The Effect of Visco-Elastic Core Thickness on Modal Loss Factors of a Thick Three-Layer Cylinder

2007 ◽  
Author(s):  
Hamid R. Hamidzadeh
Keyword(s):  
Elastic Moduli ◽  
Natural Frequencies ◽  
Middle Layer ◽  
Constrained Layer Damping ◽  
Governing Equations ◽  
Modal Damping ◽  
Core Thickness ◽  
Elastic Cylinders ◽  
Thick Layers ◽  
Loss Factors

Free vibration of damped three-layer sandwich cylinders with thick layers is considered. In particular, the effect of the different thicknesses for the middle layer on the overall natural frequencies and modal damping factors are studied. The constrained layer damping is accomplished by sandwiching a linear visco-elastic material between two isotropic elastic cylinders with the same properties. The governing equations are derived using the theory of elasto-dynamic, by employing complex elastic moduli for the sandwiched layer. Dimensionless natural frequencies and modal loss-factors for the first three thickness modes associated with wave numbers of n = 0, 1, 2, 3, and 4 are tabulated for a range of thicknesses for the middle visco-elastic layer while keeping the thicknesses of inner and outer layers unchanged.

Modal Loss Factors of Thick Three-Layer Cylinders With Viscoelastic Core

1995 ◽  
Author(s):  
Hamid R. Hamidzadeh ◽  
Yanfei Jiang
Keyword(s):  
Shear Modulus ◽  
Natural Frequencies ◽  
Core Material ◽  
Constrained Layer Damping ◽  
Material Damping ◽  
The Core ◽  
Linear Viscoelastic Material ◽  
Wide Range ◽  
Elastic Cylinders ◽  
Loss Factors

Abstract An analytical solution to the free vibration of a damped three-layer thick sandwiched cylinder of infinite extend is presented. The constrained layer damping is accomplished by sandwiching a linear viscoelastic material between two isotropic elastic cylinders with the same properties. The governing equation is derived based on elasto-dynamic theory utilizing complex elastic moduli. Dimensionless natural frequencies and modal loss-factors are extracted. Special case for a three-layer sandwiched cylinder with similar elastic properties is considered. The computed dimensionless frequencies are compared with previously established results. The comparison indicates the validity of the proposed mathematical procedures. In addition, the effects of various values of material damping for the core layer and ratio of the core shear modulus to the shear modulus of the elastic cylinders on natural frequencies and modal loss-factors are studied. For a given configuration, modal information for the first two modes for n = 0, 1, 2, 3 and 4 are presented for a wide range of core material damping and G2/G1 ratio.

scholarly journals Free Vibration of Thick Multilayer Cylinders

1995 ◽  
Vol 2 (5) ◽  
pp. 393-401 ◽  
Author(s):  
H. R. Hamidzadeh ◽  
N. N. Sawaya
Keyword(s):  
Free Vibration ◽  
Elastic Moduli ◽  
Natural Frequencies ◽  
Three Dimensional ◽  
Single Layer ◽  
Propagator Matrix ◽  
Infinite Extent ◽  
Linear Viscoelastic ◽  
Elastic Cylinders ◽  
Constant Complex

In this study of the free vibration of multilayer thick cylinders, the medium is modeled by laminated linear viscoelastic cylinders of an infinite extent. The analytical modeling is based on three-dimensional wave propagation utilizing constant complex elastic moduli. The solution is achieved by determining the displacements and stresses for each interface and by complying with requirements at the interfaces. A propagator matrix relating the boundary displacements to boundary stresses is developed. Dimensionless natural frequencies and modal loss factors for different circumferential and axial wave numbers are determined. The validity of the proposed method is verified by comparing the results for one-, two-, and three-layer elastic cylinders with properties similar to those reported for an equivalent single layer.

scholarly journals Vibration Analysis of Viscoelastically Damped Sandwich Shells

1996 ◽  
Vol 3 (6) ◽  
pp. 403-417 ◽  
Author(s):  
Ji-Fan He ◽  
Bang-An Ma
Keyword(s):  
Asymptotic Solution ◽  
Strain Energy ◽  
Natural Frequencies ◽  
Governing Equations ◽  
Modal Strain Energy ◽  
Simply Supported ◽  
Modal Strain Energy Method ◽  
Sandwich Shells ◽  
Method Accuracy ◽  
Loss Factors

The simplified governing equations and corresponding boundary conditions of vibration of viscoelastically damped unsymmetrical sandwich shells are given. The asymptotic solution to the equations is then discussed. If only the first terms of the asymptotic solution of all variables are taken as an approximate solution, the result is identical with that obtained from the modal strain energy method. By taking more terms of the asymptotic solution with successive calculations and use of the Padé approximants method, accuracy of natural frequencies and modal loss factors of sandwich shells can be improved. The lowest three or four natural frequencies and modal loss factors of simply supported cylindrical sandwich shells are calculated.

scholarly journals Vibration of Rotating and Revolving Planet Rings with Discrete and Partially Distributed Stiffnesses

2020 ◽  
Vol 11 (1) ◽  
pp. 127
Author(s):  
Fuchun Yang ◽  
Dianrui Wang
Keyword(s):  
High Speed ◽  
Differential Operators ◽  
Natural Frequencies ◽  
Rotation Speed ◽  
Distribution Area ◽  
Vibration Modes ◽  
Governing Equations ◽  
Vibration Properties ◽  
Wide Range ◽  
Forced Responses

Vibration properties of high-speed rotating and revolving planet rings with discrete and partially distributed stiffnesses were studied. The governing equations were obtained by Hamilton’s principle based on a rotating frame on the ring. The governing equations were cast in matrix differential operators and discretized, using Galerkin’s method. The eigenvalue problem was dealt with state space matrix, and the natural frequencies and vibration modes were computed in a wide range of rotation speed. The properties of natural frequencies and vibration modes with rotation speed were studied for free planet rings and planet rings with discrete and partially distributed stiffnesses. The influences of several parameters on the vibration properties of planet rings were also investigated. Finally, the forced responses of planet rings resulted from the excitation of rotating and revolving movement were studied. The results show that the revolving movement not only affects the free vibration of planet rings but results in excitation to the rings. Partially distributed stiffness changes the vibration modes heavily compared to the free planet ring. Each vibration mode comprises several nodal diameter components instead of a single component for a free planet ring. The distribution area and the number of partially distributed stiffnesses mainly affect the high-order frequencies. The forced responses caused by revolving movement are nonlinear and vary with a quasi-period of rotating speed, and the responses in the regions supported by partially distributed stiffnesses are suppressed.

Modal Loss Factor Predication in Flexible Mechanism Systems With Constrain Viscoelastic Layers

1998 ◽  
Author(s):  
Zhang Xianmin ◽  
Liu Jike
Keyword(s):  
Equations Of Motion ◽  
Sandwich Beam ◽  
Viscoelastic Layer ◽  
Treatment Technique ◽  
Constrained Layer Damping ◽  
Modal Strain Energy ◽  
Frame Element ◽  
Modal Damping ◽  
Flexible Mechanism ◽  
Viscoelastic Layers

Abstract Control of dynamic vibration is critical to the operational success of many flexible mechanism systems. This paper addresses the problem of vibration control of such mechanisms through passive damping, using constrained layer damping treatment technique. A new type of shape function for three layer frame element containing a viscoelastic layer is developed. The equations of motion of the damped flexible mechanism are derived. Modal loss factors of this kind mechanisms are predicated from undamped normal mode by means of the modal strain energy method. Comparisons between the results obtained by this paper and the results obtained by exact solution of the governing equations for a well known sandwich beam demonstrate that the method presented in this paper is correct and reliable. Application of this method in predication of modal damping ratios for damped mechanisms is discussed. It is believed that the method of this paper hold the greatest potential for optimal design of damped flexible mechanism systems.

Influence of Material Damping on In-Plane Modal Parameters for Rotating Disks

2012 ◽  
Author(s):  
Hamid R. Hamidzadeh ◽  
Ehsan Sarfaraz
Keyword(s):  
Elastic Moduli ◽  
Damping Ratio ◽  
Equations Of Motion ◽  
Elastic Stability ◽  
Rotating Disks ◽  
Governing Equations ◽  
Annular Disk ◽  
Stress Theory ◽  
Hysteretic Damping ◽  
Circumferential Wave

The linear in-plane free vibration of a thin, homogeneous, viscoelastic, rotating annular disk is investigated. In the development of an analytical solution, two dimensional elastodynamic theory is employed and the viscoelastic material for the medium is allowed by assuming complex elastic moduli. The general governing equations of motion are derived by implementing plane stress theory. Natural frequencies are computed for several modes at specific radius ratios with fixed-free boundary conditions and modal loss factors for different damping ratios are determined. The computed results were compared to previously established results. It was observed that the effects of rotational speed and hysteretic damping ratio on natural frequency and elastic stability of the rotating disks were related to the mode of vibration and type of circumferential wave occurring.

Review of Three Dimensional Dynamic Analyses of Circular Cylinders and Cylindrical Shells

1994 ◽  
Vol 47 (10) ◽  
pp. 501-516 ◽  
Author(s):  
Kostas P. Soldatos
Keyword(s):  
Cylindrical Shells ◽  
Three Dimensional ◽  
Circular Cylinders ◽  
Accurate Information ◽  
Two Dimensional ◽  
Governing Equations ◽  
Complicated Form ◽  
Dynamic Analyses ◽  
Cylindrical Panels ◽  
Elastic Cylinders

There is an increasing usefulness of exact three-dimensional analyses of elastic cylinders and cylindrical shells in composite materials applications. Such analyses are considered as benchmarks for the range of applicability of corresponding studies based on two-dimensional and/or finite element modeling. Moreover, they provide valuable, accurate information in cases that corresponding predictions based on that later kind of approximate modeling is not satisfactory. Due to the complicated form of the governing equations of elasticity, such three-dimensional analyses are comparatively rare in the literature. There is therefore a need for further developments in that area. A survey of the literature dealing with three-dimensional dynamic analyses of cylinders and open cylindrical panels will serve towards such developments. This paper presents such a survey within the framework of linear elasticity.

scholarly journals Vibration Characteristics of Piezoelectric Microbeams Based on the Modified Couple Stress Theory

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
R. Ansari ◽  
M. A. Ashrafi ◽  
S. Hosseinzadeh
Keyword(s):  
Boundary Conditions ◽  
Couple Stress ◽  
Natural Frequencies ◽  
Couple Stress Theory ◽  
Equations Of Motion ◽  
Modified Couple Stress Theory ◽  
Beam Model ◽  
Governing Equations ◽  
Stress Theory ◽  
Modified Couple Stress

The vibration behavior of piezoelectric microbeams is studied on the basis of the modified couple stress theory. The governing equations of motion and boundary conditions for the Euler-Bernoulli and Timoshenko beam models are derived using Hamilton’s principle. By the exact solution of the governing equations, an expression for natural frequencies of microbeams with simply supported boundary conditions is obtained. Numerical results for both beam models are presented and the effects of piezoelectricity and length scale parameter are illustrated. It is found that the influences of piezoelectricity and size effects are more prominent when the length of microbeams decreases. A comparison between two beam models also reveals that the Euler-Bernoulli beam model tends to overestimate the natural frequencies of microbeams as compared to its Timoshenko counterpart.

Vibrational characteristics of an earth dam

1966 ◽  
Vol 56 (6) ◽  
pp. 1207-1226
Author(s):  
W. O. Keightley
Keyword(s):  
Theoretical Analysis ◽  
Natural Frequencies ◽  
Forced Vibrations ◽  
Earth Dam ◽  
Mode Shapes ◽  
Modal Damping ◽  
Vibrational Characteristics ◽  
Good Agreement ◽  
Lower Frequencies

Abstract An earth dam was excited into vibrations, in the upstream-downstream direction, by four rotating eccentric-mass vibration generators which were operated on the crest. Natural frequencies, mode shapes, and equivalent viscous modal damping constants of the dam were revealed by the forced vibrations. A theoretical analysis of the dam, based on consideration of shearing deformations only, shows moderately good agreement with the behavior which was observed at the lower frequencies.

Natural frequencies of parabolic arches with a single crack on opposite cross-section sides

2019 ◽  
Vol 25 (7) ◽  
pp. 1313-1325 ◽  
Author(s):  
U Eroglu ◽  
G Ruta ◽  
E Tufekci
Keyword(s):  
Cross Section ◽  
Natural Vibration ◽  
Natural Frequencies ◽  
Damage Identification ◽  
Crack Opening ◽  
Curved Beams ◽  
Governing Equations ◽  
First Order ◽  
Crack Location ◽  
Original Contribution

We study natural vibration of elastic parabolic arches, modeled as plane curved beams susceptible to elongation, shear, and bending, exhibiting small concentrated cracks. The crack is simulated by springs between regular chunks, with stiffness evaluated following stress concentration in usual crack opening modes. We evaluate and compare the linear dynamic response of the undamaged and damaged arch in nondimensional form. The governing equations are turned into a system of first-order differential equations that are solved numerically by the so-called matricant. The original contribution of this study lies in highlighting the dependence of the variation of the first natural frequencies on the crack location not only along the axis but also on opposite sides of the cross-section. We obtain the relative variations of the first frequencies in terms of the two crack locations. The result of this direct problem provides information on the possibility to detect such locations, and gives indications on structural monitoring and damage identification.

Sign in / Sign up

Export Citation Format

Share Document