scholarly journals Free vibration analysis of transmission lines based on the dynamic stiffness method

2019 ◽  
Vol 6 (3) ◽  
pp. 181354 ◽  
Author(s):  
Xiaohui Liu ◽  
You Hu ◽  
Mengqi Cai
Keyword(s):  
Transmission Lines ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Dynamic Stiffness ◽  
Free Vibration Analysis ◽  
The Finite Element Method ◽  
Damping Parameter ◽  
Inclination Angles ◽  
Parametric Studies ◽  
Coupling Characteristic

An improved mathematical model used to study the coupling characteristic of the multi-span transmission lines is developed. Based on the solution method for single-span cable, an expression for the dynamic stiffness of two-span transmission lines with an arbitrary inclination angle is formulated. The continuity of displacements and forces at a suspension point is used to derive the dynamic stiffness. Interactions between insulator strings and adjacent spans are accommodated. Considering the infinite dynamic stiffness corresponds to the natural frequencies of the transmission lines, the finite-element method (FEM) is employed to assess the validity of the dynamic stiffness. In the numerical investigation, attention is focused on the effect of the inclination angles, Irvine parameter, insulator string length and damping parameter. In addition, the modal function corresponding to the natural frequencies is derived. Then, the results of comprehensive parametric studies are presented and discussed. Special attention is paid to the effect of the Irvine parameter and damping parameter on the in-plane modal shapes. Finally, according to the theoretical model of two-span transmission lines, the generalized dynamic stiffness of transmission lines with an arbitrary number of spans and inclination angles is derived. The method can be used as the basis of the vibration analysis on a wide variety of multi-span transmission lines.

scholarly journals Free vibration analysis of joined composite conical-cylindrical-conical shells containing fluid

2016 ◽  
Vol 38 (4) ◽  
pp. 249-265 ◽  
Author(s):  
Vu Quoc Hien ◽  
Tran Ich Thinh ◽  
Nguyen Manh Cuong
Keyword(s):  
Vibration Analysis ◽  
Natural Frequencies ◽  
Dynamic Stiffness ◽  
Fluid Pressure ◽  
Free Vibration Analysis ◽  
The Finite Element Method ◽  
Fluid Interface ◽  
Governing Equations ◽  
Conical Shells ◽  
Bernoulli’S Equation

A new continuous element (CE) formulation has been presented in this paper for the vibration analysis of cross-ply composite joined conical-cylindrical-conical shells containing fluid. Governing equations are obtained using thick shell theory of Midlin, taking into account the shear deflection effects. The velocity potential, Bernoulli's equation and impermeability condition have been applied to the shell-fluid interface to obtain an explicit expression for fluid pressure. The dynamic stiffness matrix has been built from which natural frequencies have been calculated. The appropriate expressions among stress resultants and deformations are extracted as continuity conditions at the joining section. A matlab program is written using the CE formulation in order to validate our model. Numerical results on natural frequencies are compared to those obtained by the Finite Element Method and validated with the available results in other investigations. This paper emphasizes advantages of CE model, the effects of the fluid filling and shell geometries on the natural frequencies of joined composite conical-cylindrical-conical shells containing fluid.

scholarly journals FREE VIBRATION ANALYSIS OF JOINED COMPOSITE CONICAL-CONICAL-CONICAL SHELLS CONTAINING FLUID

2016 ◽  
Vol 54 (5) ◽  
pp. 650 ◽  
Author(s):  
Vu Quoc Hien ◽  
Tran Ich Thinh ◽  
Nguyen Manh Cuong ◽  
Pham Ngoc Thanh
Keyword(s):  
Vibration Analysis ◽  
Natural Frequencies ◽  
Dynamic Stiffness ◽  
Free Vibration Analysis ◽  
The Finite Element Method ◽  
Fluid Interface ◽  
Governing Equations ◽  
Conical Shells ◽  
Bernoulli’S Equation ◽  
Matlab Program

ABSTRACT A new continuous element (CE) formulation has been presented in this paper for the vibration analysis of three joined cross-ply composite conical shells containing fluid. The three joined cross-ply composite conical shells containing fluid can be considered as the general case for joined conical-cylindrical-conical, joined cylindrical-conical-cylindrical, joined cylindrical-conical-conical and joined conical-conical-cylindrical shells containing fluid. Governing equations are obtained using thick shell theory of Midlin, taking into account the shear deflection effects. The velocity potential, Bernoulli’s equation and impermeability condition have been applied to the shell-fluid interface to obtain an explicit expression for fuild pressure. The dynamic stiffness matrix has been built from which natural frequencies have been calculated. The appropriate expressions among stress resultants and deformations are extracted as continuity conditions at the joining section. A matlab program is written using the CE formulation in order to validate our model. Numerical results on natural frequencies are compared to those obtained by the finite element method (FEM) and validated with the available results in other investigations. This paper emphasizes advantages of CE model and the effects of the fluid level, semi-vertex angles and lamination sequences on the natural frequencies of joined composite conical-conical-conical shells.

Uncertain Structural Free Vibration Analysis With Non-Probabilistic Spatially Varying Parameters

2019 ◽  
Vol 5 (2) ◽  
Author(s):  
Jinwen Feng ◽  
Qingya Li ◽  
Alba Sofi ◽  
Guoyin Li ◽  
Di Wu ◽  
...  
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Free Vibration Analysis ◽  
Spatial Dependency ◽  
The Finite Element Method ◽  
Engineering Structures ◽  
Spatially Varying ◽  
Computational Strategy ◽  
Bounded System

The uncertain free vibration analysis of engineering structures with the consideration of nonstochastic spatially dependent uncertain parameters is investigated. A recently proposed concept of interval field is implemented to model the intrinsic spatial dependency of the uncertain-but-bounded system parameters. By employing the appropriate discretization scheme, evaluations of natural frequencies for engineering structures involving interval fields can be executed within the framework of the finite element method. Furthermore, a robust, yet efficient, computational strategy is proposed such that the extreme bounds of natural frequencies of the structure involving interval fields can be rigorously captured by performing two independent eigen-analyses. Within the proposed computational analysis framework, the traditional interval arithmetic is not employed so that the undesirable effect of the interval overestimation can be completely eliminated. Consequently, both sharpness and physical feasibility of the results can be guaranteed to a certain extent for any discretized interval field. The plausibility of the adopted interval field model, as well as the feasibility of the proposed computational scheme, is clearly demonstrated by investigating both academic-sized and practically motivated engineering structures.

Structural Undamped Free Vibration Analysis Based on Coefficient Reduced-Basis Method

2014 ◽  
Vol 556-562 ◽  
pp. 4214-4217
Author(s):  
Yong Hong Li ◽  
Shu Zhan Li
Keyword(s):  
Vibration Analysis ◽  
Natural Frequencies ◽  
Free Vibration Analysis ◽  
Reduced Basis Method ◽  
Mode Shapes ◽  
Design Parameters ◽  
The Finite Element Method ◽  
Reduced Basis ◽  
Linear Elastic ◽  
Basis Method

Using reduced-basis method, design parameters are needed to be separated from the linear elastic operators, which is time-consuming. So, an improved reduced-basis method - coefficient reduced-basis method is introduced to calculate the low order natural frequencies and mode shapes of structure. In this method, the computing process of design parameters separated from the linear elastic operators is simplified. In this paper, a truck frame is taken as an example, frequencies and mode shapes from coefficient reduced-basis method are obtained. Comparing with results from the finite element method, coefficient reduced-basis method can obtain accurate results efficiently.

scholarly journals A Dynamic Stiffness Element for Free Vibration Analysis of Delaminated Layered Beams

2021 ◽  
Author(s):  
Nicholas H. Erdelyi ◽  
Seyed M. Hashemi
Keyword(s):  
Vibration Analysis ◽  
Natural Frequencies ◽  
Dynamic Stiffness ◽  
Closed Form Solution ◽  
Free Vibration Analysis ◽  
Beam Theory ◽  
Flexural Vibration ◽  
Form Solution ◽  
Bending Vibration ◽  
Natural Frequencies And Modes

A dynamic stiffness element for flexural vibration analysis of delaminated multilayer beams is developed and subsequently used to investigate the natural frequencies and modes of two-layer beam configurations. Using the Euler-Bernoulli bending beam theory, the governing differential equations are exploited and representative, frequency-dependent, field variables are chosen based on the closed form solution to these equations. The boundary conditions are then imposed to formulate the dynamic stiffness matrix (DSM), which relates harmonically varying loads to harmonically varying displacements at the beam ends. The bending vibration of an illustrative example problem, characterized by delamination zone of variable length, is investigated. Two computer codes, based on the conventional Finite Element Method (FEM) and the analytical solutions reported in the literature, are also developed and used for comparison. The intact and defective beam natural frequencies and modes obtained from the proposed DSM method are presented along with the FEM and analytical results and those available in the literature.

scholarly journals A Dynamic Stiffness Element for Free Vibration Analysis of Delaminated Layered Beams

2012 ◽  
Vol 2012 ◽  
pp. 1-8 ◽  
Author(s):  
Nicholas H. Erdelyi ◽  
Seyed M. Hashemi
Keyword(s):  
Vibration Analysis ◽  
Natural Frequencies ◽  
Dynamic Stiffness ◽  
Closed Form Solution ◽  
Free Vibration Analysis ◽  
Beam Theory ◽  
Flexural Vibration ◽  
Form Solution ◽  
Bending Vibration ◽  
Natural Frequencies And Modes

A dynamic stiffness element for flexural vibration analysis of delaminated multilayer beams is developed and subsequently used to investigate the natural frequencies and modes of two-layer beam configurations. Using the Euler-Bernoulli bending beam theory, the governing differential equations are exploited and representative, frequency-dependent, field variables are chosen based on the closed form solution to these equations. The boundary conditions are then imposed to formulate the dynamic stiffness matrix (DSM), which relates harmonically varying loads to harmonically varying displacements at the beam ends. The bending vibration of an illustrative example problem, characterized by delamination zone of variable length, is investigated. Two computer codes, based on the conventional Finite Element Method (FEM) and the analytical solutions reported in the literature, are also developed and used for comparison. The intact and defective beam natural frequencies and modes obtained from the proposed DSM method are presented along with the FEM and analytical results and those available in the literature.

scholarly journals A Dynamic Stiffness Element for Free Vibration Analysis of Delaminated Layered Beams

2021 ◽  
Author(s):  
Nicholas H. Erdelyi ◽  
Seyed M. Hashemi
Keyword(s):  
Vibration Analysis ◽  
Natural Frequencies ◽  
Dynamic Stiffness ◽  
Closed Form Solution ◽  
Free Vibration Analysis ◽  
Beam Theory ◽  
Flexural Vibration ◽  
Form Solution ◽  
Bending Vibration ◽  
Natural Frequencies And Modes

A dynamic stiffness element for flexural vibration analysis of delaminated multilayer beams is developed and subsequently used to investigate the natural frequencies and modes of two-layer beam configurations. Using the Euler-Bernoulli bending beam theory, the governing differential equations are exploited and representative, frequency-dependent, field variables are chosen based on the closed form solution to these equations. The boundary conditions are then imposed to formulate the dynamic stiffness matrix (DSM), which relates harmonically varying loads to harmonically varying displacements at the beam ends. The bending vibration of an illustrative example problem, characterized by delamination zone of variable length, is investigated. Two computer codes, based on the conventional Finite Element Method (FEM) and the analytical solutions reported in the literature, are also developed and used for comparison. The intact and defective beam natural frequencies and modes obtained from the proposed DSM method are presented along with the FEM and analytical results and those available in the literature.

scholarly journals The Effect of Axial Force on the Free Vibration of an Euler-Bernoulli Beam Carrying a Number of Various Concentrated Elements

2013 ◽  
Vol 20 (3) ◽  
pp. 357-367 ◽  
Author(s):  
Gürkan Şcedilakar
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Axial Load ◽  
Natural Frequencies ◽  
Free Vibration Analysis ◽  
Mode Shapes ◽  
The Finite Element Method ◽  
Bernoulli Beam ◽  
Euler Beam ◽  
Euler Bernoulli Beam

In this study, free vibration analysis of beams carrying a number of various concentrated elements including point masses, rotary inertias, linear springs, rotational springs and spring-mass systems subjected to the axial load was performed. All analyses were performed using an Euler beam assumption and the Finite Element Method. The beam used in the analyses is accepted as pinned-pinned. The axial load applied to the beam from the free ends is either compressive or tensile. The effects of parameters such as the number of spring-mass systems on the beam, their locations and the axial load on the natural frequencies were investigated. The mode shapes of beams under axial load were also obtained.

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.

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