scholarly journals Study on the Mechanism of Train Noise and its Countermeasure : Part III, Wheel Flexural Vibration Including the Effects of Shear Deformation and Rotatory Inertia

1981 ◽  
Vol 24 (191) ◽  
pp. 849-853
Author(s):  
Hiroshi Matsuhisa ◽  
Yoshihisa Honda ◽  
Susumu Sato
Keyword(s):  
Shear Deformation ◽  
Flexural Vibration ◽  
Rotatory Inertia

Influences of Large Amplitudes, Transverse Shear Deformation, and Rotatory Inertia on Lateral Vibrations of Transversely Isotropic Plates

1969 ◽  
Vol 36 (2) ◽  
pp. 254-260 ◽  
Author(s):  
Cheng-Ih Wu ◽  
J. R. Vinson
Keyword(s):  
Shear Deformation ◽  
Transverse Shear ◽  
Large Amplitude ◽  
Pyrolytic Graphite ◽  
Flexural Vibration ◽  
Transversely Isotropic ◽  
Free Vibrations ◽  
Transverse Shear Deformation ◽  
Rotatory Inertia ◽  
Special Case

In the present paper, using an improved Reissner’s variational theorem along with Berger’s hypothesis, a set of governing equations which include the effects of transverse shear deformation and rotatory inertia is derived for the large amplitude free vibrations of plates composed of a transversely isotropic material. Applying the possibility of neglecting the rotatory inertia in primarily flexural vibration (discussed in the previous work [1]2), the lateral free vibrations of simply supported plates are treated in detail and the solution is compared with those of previous investigators. The free vibration of beams is studied as a special case of plates, while the small amplitude vibrations are treated as a special case of large amplitude vibrations. The numerical results show that the effect of transverse shear deformation is significant when applying to the plate constructions made of pyrolytic graphite-type materials.

Flexural Vibration of Prestressed Concrete Bridges with Corrugated Steel Webs

2017 ◽  
Vol 17 (02) ◽  
pp. 1750023 ◽  
Author(s):  
Xia-Chun Chen ◽  
Zhen-Hu Li ◽  
Francis T. K. Au ◽  
Rui-Juan Jiang
Keyword(s):  
Finite Element ◽  
Shear Deformation ◽  
Prestressed Concrete ◽  
Natural Frequencies ◽  
Sandwich Beam ◽  
Flexural Vibration ◽  
Concrete Bridges ◽  
Mode Shapes ◽  
Beam Model ◽  
Prestressed Concrete Bridges

Prestressed concrete bridges with corrugated steel webs have emerged as a new form of steel-concrete composite bridges with remarkable advantages compared with the traditional ones. However, the assumption that plane sections remain plane may no longer be valid for such bridges due to the different behavior of the constituents. The sandwich beam theory is extended to predict the flexural vibration behavior of this type of bridges considering the presence of diaphragms, external prestressing tendons and interaction between the web shear deformation and flange local bending. To this end, a [Formula: see text] beam finite element is formulated. The proposed theory and finite element model are verified both numerically and experimentally. A comparison between the analyses based on the sandwich beam model and on the classical Euler–Bernoulli and Timoshenko models reveals the following findings. First of all, the extended sandwich beam model is applicable to the flexural vibration analysis of the bridges considered. By letting [Formula: see text] denote the square root of the ratio of equivalent shear rigidity to the flange local flexural rigidity, and L the span length, the combined parameter [Formula: see text] appears to be more suitable for considering the diaphragm effect and the interaction between the shear deformation and flange local bending. The diaphragms have significant effect on the flexural natural frequencies and mode shapes only when the [Formula: see text] value of the bridge falls below a certain limit. For a bridge with an [Formula: see text] value over a certain limit, the flexural natural frequencies and mode shapes obtained from the sandwich beam model and the classical Euler–Bernoulli and Timoshenko models tend to be the same. In such cases, either of the classical beam theories may be used.

Symmetric Flexural Vibrations of a Clamped Circular Disk

1956 ◽  
Vol 23 (2) ◽  
pp. 319
Author(s):  
H. Deresiewicz
Keyword(s):  
Shear Deformation ◽  
Frequency Spectrum ◽  
Transverse Shear ◽  
Circular Disk ◽  
Transverse Shear Deformation ◽  
Axially Symmetric ◽  
Rotatory Inertia ◽  
Flexural Vibrations ◽  
Clamped Edges

Abstract The frequency spectrum is computed for the case of free, axially symmetric vibrations of a circular disk with clamped edges, using a theory which includes the effects of rotatory inertia and transverse shear deformation.

Effect of Shear Deformation and Rotatory Inertia on Dynamic Buckling of Elastic Plates

1988 ◽  
Vol 110 (3) ◽  
pp. 282-286
Author(s):  
V. Birman
Keyword(s):  
Dynamic Response ◽  
Shear Deformation ◽  
Plate Theory ◽  
Deformation Mode ◽  
Dynamic Buckling ◽  
Rectangular Plates ◽  
Elastic Plates ◽  
Rotatory Inertia ◽  
Qualitative Effect

The influence of shear deformation and rotatory inertia on dynamic response of elastic rectangular plates subject to in-plane loads increasing with time is discussed using Mindlin’s plate theory. The qualitative effect of those factors on transverse displacements is estimated. It is shown that this effect becomes essential only if the plate is thick and the number of half-waves along the plate axes in the deformation mode is large.

scholarly journals Out-plane Vibrations of Curved Bars Considering Shear Deformation and Rotatory Inertia

1981 ◽  
Vol 24 (193) ◽  
pp. 1206-1213
Author(s):  
Katsuyoshi SUZUKI ◽  
Shin TAKAHASHI
Keyword(s):  
Shear Deformation ◽  
Rotatory Inertia

On the Importance of Shear Deformation, Rotatory Inertia, and Coriolis Forces in Turbine Blade Vibrations

1986 ◽  
Vol 108 (2) ◽  
pp. 319-324 ◽  
Author(s):  
K. A. Ansari
Keyword(s):  
Shear Deformation ◽  
Turbine Blade ◽  
Normal Modes ◽  
Functional Method ◽  
Lumped Parameter Model ◽  
Rotatory Inertia ◽  
Blade Vibration ◽  
Coriolis Forces ◽  
Analysis Technique ◽  
Blade Vibrations

This paper is concerned with the significance of the effects of shear deformation, rotatory inertia, and Coriolis forces in the analysis of turbine blade vibrations. Since these are quite pronounced at the high frequency ranges encountered in turbine blade vibration problems, they should not be overlooked although their inclusion paves the way for a complicated nonlinear analysis. An approximate analysis technique is presented which involves an application of the stationary functional method using the normal modes of a discretized model. Numerical results for a typical blade are obtained and discussed. An advantage of this analysis as applied to a lumped parameter model is that nonlinear modes higher than the fundamental can also be easily computed and assessed.

Free Vibration of Damaged Frame Structures Considering the Effects of Axial Extension, Shear Deformation and Rotatory Inertia: Exact Solution

2017 ◽  
Vol 17 (10) ◽  
pp. 1750111
Author(s):  
Ugurcan Eroglu ◽  
Ekrem Tufekci
Keyword(s):  
Exact Solution ◽  
Free Vibration ◽  
Shear Deformation ◽  
Natural Frequencies ◽  
Plane Motion ◽  
Mode Shapes ◽  
Frame Structures ◽  
Crack Identification ◽  
Rotatory Inertia ◽  
Axial Extension

In this paper, a procedure based on the transfer matrix method for obtaining the exact solution to the equations of free vibration of damaged frame structures, considering the effects of axial extension, shear deformation, rotatory inertia, and all compliance components arising due to the presence of a crack, is presented. The crack is modeled by a rotational and/or translational spring based on the concept of linear elastic fracture mechanics. Only the in-plane motion of planar structures is considered. The formulation is validated through some examples existing in the literature. Additionally, the mode shapes and natural frequencies of a frame with pitched roof are provided. The variation of natural frequencies with respect to the crack location is presented. It is concluded that considering the axial compliance, and axial-bending coupling due to the presence of a crack results in different dynamic characteristics, which should be considered for problems where high precision is required, such as for the crack identification problems.

Shear and Rotatory Inertia Effects on the Large Amplitude Vibration of the Initially Imperfect Plates

1980 ◽  
Vol 47 (3) ◽  
pp. 662-666 ◽  
Author(s):  
Z. Celep
Keyword(s):  
Transverse Shear ◽  
Vibration Mode ◽  
Initial Imperfection ◽  
Flexural Vibration ◽  
Rotatory Inertia ◽  
Inertia Effects ◽  
Amplitude Vibration ◽  
Large Amplitude Vibration ◽  
Elastic Rectangular Plate ◽  
Modal Equation

In this paper, the free flexural vibration of an elastic rectangular plate having initial imperfection is investigated including the effects of transverse shear and rotatory inertia. It is assumed that the vibration occurs with large amplitudes which leads to nonlinear differantial equations. On the basis of an assumed vibration mode, the modal equation of the plate is obtained and solved numerically.

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