scholarly journals Three Dimensional Vibration Analysis of a Class of Traction-Free Solid Elastic Bodies with an Eccentric Cavity

2012 ◽  
Vol 19 (6) ◽  
pp. 1341-1357 ◽  
Author(s):  
Seyyed M. Hasheminejad ◽  
Yaser Mirzaei
Keyword(s):  
Vibration Analysis ◽  
Three Dimensional ◽  
Free Vibration Analysis ◽  
Numerical Results ◽  
Mode Shapes ◽  
Computational Techniques ◽  
Published Data ◽  
Elastic Structures ◽  
Wide Range ◽  
Vibrational Characteristics

A three-dimensional elasticity-based continuum model is developed for describing the free vibrational characteristics of an important class of isotropic, homogeneous, and completely free structural bodies (i.e., finite cylinders, solid spheres, and rectangular parallelepipeds) containing an arbitrarily located simple inhomogeneity in form of a spherical or cylindrical defect. The solution method uses Ritz minimization procedure with triplicate series of orthogonal Chebyshev polynomials as the trial functions to approximate the displacement components in the associated elastic domains, and eventually arrive at the governing eigenvalue equations. An extensive review of the literature spanning over the past three decades is also given herein regarding the free vibration analysis of elastic structures using Ritz approach. Accuracy of the implemented approach is established through proper convergence studies, while the validity of results is demonstrated with the aid of a commercial FEM software, and whenever possible, by comparison with other published data. Numerical results are provided and discussed for the first few clusters of eigen-frequencies corresponding to various mode categories in a wide range of cavity eccentricities. Also, the corresponding 3D mode shapes are graphically illustrated for selected eccentricities. The numerical results disclose the vital influence of inner cavity eccentricity on the vibrational characteristics of the voided elastic structures. In particular, the activation of degenerate frequency splitting and incidence of internal/external mode crossings are confirmed and discussed. Most of the results reported herein are believed to be new to the existing literature and may serve as benchmark data for future developments in computational techniques.

scholarly journals Free Vibration Analysis of Patch Repaired Plates with a Through Crack byp-Convergent Layerwise Element

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Jae S. Ahn ◽  
Seung H. Yang ◽  
Kwang S. Woo
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Three Dimensional ◽  
Free Vibration Analysis ◽  
Higher Order ◽  
Mode Shapes ◽  
Bonding Layer ◽  
Shape Functions ◽  
Aspect Ratios ◽  
Dimensional Shape

The high-order layerwise element models have been used for damaged plates and shells in the presence of singularities such as crack, cutout, and delamination. In this study, the extension of a proposed finite element model has been tested for free vibration analysis of composite laminated systems. For the elements, three-dimensional displacement fields can be captured by layer-by-layer representation. For the elements, higher-order shape functions are derived by combination of one- and two-dimensional shape functions based on higher-order Lobatto shape functions, not using pure higher-order three-dimensional shape functions. The present model can relieve difficulty of aspect ratios in modeling very thin thickness of bonding layer. For verification of the model, natural frequencies and corresponding mode shapes are calculated and then compared with reference values for uncracked and cracked plates. Also, the vibration characteristics of one-sided patch repaired plates with a through internal crack are investigated with respect to variation of crack length, size and thickness of patch, and shear modulus of adhesive, respectively.

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.

A semi-analytical three-dimensional free vibration analysis of functionally graded curved panels integrated with piezoelectric layers

2014 ◽  
Vol 21 (4) ◽  
pp. 571-587 ◽  
Author(s):  
Hamid Reza Saeidi Marzangoo ◽  
Mostafa Jalal
Keyword(s):  
Boundary Conditions ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Differential Quadrature Method ◽  
Three Dimensional ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Simply Supported ◽  
Piezoelectric Layers ◽  
Curved Panels

AbstractFree vibration analysis of functionally graded (FG) curved panels integrated with piezoelectric layers under various boundary conditions is studied. A panel with two opposite edges is simply supported, and arbitrary boundary conditions at the other edges are considered. Two different models of material property variations based on the power law distribution in terms of the volume fractions of the constituents and the exponential law distribution of the material properties through the thickness are considered. Based on the three-dimensional theory of elasticity, an approach combining the state space method and the differential quadrature method (DQM) is used. For the simply supported boundary conditions, closed-form solution is given by making use of the Fourier series expansion, and applying the differential quadrature method to the state space formulations along the axial direction, new state equations about state variables at discrete points are obtained for the other cases such as clamped or free-end conditions. Natural frequencies of the hybrid curved panels are presented by solving the eigenfrequency equation, which can be obtained by using edges boundary conditions in this state equation. The results obtained for only FGM shell is verified by comparing the natural frequencies with the results obtained in the literature.

scholarly journals Free Vibration Analysis of Fiber Metal Laminated Straight Beam

2018 ◽  
Vol 16 (1) ◽  
pp. 944-948 ◽  
Author(s):  
Sinan Maraş ◽  
Mustafa Yaman ◽  
Mehmet Fatih Şansveren ◽  
Sina Karimpour Reyhan
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
High Performance ◽  
Free Vibration Analysis ◽  
Vibration Characteristics ◽  
Numerical Results ◽  
Experimental Results ◽  
Hybrid Structures ◽  
Straight Beam ◽  
Fiber Metal

AbstractIn recent years, studies on the development of new and advanced composite materials have been increasing. Among these new technological products, Fiber Metal Laminates (FML), and hybrid structures made of aluminium, carbon, glass or aramid fiber, are preferred especially in the aircraft industry due to their high performance. Therefore, free vibration analysis is necessary for the design process of such structures. In this study, the vibration characteristics of FML for clamped-free boundary conditions were investigated experimentally and numerically. Firstly, numerical results were obtained using Finite Element Method (FEM) and then these results were compared with the experimental results. It was seen that the numerical results were in good agreement with the experimental results. As the theoretical model was justified, the effects of various parameters such as number of layers, fiber orientations, and aluminium layer thickness on the in-plane vibration characteristics of the FML straight beam were analysed using FEM. Thus, most important parameters affecting the vibration characteristics of the hybrid structures were determined.

Investigations of the Effect of Annulus Taper on Transonic Turbine Cascade Flow

1986 ◽  
Vol 108 (2) ◽  
pp. 285-292 ◽  
Author(s):  
W. Bra¨unling ◽  
F. Lehthaus
Keyword(s):  
Surface Pressure ◽  
Theoretical Calculations ◽  
Three Dimensional ◽  
Computer Code ◽  
Numerical Results ◽  
Test Facility ◽  
Turbine Cascade ◽  
Pressure Distributions ◽  
Aspect Ratios ◽  
Wide Range

In a test facility for rotating annular cascades with three conical test sections of different taper angles (0, 30, 45 deg), experiments are conducted for two geometrically different turbine cascade configurations, a hub section cascade with high deflection and a tip section cascade with low deflection. The evaluation of time-averaged data derived from conventional probe measurements upstream and downstream of the test wheel in the machine-fixed absolute system is based on the assumption of axisymmetric stream surfaces. The cascade characteristics, i.e., mass flow, deflection, and losses, for a wide range of inlet flow angles and outlet Mach numbers are provided in the blade-fixed relative system with respect to the influence of annulus taper. Some of the results are compared with simple theoretical calculations. To obtain some information about the spatial structure of the flow within the cascade passages, surface pressure distributions on the profiles of the rotating test wheels are measured at three different radial blade sections. For some examples those distributions are compared with numerical results on plane cascades of the same sweep and dihedral angles and the same aspect ratios. The computer code used is based on a three-dimensional time-marching finite-volume method solving the Euler equations. Both experimental and numerical results show a fairly good qualitative agreement in the three-dimensional blade surface pressure distributions. This work will be continued with detailed investigations on the spatial flow structure.

Modeling and Free Vibration Analysis of a Complex Cable-Stayed Bridge

2012 ◽  
Author(s):  
D. Q. Cao ◽  
M. T. Song ◽  
W. D. Zhu
Keyword(s):  
Vibration Analysis ◽  
Natural Frequencies ◽  
Free Vibration Analysis ◽  
Mode Shapes ◽  
Longitudinal Vibrations ◽  
Simply Supported ◽  
Cable Stayed Bridge ◽  
Linear Partial Differential Equations ◽  
Localized Mode ◽  
Linearized Model

A complex cable-stayed bridge that consists of a simply-supported four-cable-stayed deck beam and two rigid towers is studied. The nonlinear and linear partial differential equations that govern the motions of the cables and segments of the deck beam, respectively, are derived, along with their boundary and matching conditions. The undamped natural frequencies and mode shapes of the linearized model of the cable-stayed bridge, which includes both the transverse and longitudinal vibrations of the cables, are determined. Numerical analysis of the natural frequencies and mode shapes of the cable-stayed bridge is conducted for a symmetrical case with regards to the sizes of the components of the bridge and the initial sags of the cables. The results show that there are very close natural frequencies and localized mode shapes.

Vibration Analysis of Anisotropic Simply Supported Plates by Using Variable Kinematic and Rayleigh-Ritz Method

2011 ◽  
Vol 133 (6) ◽  
Author(s):  
Erasmo Carrera ◽  
Fiorenzo Adolfo Fazzolari ◽  
Luciano Demasi
Keyword(s):  
Vibration Analysis ◽  
Ritz Method ◽  
Single Layer ◽  
Free Vibration Analysis ◽  
Mode Shapes ◽  
Virtual Displacement ◽  
Simply Supported ◽  
Order Expansion ◽  
Thickness Layer ◽  
Made In

This work deals with accurate free-vibration analysis of anisotropic, simply supported plates of square planform. Refined plate theories, which include layer-wise, equivalent single layer and zig-zag models, with increasing number of displacement variables are take into account. Linear up to fourth N-order expansion, in the thickness layer-plate direction have been implemented for the introduced displacement field. Rayleigh-Ritz method based on principle of virtual displacement is derived in the framework of Carrera’s unified formulation. Regular symmetric angle-ply and cross-ply laminates are addressed. Convergence studies are made in order to demonstrate that accurate results are obtained by using a set of trigonometric functions. The effects of the various parameters (material, number of layers, and fiber orientation) upon the frequencies and mode shapes are discussed. Numerical results are compared with available results in literature.

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