 1 M ∑ n = 1 N q m n τ q s 2 τ ϕ m ξ e ψ n η e ,

C s w = ∑ m = 1 M ∑ n = 1 N q ̇ m n τ ϕ m ξ e ψ n η e ,

N L w w w = ∑ m = 1 M ∑ n = 1 N ∑ m 1 = 1 M ∑ n 1 = 1 N ∑ m 2 = 1 M ∑ n 2 = 1 N q m n τ q m 1 n 1 τ q m 2 n 2 τ ϕ m ξ e × ϕ m ξ e ϕ m 1 ξ e ϕ m 2 ξ e ψ n ( η e ) ψ n η e ψ n 1 η e ψ n 2 η e

N L w w q = ∑ m = 1 M ∑ n = 1 N ∑ m 1 = 1 M ∑ n 1 = 1 N q m n τ q m 1 n 1 τ q s τ ϕ m ξ e ϕ m ξ e ϕ m 1 ξ e ψ n η e ψ n η e ψ n 1 η e ,

N L w q q = ∑ m = 1 M ∑ n = 1 N q m n τ q s 2 τ ϕ m ξ e ϕ m ξ e ψ n η e ψ n η e ,

N L q q q = q s 3 τ ϕ m ξ e ψ n ( η e )

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Received: 2020-11-03
Revised: 2021-03-13
Accepted: 2021-07-20
Published Online: 2021-09-03

© 2021 Walter de Gruyter GmbH, Berlin/Boston

Artikel in diesem Heft

  1. Frontmatter
  2. Original Research Articles
  3. Frequency responses for induced neural transmembrane potential by electromagnetic waves (1 kHz to 1 GHz)
  4. Investigating existence results for fractional evolution inclusions with order r ∈ (1, 2) in Banach space
  5. Optimal control of non-instantaneous impulsive second-order stochastic McKean–Vlasov evolution system with Clarke subdifferential
  6. Generalized forms of fractional Euler and Runge–Kutta methods using non-uniform grid
  7. Controllability of coupled fractional integrodifferential equations
  8. A new generalized approach to study the existence of solutions of nonlinear fractional boundary value problems
  9. Rational soliton solutions in the nonlocal coupled complex modified Korteweg–de Vries equations
  10. Buoyancy driven flow characteristics inside a cavity equiped with diamond elliptic array
  11. Analysis and numerical effects of time-delayed rabies epidemic model with diffusion
  12. Two occurrences of fractional actions in nonlinear dynamics
  13. Multiwave interaction solutions for a (3 + 1)-dimensional B-type Kadomtsev–Petviashvili equation in fluid dynamics
  14. Effects of mixed time delays and D operators on fixed-time synchronization of discontinuous neutral-type neural networks
  15. Solvability and stability of nonlinear hybrid ∆-difference equations of fractional-order
  16. Weak and strong boundedness for p-adic fractional Hausdorff operator and its commutator
  17. Simulation and modeling of different cell shapes for closed-cell LM-13 alloy foam for compressive behavior
  18. Pandemic management by a spatio–temporal mathematical model
  19. Adaptive ADI difference solution of quenching problems based on the 3D convection–reaction–diffusion equation
  20. Null controllability of Hilfer fractional stochastic integrodifferential equations with noninstantaneous impulsive and Poisson jump
  21. Application of modified Mickens iteration procedure to a pendulum and the motion of a mass attached to a stretched elastic wire
  22. Modeling the spatiotemporal intracellular calcium dynamics in nerve cell with strong memory effects
  23. Switched coupled system of nonlinear impulsive Langevin equations involving Hilfer fractional-order derivatives
  24. Improving the dynamic behavior of the plate under supersonic air flow by using nonlinear energy sink
https://doi.org/10.1515/ijnsns-2020-0249
Schlagwörter für diesen Artikel
bifurcation diagram; nonlinear energy sink; plate; Poincarémap; Rayleigh–Ritz method; supersonic flow

Artikel in diesem Heft

  1. Frontmatter
  2. Original Research Articles
  3. Frequency responses for induced neural transmembrane potential by electromagnetic waves (1 kHz to 1 GHz)
  4. Investigating existence results for fractional evolution inclusions with order r ∈ (1, 2) in Banach space
  5. Optimal control of non-instantaneous impulsive second-order stochastic McKean–Vlasov evolution system with Clarke subdifferential
  6. Generalized forms of fractional Euler and Runge–Kutta methods using non-uniform grid
  7. Controllability of coupled fractional integrodifferential equations
  8. A new generalized approach to study the existence of solutions of nonlinear fractional boundary value problems
  9. Rational soliton solutions in the nonlocal coupled complex modified Korteweg–de Vries equations
  10. Buoyancy driven flow characteristics inside a cavity equiped with diamond elliptic array
  11. Analysis and numerical effects of time-delayed rabies epidemic model with diffusion
  12. Two occurrences of fractional actions in nonlinear dynamics
  13. Multiwave interaction solutions for a (3 + 1)-dimensional B-type Kadomtsev–Petviashvili equation in fluid dynamics
  14. Effects of mixed time delays and D operators on fixed-time synchronization of discontinuous neutral-type neural networks
  15. Solvability and stability of nonlinear hybrid ∆-difference equations of fractional-order
  16. Weak and strong boundedness for p-adic fractional Hausdorff operator and its commutator
  17. Simulation and modeling of different cell shapes for closed-cell LM-13 alloy foam for compressive behavior
  18. Pandemic management by a spatio–temporal mathematical model
  19. Adaptive ADI difference solution of quenching problems based on the 3D convection–reaction–diffusion equation
  20. Null controllability of Hilfer fractional stochastic integrodifferential equations with noninstantaneous impulsive and Poisson jump
  21. Application of modified Mickens iteration procedure to a pendulum and the motion of a mass attached to a stretched elastic wire
  22. Modeling the spatiotemporal intracellular calcium dynamics in nerve cell with strong memory effects
  23. Switched coupled system of nonlinear impulsive Langevin equations involving Hilfer fractional-order derivatives
  24. Improving the dynamic behavior of the plate under supersonic air flow by using nonlinear energy sink
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