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Curved Fiber-Reinforced Laminated Composite Panel and Variable Stiffness Influence on Eigenfrequency Responses: A Higher-Order FE Approach

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Abstract

Purpose

In the present work, modal characteristics and mode shapes of variable stiffness composite laminate (VSCL) flat-panel structure are analyzed using a numerical model. The variable stiffness configuration of the panel structure is achieved by considering the curved fiber as a reinforcement.

Methods

The numerical model of the VSCL panel has been derived by combining the finite element (FE) and well-suited higher-order shear deformation theory. The flat-panel model is discretized via isoparametric elements (eighty-one degrees of freedom per element) to achieve the necessary mathematical form. The frequency responses are obtained using a governing differential equation derived from Hamilton’s principle.

Results

The numerical model’s consistency and exactness have been verified as a priory. Further, the model’s capability has been expanded by solving number of numerical examples to investigate the influence of various parameters related to material, geometry and boundaries of the panel.

Conclusions

The satisfactory performance test (element convergence and comparison) of the derived numerical model infers that the model is capable of analyzing the modal behavior of the VSCL flat-panel structures with adequate accuracy. Also, the fundamental frequency values follow a downward trend with the increase in span ratio, length to thickness ratios and ratios of Young's modulus.

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Abbreviations

\(P_{0} ,\,\,P_{1}\) :

Path orientation in the center and on the vertical edges of the VSCL plate, respectively

\(a,\,\,b\) :

Length and breadth of the flat panel

\(\chi_{1} ,\,\,\chi_{2} ,\,\,\chi_{3}\) :

Displacements along major coordinate (X, Y and Z), respectively

\(\chi_{1}^{0} ,\,\,\chi_{2}^{0} ,\,\,\chi_{3}^{0}\) :

Displacements (mid-plane), along X, Y and Z, respectively

\(\chi_{1}^{1} ,\,\,\chi_{2}^{1}\) :

Rotational of perpendicular to the mid-surface about transverse and longitudinal direction, respectively

\(\left\{ \sigma \right\}^{\left( k \right)} ,\,\,\left\{ \varepsilon \right\}^{\left( k \right)} ,\,\,\,\left[ {Q_{{{\text{ij}}}} } \right]^{\left( k \right)}\) :

Stress, strain and material properties matrix, respectively

\(U\) :

Total strain energy

\(T\) :

Total kinetic energy

\(\left[ B \right]\) :

General strain–displacement relation matrix

\(\left[ m \right]\) :

Mass matrix (elemental)

\(\left[ k \right]\) :

Stiffness matrix (elemental)

\(\ddot{d}_{0} ,\,\,d_{0}\) :

Acceleration and displacements, respectively

\(\left[ M \right],\,\,\left[ K \right]\) :

Represents global form of mass and stiffness matrices, respectively

\(\left\{ {\ddot{d}} \right\},\,\,\left\{ d \right\}\) :

Represents global acceleration and displacement vectors, respectively

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Authors and Affiliations

  1. Department of Mechanical Engineering, NIT Patna, Patna, Bihar, 800005, India

    Prasoon Kumar, Rahul Arya & Chetan Kumar Hirwani

  2. School of Mechanical Engineering, KIIT (Deemed to Be University) Bhubaneswar, Bhubaneswar, Odisha, 751024, India

    Nitin Sharma

  3. Department of Mechanical Engineering, NIT Rourkela, Rourkela, Odisha, 769008, India

    Subrata Kumar Panda

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Correspondence to Subrata Kumar Panda.

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Kumar, P., Arya, R., Sharma, N. et al. Curved Fiber-Reinforced Laminated Composite Panel and Variable Stiffness Influence on Eigenfrequency Responses: A Higher-Order FE Approach. J. Vib. Eng. Technol. 11, 2349–2359 (2023). https://doi.org/10.1007/s42417-022-00706-6

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