Vibration of rotating rectangular plates

Wang, J.T.-S.; Shaw, Dein; Mahrenholtz, O.

doi:10.1016/s0022-460x(87)80111-6

Cited by 34 publications

(23 citation statements)

References 8 publications

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“…T xy y xy + r yz y yz + r xz y xz ) dz dA (9) The variation in the strain energy dU is determined by substituting Eqs. (4-7) into Eq.…”

Section: Theoretical Developmentmentioning

confidence: 99%

“…The dynamic behavior of turbopropellers has been studied by Kosmatka and Friedmann, 2 ' 3 Subrahmanyam and Kaza, 4 Mehmed et al, 5 and Maser et al 6 Since low-aspect ratio blades tend to behave like plates rather than beams, it is expected that a plate model will provide better results for propellers with high width-to-length ratios. Dokainish and Rawtani, 7 Ramamurti and Kielb, 8 Wang et al, 9 and Shaw et al 10 have studied vibrations in rotating plates. Only Refs.…”

Section: Introductionmentioning

confidence: 99%

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Free vibration behavior of spinning shear-deformable plates composedof composite materials

1990

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A first-order shear-deformation plate theory is used to predict the free vibration frequencies and mode shapes in spinning laminated composite plates. The theory accounts for geometric nonlinearity in the form of the von Karman strains and the effects of rotatory inertia. The plate is permitted to have an arbitrary orientation offset from the axis of rotation. A finite element model is developed to obtain numerical solutions to this class of problems. The model is validated by comparing the results for isotropic plates with those available in literature. The natural frequencies and mode shapes of isotropic and laminated composite plates as functions of angular velocity, pitch angle, and sweep angle are presented. Though the expected increase in frequency with angular velocity is observed for most modes, it is seen that there is a decrease in the free vibration frequency with angular velocity for torsional modes of swept and pitched plates.

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“…T xy y xy + r yz y yz + r xz y xz ) dz dA (9) The variation in the strain energy dU is determined by substituting Eqs. (4-7) into Eq.…”

Section: Theoretical Developmentmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Free vibration behavior of spinning shear-deformable plates composedof composite materials

1990

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“…2 Here, the method of stress smoothing has been used for reducing numerical errors when calculating the improved stiffness matrix. The free vibration analysis of rotating rectangular plates has been studied by Wang et al 3 Yoo et al derived the equation of motion for the vibration analysis of a rotating pre-twisted blades. 4 They have used a modelling method that employs hybrid deformation variables.…”

Section: Introductionmentioning

confidence: 99%

Free Vibration Analysis of Rotating Plates in High Thermal Environments Using the Finite Element Method

Ramu¹,

Mohanty²

2017

IJAV

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The aim of the work is to study the vibration characteristics of rotating functionally graded material (FGM) plates using the finite element method. The mechanical properties of the ordinary and temperature dependent FGM plates are assumed to be varying in the thickness direction according to a power law distribution in terms of the volume fractions of the constituents. The temperature field is ascertained using a nonlinear distribution in the thickness direction only. The present method results are compared with numerical results available in the literature. The frequency characteristics of the rotating ordinary FGM and temperature dependent FGM plates are examined. The effect of parameters such as hub radius, rotating speed, temperature change, and power law index value on the natural frequencies of rotating FGM plates are investigated through this study. The plots reveal that the temperature field, rotational speed, and the gradient index in the material properties have a significant effect on the vibration characteristics of the rotating ordinary FGM and temperature dependent FGM plates.

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“…The pioneering work on pretwisted composite plates (1) involved the determination of the non-dimensional natural frequencies of stationary plates using the laminated shallow shell theory in conjunction with the Ritz method, while two earlier investigations (2), (3) provided the first known results on natural frequencies of rotating composite plates. The analyses of rotating composite blades using the plate model (4) - (6) focussed, respectively on the derivation of two approximate analytical models for determining the stress-strain field, the details of fabrication and experimentation for determining natural frequencies and steady state strain along with the effect of rotational speed on it and the vibration characteristics including geometric nonlinearity.…”

Section: Introductionmentioning

confidence: 99%

Free Vibration Analysis of Delaminated Composite Pretwisted Rotating Shells-A Finite Element Approach

Karmakar

Kishimoto

2006

JSME Int. J., Ser. A

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In this paper a finite element method is presented to study the effects of delamination on free vibration characteristics of graphite-epoxy composite pretwisted rotating shells. Lagrange's equation of motion is used to derive the dynamic equilibrium equation and moderate rotational speeds are considered wherein the Coriolis effect is negligible. An eight noded isoparametric plate bending element is employed in the formulation incorporating rotary inertia and effects of transverse shear deformation based on Mindlin's theory. To satisfy the compatibility of deformation and equilibrium of resultant forces and moments at the delamination crack front, a multipoint constraint algorithm is incorporated which leads to unsymmetric stiffness matrices. Parametric studies are performed in respect of location of delamination, fibre orientation, rotational speed and twist angle on natural frequencies of cylindrical shallow shells. Numerical results obtained for symmetric and unsymmetric laminates are the first known non-dimensional frequencies for the analyses carried out here.

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Vibration of rotating rectangular plates

Cited by 34 publications

References 8 publications

Free vibration behavior of spinning shear-deformable plates composedof composite materials

Free vibration behavior of spinning shear-deformable plates composedof composite materials

Free Vibration Analysis of Rotating Plates in High Thermal Environments Using the Finite Element Method

Free Vibration Analysis of Delaminated Composite Pretwisted Rotating Shells-A Finite Element Approach

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