Numerical thermoelastic eigenfrequency prediction of damaged layered shell panel with concentric/eccentric cutout and co
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ORIGINAL ARTICLE
Numerical thermoelastic eigenfrequency prediction of damaged layered shell panel with concentric/eccentric cutout and corrugated (TD/TID) properties Hukum Chand Dewangan1 · Subrata Kumar Panda1 Received: 6 August 2020 / Accepted: 6 October 2020 © Springer-Verlag London Ltd., part of Springer Nature 2020
Abstract The vibrational responses are predicted numerically for the layered shell panel structure with and without cutout under the variable temperature loading and corrugated composite properties. The presence of variable cutout shapes (circular/elliptical/ square and rectangular) and sizes are modelled via a generic mathematical macro-mechanical model in the framework of the cubic-order kinematic model. Also, the present model includes the variation of composite properties due to the change in environmental conditions, i.e. the temperature-dependent (TD) and -independent (TID) cases. The computational responses are obtained by taking advantages of the isoparametric finite element technique and the Hamilton principle to derive the final governing equation. The total Lagrangian approach is adopted to compute the responses using the specialized computer code prepared in the MATLAB platform. The frequency responses are predicted considering the effect of a cutout, including the environmental variation and compared with previously published eigenvalues. The model versatility is tested over a variety of examples considering the shell configurations (plate, cylindrical, spherical, hyperboloid, and elliptical), the influential cutout parameter (shape, size, and position) and temperature loading including the corrugated composite properties. Keywords Laminated composite · Cutout · FEM · HSDT · Vibration · Temperature-dependent properties List of symbols n Number of layers in the laminated shell panel 𝜃 Angle of fibre orientation [H] Thickness of coordinate matrix {𝜎} [ ] Stress Q Reduced transformed elastic constant matrix 𝜀 Strain 𝛼 Thermal expansion coefficient ΔT Temperature difference S Strain energy T Kinetic energy [M] Mass matrix 𝜌 Mass density * Subrata Kumar Panda [email protected]; [email protected] Hukum Chand Dewangan [email protected] 1
Department of Mechanical Engineering, National Institute of Technology Rourkela, Rourkela 769008, Odisha, India
N Shape function [K] Stiffness matrix {Φ} Eigenvector 𝜔 Natural frequency 𝜔nd Normalized natural frequency E1 , E2 and E3 Young’s modulus G12 , G13 and G23 Shear modulus [𝜇12 ,] 𝜇13 and 𝜇23 Poisson’s ratio KG Geometrical stiffness matrix u0𝜁x , u0𝜁y and u0𝜁z Displacement of a point at mid-plane u1𝜁y and u1𝜁x Rotation along 𝜁y and 𝜁y R𝜁x , R𝜁y and R𝜁xy Radius of curvature of the shell panel 𝜁x , 𝜁y and 𝜁z Global reference axis of the laminate’s shell panel [ ] D and Material property matrix [D] G [ ] [ ] Bl and BG Strain displacement matrix L, W and h Length, width and thickness of the shell panel U𝜁x , U𝜁y and U𝜁z Global displacement
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u2𝜁x , u2𝜁y , u3𝜁x and u3𝜁y Higher-ord
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