TY - JOUR

T1 - Nonlinear dynamic modeling of bistable variable stiffness composite laminates

AU - Anilkumar, P. M.

AU - Scheffler, S.

AU - Haldar, A.

AU - Brod, M.

AU - Rao, B. N.

AU - Jansen, E. L.

AU - Rolfes, R.

N1 - Funding Information: The first author would like to acknowledge the Prime Minister’s Research Fellowship, India and German Academic Exchange Service: Deutscher Akademischer Austauschdienst - DAAD for the doctoral fellowship during the course of this research. The authors gratefully extend their acknowledgment to Mr. Oliver Dorn, Mrs. Marlene Wolniak and Mr. Christian Hente for the helpful discussions during the experimental campaign.

PY - 2023/2/17

Y1 - 2023/2/17

N2 - The room-temperature equilibrium stable states of cured unsymmetric composite laminates have been the focus of recent research, with a particular emphasis on shape morphing applications. It has been shown that changing the fiber orientation of unsymmetrical laminates using curvilinear fiber path description can results in a plethora of bistable configurations with an enriched design space. In bistable structures, snap-through involves transition from one stable shape to another, which is a non-linear phenomenon exhibiting rich dynamics during the shape transition. Past works involving such dynamic characteristics show encouraging potential in designing efficient morphing strategies. In this work, a novel semi-analytical model using Föppl von Kármán kinematics has been formulated to predict the non-linear dynamic characteristic of bistable variable stiffness (VS) laminates. An efficient energy formulation is adopted where the membrane and bending energies are decoupled using the semi-inverse constitutive equation. The in-plane stress resultants and the energy components are expressed in terms of curvatures using the in-plane equilibrium equations and compatibility conditions. Using Hamilton's principle in conjunction with the Rayleigh–Ritz approach, a set of non-linear equations are generated, which is solved to obtain the dynamics of the snap-through process. The accuracy of the predicted non-linear vibration results of bistable plates from the semi-analytical model is verified using a fully non-linear finite element framework and validated exemplarily by tests on a straight fiber laminate configuration. Finally, a parametric study is performed by tailoring the VS parameters to identify the effect of different curvilinear fiber alignments on the dynamic characteristics of bistable VS laminates.

AB - The room-temperature equilibrium stable states of cured unsymmetric composite laminates have been the focus of recent research, with a particular emphasis on shape morphing applications. It has been shown that changing the fiber orientation of unsymmetrical laminates using curvilinear fiber path description can results in a plethora of bistable configurations with an enriched design space. In bistable structures, snap-through involves transition from one stable shape to another, which is a non-linear phenomenon exhibiting rich dynamics during the shape transition. Past works involving such dynamic characteristics show encouraging potential in designing efficient morphing strategies. In this work, a novel semi-analytical model using Föppl von Kármán kinematics has been formulated to predict the non-linear dynamic characteristic of bistable variable stiffness (VS) laminates. An efficient energy formulation is adopted where the membrane and bending energies are decoupled using the semi-inverse constitutive equation. The in-plane stress resultants and the energy components are expressed in terms of curvatures using the in-plane equilibrium equations and compatibility conditions. Using Hamilton's principle in conjunction with the Rayleigh–Ritz approach, a set of non-linear equations are generated, which is solved to obtain the dynamics of the snap-through process. The accuracy of the predicted non-linear vibration results of bistable plates from the semi-analytical model is verified using a fully non-linear finite element framework and validated exemplarily by tests on a straight fiber laminate configuration. Finally, a parametric study is performed by tailoring the VS parameters to identify the effect of different curvilinear fiber alignments on the dynamic characteristics of bistable VS laminates.

KW - Bistability

KW - Composites

KW - Dynamics

KW - Semi-analytical

KW - Snap-through

KW - Variable stiffness

UR - http://www.scopus.com/inward/record.url?scp=85142172966&partnerID=8YFLogxK

U2 - 10.1016/j.jsv.2022.117417

DO - 10.1016/j.jsv.2022.117417

M3 - Article

AN - SCOPUS:85142172966

VL - 545

JO - Journal of sound and vibration

JF - Journal of sound and vibration

SN - 0022-460X

M1 - 117417

ER -