Effects of Shear Deformation and Rotary Inertia on the Free Vibration of a Rotating Annular Plate

1997 ◽  
Vol 119 (4) ◽  
pp. 641-643 ◽  
Author(s):  
A. Coˆte´ ◽  
N. Atalla ◽  
J. Nicolas
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Annular Plate ◽  
Outer Radius ◽  
Thickness Ratio ◽  
Rotary Inertia ◽  
Rotating Annular Plate ◽  
Heuristic Criterion

This Tech Brief addresses the effects of shear deformation and rotary inertia on the free vibration of a rotating annular plate. Several studies have been done to understand these effects (Irie et al, 1982; Sinha, 1987). In particular, the importance of these terms is well known for disks with a thickness ratio h/a > 0.05 where h is the thickness of the disk and a is its outer radius. However, there is a need to show how they affect the disk vibration as the thickness ratio increases. It is well accepted that shear deformation and rotary inertia should be included in the analysis when h/a > 0.05 (Batoz and Dhatt, 1990). However, this Tech Brief will show that this criterion is not valid for all the modes. It will present the evolution of the number of modes correctly evaluated versus the thickness ratio, and, finally, will give a heuristic criterion to predict when it is necessary to consider shear deformation and rotary inertia.

Effects of Rotary Inertia and Shear Deformation on Nonlinear Free Vibration of Microbeams

2006 ◽  
Vol 128 (5) ◽  
pp. 611-615 ◽  
Author(s):  
Asghar Ramezani ◽  
Aria Alasty ◽  
Javad Akbari
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Free Vibration ◽  
Shear Deformation ◽  
Large Amplitude ◽  
Multiple Scales ◽  
Rotary Inertia ◽  
Partial Differential ◽  
Amplitude Vibration ◽  
Large Amplitude Vibration

In this paper, the large amplitude free vibration of a doubly clamped microbeam is considered. The effects of shear deformation and rotary inertia on the large amplitude vibration of the microbeam are investigated. To this end, first Hamilton’s principle is used in deriving the partial differential equation of the microbeam response under the mentioned conditions. Then, implementing the Galerkin’s method the partial differential equation is converted to an ordinary nonlinear differential equation. Finally, the method of multiple scales is used to determine a second-order perturbation solution for the obtained ODE. The results show that nonlinearity acts in the direction of increasing the natural frequency of the doubly clamped microbeam. Shear deformation and rotary inertia have significant effects on the large amplitude vibration of thick and short microbeams.

Axisymmetric Vibration of Rotating Annular Plate with Variable Thickness Subjected to Tensile Centrifugal Body Force

2017 ◽  
Vol 17 (09) ◽  
pp. 1750101 ◽  
Author(s):  
Jae-Hoon Kang
Keyword(s):  
Variable Thickness ◽  
Body Force ◽  
Annular Plate ◽  
Ritz Method ◽  
Free Vibration Analysis ◽  
Angular Speed ◽  
Plane Elasticity ◽  
Outer Radius ◽  
Axisymmetric Vibration ◽  
Rotating Annular Plate

This paper is concerned with the axisymmetric free vibration analysis of a rotating annular plate with variable thickness by using the Ritz method. The rotating plate has a constant angular speed and subjected to a tensile centrifugal body force. The annular plate is fixed at the inner edge and free at the outer edge. Exact stresses, strains, and radial displacement of the rotating annular plate are obtained via plane elasticity. Presented herein are the natural frequencies and modes shapes for the rotating, nonuniform annular plate with various angular speeds and different ratios of the inner radius to the outer radius.

Free vibration analysis of large deformed curved beam incorporating rotary inertia and shear deformation effects and its experimental validation

2020 ◽  
Vol 234 (24) ◽  
pp. 4780-4800
Author(s):  
Sushanta Ghuku ◽  
Kashinath Saha
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Shear Deformation ◽  
Governing Equation ◽  
Free Vibration Analysis ◽  
Static Problem ◽  
Rotary Inertia ◽  
Curved Beam ◽  
Free Vibration Frequency ◽  
Different Thickness

The paper theoretically and experimentally analyzes free vibration characteristics of statically loaded moving boundary type curved beam considering rotary inertia and shear deformation effects. Effects of rotary inertia and shear deformation are observed for different thickness to span ratios of curved beam. The subject problem is decoupled into two interrelated problems: determining equilibrium configuration under static load and finding the corresponding free vibration frequency. The static problem is analyzed incrementally in body fitted curvilinear frame as it involves geometric nonlinearity due to generalized curvature, large deformation, and moving boundaries. Variational energy principle is employed to derive governing equation. The nonlinear governing equation associated with complicated boundary conditions is solved through iterative geometry updation. Once static problem is solved for current load step, governing equation for dynamic characteristics is derived using Hamilton’s principle. The governing equation gets linearized by using the static configuration, which finally yields a linear eigenvalue problem. Experiment is performed in a dedicated setup with two master leafs having different thickness to span ratios. The roller supported specimens are excited with an instrumented hammer and response signals are captured by accelerometers. The excitation and response signals are recorded using HBM-MX840B data acquisition system. Frequency response functions of the curved beam systems under different static loads are obtained from postprocessing of the dynamic signals in MATLAB®. First two natural frequencies of the specimens are noted from the experimental results and the corresponding theoretical results are generated. The specimens are also modeled in ABAQUS® CAE and finite element results are computed. Comparison between the theoretical, experimental, and finite element results validates the present model. The study also provides some meaningful observations on effects of rotary inertia and shear deformation. Based on the observations, more results are generated for different thickness to span ratios and findings are reported suitably.

A Parametric Study on the Free Vibration of Noncylindrical Helical Springs

1998 ◽  
Vol 65 (1) ◽  
pp. 157-163 ◽  
Author(s):  
V. Yıldırım
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Parametric Study ◽  
Natural Frequencies ◽  
Rotary Inertia ◽  
Helical Springs ◽  
Wide Range ◽  
Stiffness Method

In the work based on the stiffness method reported in this paper, considering the rotary inertia, the axial and shear deformation terms, the natural frequencies of conical, barrel and hyperboloidal-type helical springs fixed at both ends are calculated. The results are presented in dimensionless graphical forms for the six lowest natural frequencies of all types of noncylindrical helices for a wide range of vibrational parameters which influence the natural frequencies. A discussion about the effects of vibrational parameters on the natural frequencies is also presented.

Vibration and Buckling Analysis of a Rotating Annular Plate Subjected to a Compressive Centrifugal Body Force

2018 ◽  
Vol 18 (07) ◽  
pp. 1850097
Author(s):  
Y. B. Yang ◽  
J. H. Kang
Keyword(s):  
Body Force ◽  
Annular Plate ◽  
Ritz Method ◽  
Angular Speed ◽  
Plane Elasticity ◽  
Outer Edge ◽  
Outer Radius ◽  
Mode Shapes ◽  
Rotating Annular Plate ◽  
Significant Figures

The free vibration and buckling of a rotating annular plate with constant angular speed free at the inner edge and fixed at the outer edge subjected to a compressive centrifugal body force are analyzed using the Ritz method. Exact stress components and radial displacement of the rotating annular plate are obtained via the plane elasticity. Convergence studies in the frequencies and the critical buckling angular speed are made up to four significant figures. The natural frequencies and the corresponding mode shapes and the critical buckling angular speeds are presented for the rotating annular plates with various angular speeds and ratios of the inner radius to the outer radius.

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