Differential quadrature based nonlocal flapwise bending vibration analysis of rotating nanotube with consideration of transverse shear deformation and rotary inertia

2012 ◽  
Vol 219 (3) ◽  
pp. 1232-1243 ◽  
Author(s):  
S. Narendar
Keyword(s):  
Shear Deformation ◽  
Transverse Shear ◽  
Vibration Analysis ◽  
Differential Quadrature ◽  
Rotary Inertia ◽  
Transverse Shear Deformation ◽  
Bending Vibration

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

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.

VIBRATION OF INITIALLY STRESSED MICRO- AND NANO-BEAMS

2007 ◽  
Vol 07 (04) ◽  
pp. 555-570 ◽  
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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