Free Vibration of Rotating Twisted Composite Stiffened Plate

• Mrutyunjay Rout
• Amit Karmakar
Conference paper
Part of the Lecture Notes on Multidisciplinary Industrial Engineering book series (LNMUINEN)

Abstract

The paper presents a first-order shear deformation-based finite element model to investigate the free vibration response of the rotating twisted composite stiffened plate. An eight-noded isoparametric plate element having five degrees of freedom per node is combined with an isoparametric three-noded beam element of four degrees of freedom per node for modelling the plate and the stiffener element, respectively. The present formulation employs a constraint method to calculate the stiffness and mass matrices of the stiffener element attached to the plate element, wherein the degrees of freedom of the nodes of the stiffener element are transferred to the respective nodes of the plate element considering eccentricity to maintain the compatibility between plate and stiffener. The advantage of such method is that total number of degrees of freedom due to addition of the stiffener does not increase, thereby reducing the computational time. The governing equilibrium equation is derived from Lagrangian equation of motion. The Coriolis effect is not considered as the stiffened plate is allowed to rotate at moderate rotational speed only. Parametric studies have been conducted to investigate the effect of angle of fibre orientation, pretwist angle, stiffener depth-to-plate thickness ratio and rotational speeds on the fundamental frequency and mode shapes of the stiffened plate.

Keywords

Composite Stiffener Finite element Vibration Twisted plate

Nomenclature

L

Length of the plate (m)

b

Width of the plate (m)

h

Thickness of the plate (m)

bst

Width of stiffener (m)

dst

Depth of stiffener (m)

ϕ

Pretwist angle of the plate (deg.)

ωn

Fundamental natural frequency of the stiffened plate without rotation (rad/s)

$$\Omega^{\prime }$$

Ω

Non-dimensional rotational speed $$\left( {\Omega =\Omega ^{{\prime }} /\omega_{\text{n}} } \right)$$ (dimensionless)

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