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Free vibration studies on plates with central cut-out

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Abstract

The present work deals with the experimental and finite element free vibration studies on isotropic and laminated anti-symmetric angle-ply composite plates with central cut-out under clamped-free–clamped-free boundary condition. The natural frequencies were determined using the CQUAD8 finite element of MSC/NASTRAN and comparison made between the experimental values and the finite element solution. The effects of aspect ratio, cut-out size and cut-out shape on the natural frequencies of plates were studied. The experimental values of the first, second and third natural frequencies are in good agreement with those of the finite element solution in the case of both isotropic and laminated composite plates with and without cut-outs. The non-dimensional frequency coefficient Kf  are found increases with increase in length-to-cut-out size ratio (d/a) irrespective of the cut-out shape. In case of laminated composite plates, the non-dimensional frequency coefficient Kf increases monotonically with an increase in the aspect ratio irrespective of hole size and shapes for all the three modes of vibration.

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Abbreviations

a :

Plate length (mm)

b :

Plate width (mm)

d :

Diameter of the circular hole/side of the square cut-out (mm)

a/b :

Aspect ratio

a/t :

Length-to-thickness ratio

t :

Plate thickness (mm)

NL:

Number of layers in the laminate

E :

Modulus of elasticity of the material of the isotropic plate (GPa)

µ :

Poisson’s ratio of the material of the isotropic plate

\({E_{\text{1}}}\) :

Young’s modulus of the lamina in the longitudinal direction (GPa)

\({E_{\text{2}}}\) :

Young’s modulus of the lamina in the transverse direction (GPa)

\({E_x}\) :

Young’s modulus of the lamina in the along 45° to the longitudinal direction (GPa)

\({G_{{\text{12}}}}\) :

In-plane shear modulus of the lamina (GPa)

θ :

Fiber orientation angle of the lamina (° degrees)

\({v_{{\text{12}}}}\) :

Major Poisson’s ratio

ρ :

Mass density (kg/mm3)

\({\rho _{\text{1}}}\) :

Mass density per unit area [(kg/mm3)/unit area]

D :

Flexural rigidity of isotropic plate, Et3/12(1 − µ2) (GPa mm3)

ω :

Natural angular frequency of plate (rad/s)

λ :

Eigen value

\({K_{\text{f}}}\) :

Non-dimensional frequency coefficient

K :

Stiffness matrix (N/mm)

\({K_{\text{d}}}\) :

Differential stiffness matrix (N/mm)

M :

Mass matrix (kg)

{ϕ}:

Eigenvector

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Acknowledgements

The first author would like to thank the Management and Principal, GM Institute of Technology, Davangere, Karnataka, India 577 006, for their encouragement and support. The second and third authors would like to Dr. S. Subramanya Swamy, Principal, Bapuji Institute of Engineering and Technology, Davangere, Karnataka, India 577 004, for their constant encouragement and support.

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Authors and Affiliations

  1. Department of Mechanical Engineering, GM Institute of Technology, Davangere, Karnataka, 577006, India

    Srinivasa Chikkol Venkateshappa

  2. Department of Mechanical Engineering, Bapuji Institute of Engineering and Technology, Davangere, Karnataka, 577004, India

    Pavan Kumar & Thippeswamy Ekbote

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  1. Srinivasa Chikkol Venkateshappa
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  2. Pavan Kumar
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Correspondence to Srinivasa Chikkol Venkateshappa.

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Chikkol Venkateshappa, S., Kumar, P. & Ekbote, T. Free vibration studies on plates with central cut-out. CEAS Aeronaut J 10, 623–632 (2019). https://doi.org/10.1007/s13272-018-0339-7

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