TY - JOUR

T1 - Refined semi-analytical framework to predict the natural vibration characteristics of bistable laminates

AU - Anilkumar, P. M.

AU - Rao, B. N.

AU - Scheffler, Sven

AU - Wolniak, Marlene

AU - Rolfes, Raimund

AU - Haldar, Ayan

AU - Jansen, Eelco Luc

N1 - Funding Information: The first author would like to acknowledge the support of the German Academic Exchange Service: Deutscher Akademischer Austauschdienst—DAAD, and Prime Minister’s Research Fellowship, Ministry of Education, India, during the course of this research. The authors gratefully acknowledge the helpful comments and discussions with Martin Brod, Oliver Dorn, and Jens Breyer during the preparation of the paper.

PY - 2023/7

Y1 - 2023/7

N2 - Bistable unsymmetrical laminates have received significant attention in morphing applications due to their ability to attain multiple shapes when subjected to thermal loads. Morphing structures in general are subjected to dynamic operating conditions. Also, the highly nonlinear snap-through transition between stable configurations possesses rich dynamic characteristics. Therefore, understanding the dynamic characteristics of bistable laminates is essential for designing morphing structures constituting bistable elements. Thus, the present study aims to explore the dynamics of bistable unsymmetrical laminates by evaluating their natural vibration characteristics associated with small­amplitude dynamic excitation around the static equilibrium configurations. A refined semi-analytical framework is proposed to analyze the natural vibration characteristics of the bistable laminate, where the potential energy is expressed only in terms of the unknow n coefficients of the assumed out-of-plane displacement function. The in-plane components are separately evaluated using the in-plane equilibrium equations and compatibility conditions. In the dynamic analysis, perturbations are imposed on the static equilibrium configurations to capture the modal characteristics. A full geometrically nonlinear finite element (FE) model of the bistable laminate has been created in a commercially available FE package to compare semi-analytical solutions. To validate the proposed frameworks, an experimental strategy to capture the natural frequencies of a bistable laminate is presented in this paper. Unsymmetric laminates mounted at its center have been used for the experimental testing, where the vibrations are measured using miniature integrated electronics piezoelectric accelerometer sensors attached at the corners. The semi-analytical and FE results are validated against the experimental observations for the selected unsymmetrical cross-ply laminates. The proposed framew orks are further extended to a family of unsymmetrical variable-stiffness (VS) laminates generated using curvilinear fiber alignments. The selected VS family can generate bistable shapes w ithout any twisting curvature similar to that of an unsymmetrical cross-ply laminate, where the designer can expand the design space w ith a plethora of multiple configurations. A parametric study is performed by tailoring the VS parameters to investigate the influence of curvilinear fiber alignments on the natural vibration characteristics of bistable VS laminates.

AB - Bistable unsymmetrical laminates have received significant attention in morphing applications due to their ability to attain multiple shapes when subjected to thermal loads. Morphing structures in general are subjected to dynamic operating conditions. Also, the highly nonlinear snap-through transition between stable configurations possesses rich dynamic characteristics. Therefore, understanding the dynamic characteristics of bistable laminates is essential for designing morphing structures constituting bistable elements. Thus, the present study aims to explore the dynamics of bistable unsymmetrical laminates by evaluating their natural vibration characteristics associated with small­amplitude dynamic excitation around the static equilibrium configurations. A refined semi-analytical framework is proposed to analyze the natural vibration characteristics of the bistable laminate, where the potential energy is expressed only in terms of the unknow n coefficients of the assumed out-of-plane displacement function. The in-plane components are separately evaluated using the in-plane equilibrium equations and compatibility conditions. In the dynamic analysis, perturbations are imposed on the static equilibrium configurations to capture the modal characteristics. A full geometrically nonlinear finite element (FE) model of the bistable laminate has been created in a commercially available FE package to compare semi-analytical solutions. To validate the proposed frameworks, an experimental strategy to capture the natural frequencies of a bistable laminate is presented in this paper. Unsymmetric laminates mounted at its center have been used for the experimental testing, where the vibrations are measured using miniature integrated electronics piezoelectric accelerometer sensors attached at the corners. The semi-analytical and FE results are validated against the experimental observations for the selected unsymmetrical cross-ply laminates. The proposed framew orks are further extended to a family of unsymmetrical variable-stiffness (VS) laminates generated using curvilinear fiber alignments. The selected VS family can generate bistable shapes w ithout any twisting curvature similar to that of an unsymmetrical cross-ply laminate, where the designer can expand the design space w ith a plethora of multiple configurations. A parametric study is performed by tailoring the VS parameters to investigate the influence of curvilinear fiber alignments on the natural vibration characteristics of bistable VS laminates.

UR - http://www.scopus.com/inward/record.url?scp=85175365795&partnerID=8YFLogxK

U2 - 10.2514/1.J062289

DO - 10.2514/1.J062289

M3 - Article

AN - SCOPUS:85175365795

VL - 61

SP - 3158

EP - 3171

JO - AIAA journal

JF - AIAA journal

SN - 0001-1452

IS - 7

ER -