scholarly journals Free Vibrations of a Series of Beams Connected by Viscoelastic Layers

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
S. Graham Kelly ◽  
Clint Nicely
Keyword(s):  
Exact Solution ◽  
Free Vibrations ◽  
Geometric Properties ◽  
End Conditions ◽  
Viscoelastic Layers

An exact solution for free vibrations of a series of uniform Euler-Bernoulli beams connected by Kelvin-Voigt is developed. The beams have the same length and end conditions but can have different material or geometric properties. An example of five concentric beams connected by viscoelastic layers is considered.

Vibration Control of Conical Shells Using Viscoelastic Materials

1992 ◽  
Vol 206 (3) ◽  
pp. 167-178 ◽  
Author(s):  
K N Khatri
Keyword(s):  
Equations Of Motion ◽  
Geometrical Parameters ◽  
Viscoelastic Materials ◽  
Complex Moduli ◽  
Conical Shells ◽  
Harmonic Vibrations ◽  
End Conditions ◽  
Layered Shells ◽  
The Subject ◽  
Viscoelastic Layers

The vibration and damping analysis of multi-layered conical shells incorporating layers of viscoelastic materials in addition to elastic ones, the former causing dissipation of vibratory energy, is the subject matter of this paper. The analysis given herein uses Hamilton's variational principle for deriving equations of motion of a general multi-layered conical shell. In view of the correspondence principle of linear viscoelasticity which is valid for harmonic vibrations, the solution is obtained by replacing the moduli of viscoelastic layers by complex moduli. An approximate solution for axisymmetric vibrations of multi-layered conical shells with two end conditions—simply supported edges and clamped edges—is obtained by utilizing the Galerkin procedure. The damping effectiveness in terms of the system loss factor for all families of modes of vibrations for three-, five- and seven-layered shells is evaluated and its variation with geometrical parameters is investigated.

An Exact Solution for the Natural Frequencies of Flexible Beams Undergoing Overall Motions

2003 ◽  
Vol 9 (11) ◽  
pp. 1221-1229 ◽  
Author(s):  
Ali H Nayfeh ◽  
S.A. Emam ◽  
Sergio Preidikman ◽  
D.T. Mook
Keyword(s):  
Exact Solution ◽  
Natural Frequencies ◽  
Three Dimensional ◽  
Beam Theory ◽  
Free Vibrations ◽  
Mode Shapes ◽  
Flexible Beam ◽  
Bernoulli Beam ◽  
Flexible Beams ◽  
Euler Bernoulli Beam

We investigate the free vibrations of a flexible beam undergoing an overall two-dimensional motion. The beam is modeled using the Euler-Bernoulli beam theory. An exact solution for the natural frequencies and corresponding mode shapes of the beam is obtained. The model can be extended to beams undergoing three-dimensional motions.

scholarly journals ANALYTICAL CALCULATIONS OF THE VIBRATIONS OF VERTICAL STRUCTURES CONSIDERING THEIR DEAD WEIGHT

2021 ◽  
Vol 12 (22) ◽  
pp. 29-40
Author(s):  
Yurii Krutii ◽  
◽  
Victor Vandynskyi ◽  
Petr Konstantinov ◽  
◽  
...  
Keyword(s):  
Differential Equation ◽  
Exact Solution ◽  
Mechanical Characteristics ◽  
Free Vibrations ◽  
Approximate Methods ◽  
Dead Weight ◽  
Distributed Load ◽  
Analytical Formulas ◽  
Rod Structures ◽  
Physical And Mechanical Characteristics

This paper presents the results of studies on the analytical dependence between the value of a longitudinal distributed load and the frequency of free vibrations in a uniform rod. Based on the exact solution of the corresponding differential equation, a method for calculating vibrations in rod structures, while considering their dead weight, is implemented. The method algorithm is shown using the example of a rod with both ends clamped. This article contains graphs and analytical formulas for displaying dependencies. A table is provided that contains all the necessary coefficients to perform similar calculations for other boundary conditions. These results allow the physical and mechanical characteristics of a system to be used to determine the natural frequency of rod structures without using approximate methods.

Vibration and Damping Analysis of Curved Multilayered Beams

1985 ◽  
Vol 9 (2) ◽  
pp. 59-63
Author(s):  
J. Vaswani ◽  
N.T. Asnani ◽  
B.C. Nakra
Keyword(s):  
Equations Of Motion ◽  
Harmonic Excitation ◽  
Governing Equations ◽  
Resonant Frequencies ◽  
Constant Weight ◽  
Simply Supported ◽  
Constant Size ◽  
End Conditions ◽  
Multilayered Beam ◽  
Viscoelastic Layers

Governing equations of motion for a general curved multilayered beam with alternate elastic and viscoelastic layers, subjected to harmonic excitation are derived using an energy method. A solution for simply supported end conditions has been obtained, to determine the resonant frequencies and associated system loss factors of beams with 3, 5 and 7 layers. Both constant size and constant weight criteria have been used for comparison.

scholarly journals An Investigation on the Nonlinear Free Vibration Analysis of Beams with Simply Supported Boundary Conditions Using Four Engineering Theories

2011 ◽  
Vol 2011 ◽  
pp. 1-17 ◽  
Author(s):  
R. A. Jafari-Talookolaei ◽  
M. H. Kargarnovin ◽  
M. T. Ahmadian ◽  
M. Abedi
Keyword(s):  
Natural Frequencies ◽  
Free Vibration Analysis ◽  
Free Vibrations ◽  
Geometrically Nonlinear ◽  
Timoshenko Beams ◽  
Analysis Method ◽  
Nonlinear Free Vibration ◽  
End Conditions ◽  
Homotopy Analysis ◽  
Transverse Deflection

The objective of this study is to present a brief survey on the geometrically nonlinear free vibrations of the Bernoulli-Euler, the Rayleigh, shear, and the Timoshenko beams with simple end conditions using the Homotopy Analysis Method (HAM). Expressions for the natural frequencies, the transverse deflection, postbuckling load-deflection relation to, and critical buckling load are presented. The results of nonlinear analysis are validated with the published results, and excellent agreement is observed. The effects of some parameters, such as slender ratio, the rotary inertia, and the shear deformation, are examined as other parameters are fixed.

IN-PLANE VIBRATION OF CIRCULAR ARCHES WITH VARYING CROSS-SECTIONS

2013 ◽  
Vol 13 (01) ◽  
pp. 1350003 ◽  
Author(s):  
EKREM TUFEKCI ◽  
OZNUR OZDEMIRCI YIGIT
Keyword(s):  
Exact Solution ◽  
Cross Section ◽  
Cross Sections ◽  
Free Vibrations ◽  
Transverse Shear Deformation ◽  
Mode Transition ◽  
Rotatory Inertia ◽  
Initial Value ◽  
Inertia Effects ◽  
Circular Arch

The in-plane free vibration of circular arches with continuously varying cross-sections is studied by means of the exact solution. The exact solution can be obtained only for a circular arch with constant cross-section. As an approximation, the circular arch with varying cross-sections is divided into a number of arch elements with constant cross-sections. The cross-section of each arch element is determined by averaging the upper and lower cross-sections. Then, the exact solution of free vibrations for each arch element can be obtained by using the initial value method. The axial extension, transverse shear deformation and rotatory inertia effects are included in the analysis. As the number of the arch elements increases, the fast convergence of the frequencies to those of the original arch is observed. Clamped–clamped (CC), hinged–hinged (HH), hinged–clamped (HC), clamped–free (CF) and free–free (FF) boundary conditions are studied for different opening angles, taper types and taper ratios. A detailed parametric study is performed, by which the mode transition phenomenon is observed. The results obtained are compared with those available in the literature.

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