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.

Forced Vibration of Thick Viscoelastic Cylinders

1993 ◽  
Author(s):  
H. R. Hamidzadeh ◽  
G. R. Minor
Keyword(s):  
Forced Vibration ◽  
Elastic Moduli ◽  
Natural Frequencies ◽  
Three Dimensional ◽  
Dimensional Theory ◽  
Material Loss ◽  
Resonant Frequencies ◽  
Frequency Responses ◽  
Infinite Extent ◽  
Hollow Cylinders

Abstract Harmonic forced vibration of thick viscoelastic hollow cylinders of infinite extent is considered. The cylinder is excited by stresses applied at the inner and outer boundaries. The governing equation of motion is developed by utilizing three dimensional theory of elastodynamics. The material damping is allowed using complex elastic moduli for the viscoelastic medium. Modal displacements and stresses at any point in the medium are formulated in terms of boundary stresses. Frequency responses for radial, tangential and axial displacements are computed for different circumferential and axial wave numbers. The effect of different material loss factors on the frequency responses is examined for axial and nonaxisymmetric modes. The dimensionless resonant frequencies for zero loss factor are compared with dimensionless natural frequencies available for elastic material. Comparison indicates excellent agreement between the results.

Modal Characteristics of Simply Supported Lightweight Long Cylinders

2002 ◽  
Author(s):  
L. Moxey ◽  
H. Hamidzadeh
Keyword(s):  
Analytical Modeling ◽  
Natural Frequencies ◽  
Three Dimensional ◽  
Mode Shapes ◽  
Infinite Length ◽  
Solid Cylinder ◽  
Complex Moduli ◽  
Boundary Stress ◽  
Linear Viscoelastic ◽  
Constant Complex

In the study of free vibration of solid cylinders a linear viscoelastic cylinder of an infinite length models the medium. The analytical modeling is based on three dimensional wave propagation utilizing constant complex moduli. The solution is achieved by determining the displacement and stress on the surface, and by complying with requirements at the boundary. Analysis was conducted to express displacement stresses at any point of the solid cylinder to boundary stress. Dimensionless natural frequencies and mode shapes for different circumferential and axial wave numbers are determined.

Free Vibration of Coupled Disk-Hat Structures

1999 ◽  
Author(s):  
Jun-Chul Bae ◽  
Jonathan Wickert
Keyword(s):  
Free Vibration ◽  
Natural Frequencies ◽  
Three Dimensional ◽  
Phase Relationship ◽  
Vibration Modes ◽  
Pure Bending ◽  
Brake Rotors ◽  
Automotive Brake ◽  
Ordered Pairs

Abstract The free vibration of disk-hat structures, such as automotive brake rotors, is investigated analytically and through laboratory experimentation. Of particular interest are the role played by the hat element’s depth in influencing the three-dimensional vibration of the disk, and the manner in which the bending and in-plane modes of the disk alone evolve as a hat of increasing depth is incorporated in the model. The lower vibration modes of disk-hat structures are shown to be characterized by the numbers of nodal circles NC and diameters ND present on the disk, as well as the phase relationship between the disk’s transverse and radial displacements due to coupling with the hat element. Such modes map continuously back to the pure bending and in-plane modes of the disk alone, appear in ordered pairs, and can exist at close frequencies. Those characteristics are explored particularly with respect to sensitivities in the disk’s thickness and the hat’s depth with a view towards shifting particular natural frequencies, or minimizing transverse disk motion in certain vibration modes. Results obtained through analysis and measurement of a prototypical disk-hat structure are applied in a case study with a ventilated automotive brake rotor.

Free Vibration of a Multilayered One-Dimensional Quasi-Crystal Plate

2014 ◽  
Vol 136 (4) ◽  
Author(s):  
Natalie Waksmanski ◽  
Ernian Pan ◽  
Lian-Zhi Yang ◽  
Yang Gao
Keyword(s):  
Free Vibration ◽  
Natural Frequencies ◽  
Closed Form Solution ◽  
Form Solution ◽  
Crystal Plate ◽  
Mode Shapes ◽  
Sandwich Plates ◽  
One Dimensional ◽  
Propagator Matrix ◽  
Multilayered Plates

An exact closed-form solution of free vibration of a simply supported and multilayered one-dimensional (1D) quasi-crystal (QC) plate is derived using the pseudo-Stroh formulation and propagator matrix method. Natural frequencies and mode shapes are presented for a homogenous QC plate, a homogenous crystal plate, and two sandwich plates made of crystals and QCs. The natural frequencies and the corresponding mode shapes of the plates show the influence of stacking sequence on multilayered plates and the different roles phonon and phason modes play in dynamic analysis of QCs. This work could be employed to further expand the applications of QCs especially if used as composite materials.

Flexural Vibrations of Thick Cylindrical Panels

1997 ◽  
Author(s):  
H. R. Hamidzadeh
Keyword(s):  
Elastic Moduli ◽  
Normal Modes ◽  
Tangential Direction ◽  
Cylindrical Panel ◽  
Harmonic Vibrations ◽  
Wide Range ◽  
End Conditions ◽  
Cylindrical Panels ◽  
Infinite Extent ◽  
Linear Viscoelastic

Abstract Harmonic vibrations of thick viscoelastic cylindrical panels are investigated. The medium is considered to be a homogeneous, isotropic, linear viscoelastic, thick cylindrical panel of infinite extent. In the development of an analytical solution, the two dimensional elastodynamic theory is employed and the material damping is considered by introducing complex elastic moduli. The panels end conditions do not allow the displacement along the tangential direction; however, the radial displacements are not constrained. The displacements on the surface of the panel are formulated in terms of boundary stresses and their harmonic responses due to the radial and tangential boundary stresses are determined. Displacements and stresses in both the radial and tangential direction for each of the normal modes in the medium are computed. This is achieved by utilizing an algorithm for the Bessel functions of complex argument and fractional order. The algorithm is numerically stable for a wide range of exciting frequencies, circumferential mode numbers, and loss factors.

Large amplitude free vibration study of non-uniform plates with in-plane material inhomogeneity

2016 ◽  
Vol 232 (5) ◽  
pp. 371-387 ◽  
Author(s):  
Saurabh Kumar ◽  
Anirban Mitra ◽  
Haraprasad Roy
Keyword(s):  
Free Vibration ◽  
Large Amplitude ◽  
Natural Frequencies ◽  
Three Dimensional ◽  
Static Problem ◽  
Solution Procedure ◽  
Mode Shapes ◽  
Material Inhomogeneity ◽  
Contour Plots ◽  
Variational Form

Free vibration study of non-uniform plates with in-plane material inhomogeneity is carried out in the present work considering geometric nonlinearity. Inhomogeneous plates where the material properties vary along only x-axis (unidirectional) and along both x- and y-axis (bidirectional) are considered. The analysis is performed for two boundary conditions namely clamped and simply supported at all edges, under the action of a transverse uniformly distributed load. The large amplitude problem is formulated using nonlinear strain–displacement relations along with a variational form of energy method. A two-step solution procedure is utilised where, in the first part the static problem is solved and undetermined coefficients are found, subsequently the dynamic problem is taken up on the basis of previously determined coefficients. Validity of the results is successfully confirmed by comparison with the works of other researchers. The analysis reveals that the amplitude and taper parameter affect the loaded natural frequencies significantly. Three-dimensional mode shapes for linear and nonlinear cases are presented along with their respective contour plots.

scholarly journals Vibration Analysis of a Tire in Ground Contact under Varied Conditions

2017 ◽  
Vol 47 (1) ◽  
pp. 3-17 ◽  
Author(s):  
Murat Karakus ◽  
Aydin Cavus ◽  
Mehmet Colakoglu
Keyword(s):  
Free Vibration ◽  
Natural Frequencies ◽  
Three Dimensional ◽  
Concrete Block ◽  
Ground Contact ◽  
Tire Model ◽  
Inflation Pressure ◽  
Monitoring Method ◽  
The Impact ◽  
Good Agreement

Abstract The effect of three different factors, which are inflation pressure, vertical load and coefficient of friction on the natural frequencies of a tire (175/70 R13) has been studied. A three dimensional tire model is constructed, using four different material properties and parts in the tire. Mechanical properties of the composite parts are evaluated. After investigating the free vibration, contact analysis is carried out. A concrete block and the tire are modelled together, using three different coefficients of friction. Experiments are run under certain conditions to check the accuracy of the numerical model. The natural frequencies are measured to describe free vibration and vibration of the tire contacted by ground, using a damping monitoring method. It is seen, that experimental and numerical results are in good agreement. On the other hand, investigating the impact of three different factors together is quite difficult on the natural frequencies. When some of these factors are assumed to be constant and the variables are taken one by one, it is easier to assess the effects.

Analytical Piezoelasticity Solution for Natural Frequencies of Levy-Type Piezolaminated Plates

2019 ◽  
Vol 11 (03) ◽  
pp. 1950023 ◽  
Author(s):  
Susanta Behera ◽  
Poonam Kumari
Keyword(s):  
Natural Frequencies ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Single Layer ◽  
Free Vibration Analysis ◽  
Mode Shapes ◽  
Kantorovich Method ◽  
Extended Kantorovich Method ◽  
Aspect Ratios ◽  
Support Conditions

First time, an analytical solution based on three-dimensional (3D) piezoelasticity is developed for the free vibration analysis of Levy-type piezolaminated plates using 3D extended Kantorovich method (EKM). Extended Hamilton principle (which is extended from elastic to piezoelectric case) is further extended to the dynamic version of mixed form containing contributions from the electrical terms. Multi-term multi-field extended Kantorovich method in conjunction with Fourier series (along [Formula: see text]-direction) is employed to obtain two sets of first-order homogeneous ordinary differential equations (8[Formula: see text] along [Formula: see text]- and [Formula: see text]-axes). A robust algorithm is designed (Fortran Code) to extract the natural frequencies and mode shapes of Levy-type piezolaminated plates. The accuracy and efficacy of this technique are verified thoroughly by comparing it with the existing results in the literature and with the 3D finite element (FE) solutions. Numerical results are presented for single-layer piezoelectric and smart sandwich plates considering five different boundary support conditions, three aspect ratios (length to thickness ratio) and electric open and close circuit conditions. The present results shall be used as a benchmark to assess various two-dimensional (2D) and 3D numerical solutions (e.g., FEM, DQM, etc.).

scholarly journals Free Vibration Analysis of Cable Stayed-Bridge by Finite Element Method

2019 ◽  
Vol 12 (4) ◽  
pp. 67-72
Author(s):  
Haneen A. Mahmood ◽  
Zaid S. Hammoudi ◽  
Ali Laftah Abbas
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Three Dimensional ◽  
Free Vibration Analysis ◽  
Element Model ◽  
Dynamic Responses ◽  
Mode Shapes ◽  
Cable Stayed Bridge

A delicate analysis of the natural frequencies and mode shapes of a cable stayed bridge is essential to the solution of its dynamic responses due to seismic, wind and traffic loads. In this paper, a bridge with geometry comparable to the Quincy Bayview Bridge was modelled in order to explore the significance of the three dimensional and free vibration analysis. This paper provides a detail of the bridge and the equivalent cross section of the three-dimensional finite element model implicating cables, the bridge deck and pylons as well as the boundary conditions and free vibration analysis by Ansys15.0. The bridge was analyzed to free vibration to obtaine the natural frequency and mode shape. result of this paper present the natural frequencies and mode shapes of the bridge. The method of modelling cables is also studied. It is found that modelling cables as multi beam elements provides better results than using the traditional (and simpler) method of modeling them as single tensile elements.

Static Bending and Free Vibration Analysis of Hybrid Fuzzy-Fiber Reinforced Nanocomposite Beam-A Multiscale Modeling

2018 ◽  
Vol 10 (05) ◽  
pp. 1850053 ◽  
Author(s):  
Mohammad Javad Mahmoodi ◽  
Mohsen Maleki ◽  
Mohammad Kazem Hassanzadeh-Aghdam
Keyword(s):  
Carbon Fiber ◽  
Free Vibration ◽  
Natural Frequencies ◽  
Volume Fraction ◽  
Micromechanical Model ◽  
Three Dimensional ◽  
Fiber Surface ◽  
Free Vibration Analysis ◽  
Beam Deflection ◽  
Fiber Reinforced

Static and free vibration multiscale analysis of fuzzy-fiber-reinforced composite (FFRC) beam is investigated using a three-dimensional micromechanical model together with two-dimensional elasticity macromechanical theory. In the hybrid nanocomposite, aligned carbon nanotubes (CNTs) are radially grown on the circumferential surfaces of carbon fibers. Influence of the carbon fiber orientation, volume fraction and arrangement; CNT volume fraction and interphase region characteristics on the FFRC beam deflection and natural frequencies are studied. Good agreements are reported for the presented results compared with available experiments and the other modeling strategies at both micro and macro levels. The results reveal that the FFRCs properties are strongly dependent on the carbon fiber off-axis angle. By increasing the off-axis angle from [Formula: see text] to [Formula: see text], the FFRC beam deflection sharply increases up to [Formula: see text] fiber angle and then its value decreases. It is shown that the growth of CNTs on the carbon fiber surface leads to the highest decrease in the beam deflection for 90[Formula: see text] coupon. Also, increasing the interphase thickness decreases the beam deflection and increases the natural frequencies, especially for [Formula: see text] coupon. Moreover, the increasing the interphase Young’s modulus gives maximum 1.74% increase in the natural frequencies.

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