Effect of transverse shear deformation and rotary inertia on the natural frequencies of rectangular plates with cutouts

An analysis is presented for the study of the effect of transverse shear deformation on the natural frequencies of layered composite paraboloidal shells. The applicability of linear shell theory due to Reissner is assumed and governing equations are solved for the natural frequencies using the transfer matrix approach. The results of the present analysis are compared with the results for paraboloidal shells reported in the literature and good agreement is found. Transverse shear deformation effects are carried out separately for axisymmetric torsional vibration modes, axisymmetric bending-extensional vibration modes and nonsymmetric vibration modes. The variation of the effect of transverse shear deformation with respect to different rim boundary conditions, geometry of the paraboloid, material type (isotropic-orthotropic), lamination arrangement and particular meridional and circumferential vibration modes is investigated.

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Finite Element Analysis on Modal Parameters of Anisotropic Laminated Plates

Journal of Vibration and Acoustics ◽

10.1115/1.3269553 ◽

1988 ◽

Vol 110 (4) ◽

pp. 473-477 ◽

Cited By ~ 4

Author(s):

C. Z. Xiao ◽

D. X. Lin ◽

F. Ju

Keyword(s):

Finite Element ◽

Shear Deformation ◽

Transverse Shear ◽

Natural Frequencies ◽

Dynamic Properties ◽

Shear Deformation Theory ◽

Laminated Plates ◽

Mode Shapes ◽

Transverse Shear Deformation ◽

Element Technique

This paper is concerned with the finite element technique for predicting the dynamic properties of anisotropic fiber-reinforced composite laminated plates. Considering the effect of transverse shear deformation, a higher order shear deformation theory which satisifes the zero shear stress conditions at the upper and bottom surfaces is assumed. The natural frequencies and mode shapes of a rectangular plate with all free edges are obtained by finite element method and the modal damping values by finite damped element technique. An equivalent stiffness method is introduced to reduce computation time. Four different theoretical predictions of natural frequencies and damped values of a laminated plate are compared with experimental results. Discussions on the effect of transverse shear deformation to the dynamic properties of composite plates are given.

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Modal density and critical frequency of composite panels considering transverse shear deformation and rotary inertia

Journal of Vibration and Control ◽

10.1177/1077546319898980 ◽

2020 ◽

Vol 26 (17-18) ◽

pp. 1503-1513

Author(s):

K Renji

Keyword(s):

Shear Deformation ◽

Transverse Shear ◽

Critical Frequency ◽

Rotary Inertia ◽

Transverse Shear Deformation ◽

Bending Waves ◽

Modal Density ◽

The Face ◽

Orthotropic Properties ◽

Bending Wave

In this work, expressions for estimating the modal density, speed of the bending wave, critical frequency and coincidence frequency of panels are derived considering orthotropic properties of the face sheets, transverse shear deformation and the rotary inertia. Presence of rotary inertia results in an increase in the modal density and a reduction in the speed of the bending waves. The influence is significant at higher frequencies. The critical and coincidence frequencies increase due to rotary inertia. Results for a typical equipment panel of spacecraft are presented and they show the need for incorporating rotary inertia while determining these parameters.

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FREE VIBRATIONS OF SHEAR DEFORMABLE CIRCULAR CURVED BEAMS RESTING ON ELASTIC FOUNDATIONS

International Journal of Structural Stability and Dynamics ◽

10.1142/s0219455402000440 ◽

2002 ◽

Vol 02 (01) ◽

pp. 77-97 ◽

Cited By ~ 22

Author(s):

BYOUNG KOO LEE ◽

SANG JIN OH ◽

KWANG KYOU PARK

Keyword(s):

Shear Deformation ◽

Natural Frequencies ◽

Free Vibrations ◽

Rotary Inertia ◽

Transverse Shear Deformation ◽

Curved Beams ◽

System Parameters ◽

Elastic Foundations ◽

Out Of Plane ◽

Shear Deformable

The governing differential equations for the out-of-plane, free vibration of circular curved beams resting on elastic foundations are derived and solved numerically. The formulation takes into consideration the effects of rotary inertia and transverse shear deformation. The lowest three natural frequencies are calculated for beams with hinged–hinged, hinged-clamped, and clamped–clamped end constraints. The effects of various system parameters as well as rotary inertia and shear deformation on the natural frequencies are investigated.

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VIBRATION OF INITIALLY STRESSED MICRO- AND NANO-BEAMS

International Journal of Structural Stability and Dynamics ◽

10.1142/s0219455407002423 ◽

2007 ◽

Vol 07 (04) ◽

pp. 555-570 ◽

Cited By ~ 50

Author(s):

C. M. WANG ◽

Y. Y. ZHANG ◽

S. KITIPORNCHAI

Keyword(s):

Boundary Conditions ◽

Shear Deformation ◽

Initial Stress ◽

Transverse Shear ◽

Virtual Work ◽

Nonlocal Elasticity Theory ◽

Rotary Inertia ◽

Small Scale ◽

Transverse Shear Deformation ◽

Vibration Problem

This paper is concerned with the vibration problem of initially stressed micro/nano-beams. The vibration problem is formulated on the basis of Eringen's nonlocal elasticity theory and the Timoshenko beam theory. The small scale effect is taken into consideration in the former theory while the effects of initial stress, transverse shear deformation and rotary inertia are accounted for in the latter theory. The governing equations and the boundary conditions are derived using the principle of virtual work. These equations are solved analytically for the vibration frequencies of micro/nano-beams with different initial stress values and boundary conditions. The effect of the initial stress on the fundamental frequency and vibration mode shape of the beam is investigated. The solutions obtained provide a better representation of the vibration behavior of initially stressed micro/nano-beams which are stubby and short, since the effects of small scale, transverse shear deformation and rotary inertia are significant and cannot be neglected.

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