Multistage Coupling of Eight Mistuned Bladed Disk on a Solid Shaft: Part 1—Free Vibration Analysis

2012 ◽  
Author(s):  
Romuald Rzadkowski ◽  
Artur Maurin
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Free Vibration Analysis ◽  
Free Vibrations ◽  
Rotor Blades ◽  
Mode Shapes ◽  
Bladed Disk ◽  
Centrifugal Stiffening

Considered here was the effect of multistage coupling on the dynamics of a rotor consisting of eight mistuned bladed discs on a solid shaft. Each bladed disc had a different number of rotor blades. Free vibrations were examined using finite element representations of rotating single blades, bladed discs, and the entire rotor. In this study the global rotating mode shapes of eight flexible mistuned bladed discs on shaft assemblies were calculated, taking into account rotational effects such as centrifugal stiffening. The thus obtained natural frequencies of the blade, shaft, bladed disc and entire shaft with discs were carefully examined to discover resonance conditions and coupling effects. This study found that mistuned systems cause far more intensive multistage coupling than tuned ones. The greater the mistuning, the more intense the multistage coupling.

Multistage Coupling of Eight Bladed Discs on a Solid Shaft

2010 ◽  
Author(s):  
Romuald Rza˛dkowski ◽  
Marcin Drewczynski
Keyword(s):  
Finite Element ◽  
Forced Vibration ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Free Vibrations ◽  
Rotor Blades ◽  
Mode Shapes ◽  
Centrifugal Stiffening ◽  
Shaft Deflection ◽  
Forced Vibration Analysis

Considered here is the effect of multistage coupling on the dynamics of a rotor consisting of eight bladed discs on a solid shaft. Each bladed disc had a different number of rotor blades. Free vibrations were examined using finite element representations of rotating single blades, bladed discs, and the entire rotor. In this study, the global rotating mode shapes of flexible tuned bladed discs-shaft assemblies were calculated, taking into account rotational effects, such as centrifugal stiffening. The thus obtained natural frequencies of the blade, the shaft, the bladed disc, and the entire shaft with discs were carefully examined to discover resonance conditions and coupling effects. This study found that the flexible modes of the tuned bladed discs affected by shaft motion were those with zero, one and two nodal diameters. In these modes shaft deflection was clearly visible. In forced vibration analysis a different EO excitation was applied for each stage. The importance of using models with different numbers of blades on each disc is apparent when compared with earlier results concerning discs with identical numbers of blades. Here the model of 8 discs with an equal number of blades on each disc is referred to as (Model 1), and the model of 8 discs with a different number of blades on each disc is referred to as (Model 2).

Free vibration analysis of a rectangular plate carrying multiple various concentrated elements

2003 ◽  
Vol 217 (2) ◽  
pp. 171-183 ◽  
Author(s):  
J-S Wu ◽  
H-M Chou ◽  
D-W Chen
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Boundary Conditions ◽  
Rectangular Plate ◽  
Normal Mode ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Free Vibration Analysis ◽  
Equation Of Motion ◽  
Mode Shapes

The dynamic characteristic of a uniform rectangular plate with four boundary conditions and carrying three kinds of multiple concentrated element (rigidly attached point masses, linear springs and elastically mounted point masses) was investigated. Firstly, the closed-form solutions for the natural frequencies and the corresponding normal mode shapes of a rectangular ‘bare’ (or ‘unconstrained’) plate (without any attachments) with the specified boundary conditions were determined analytically. Next, by using these natural frequencies and normal mode shapes incorporated with the expansion theory, the equation of motion of the ‘constrained’ plate (carrying the three kinds of multiple concentrated element) were derived. Finally, numerical methods were used to solve this equation of motion to give the natural frequencies and mode shapes of the ‘constrained’ plate. To confirm the reliability of previous free vibration analysis results, a finite element analysis was also conducted. It was found that the results obtained from the above-mentioned two approaches were in good agreement. Compared with the conventional finite element method (FEM), the approach employed in this paper has the advantages of saving computing time and achieving better accuracy, as can be seen from the existing literature.

scholarly journals Free Vibrations of a Reddy-Bickford Multi-Span Beam Carrying Multiple Spring-Mass Systems

2011 ◽  
Vol 18 (5) ◽  
pp. 709-726 ◽  
Author(s):  
Yusuf Yesilce
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Free Vibration Analysis ◽  
Beam Theory ◽  
Free Vibrations ◽  
Mode Shapes ◽  
Structural Elements ◽  
Mass System ◽  
Assembly Technique

The structural elements supporting motors or engines are frequently seen in technological applications. The operation of machine may introduce additional dynamic stresses on the beam. It is important, then, to know the natural frequencies of the coupled beam-mass system, in order to obtain a proper design of the structural elements. The literature regarding the free vibration analysis of Bernoulli-Euler and Timoshenko single-span beams carrying a number of spring-mass system and multi-span beams carrying multiple spring-mass systems are plenty, but the free vibration analysis of Reddy-Bickford multi-span beams carrying multiple spring-mass systems has not been investigated by any of the studies in open literature so far. This paper aims at determining the exact solutions for the natural frequencies and mode shapes of Reddy-Bickford beams. The model allows analyzing the influence of the shear effect and spring-mass systems on the dynamic behavior of the beams by using Reddy-Bickford Beam Theory (RBT). The effects of attached spring-mass systems on the free vibration characteristics of the 1–4 span beams are studied. The natural frequencies of Reddy-Bickford single-span and multi-span beams calculated by using the numerical assembly technique and the secant method are compared with the natural frequencies of single-span and multi-span beams calculated by using Timoshenko Beam Theory (TBT); the mode shapes are presented in graphs.

FINITE ELEMENT ANALYSIS OF CONTROLLED LOW STRENGTH MATERIAL PAVEMENT BASES: FREE VIBRATION ANALYSIS

2017 ◽  
Vol 4 (1) ◽  
Author(s):  
Li-Jeng Huang ◽  
Her-Yung Wang ◽  
Wen-Ling Huang ◽  
Ming-Chao Lin
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Free Vibration Analysis ◽  
Crushed Stone ◽  
Mode Shapes ◽  
Strength Material ◽  
Low Strength ◽  
Controlled Low Strength Material

This paper presents free vibration analysis of pavement bases constructed using sustainable material, a controlled low-strength material (CLSM), using finite element (FE) method. The CLSM concrete is introduced as pavement bases for its special features of easy compaction, high workability and relatively low cost. Rut-resistant stone matrix asphalt is placed on top of CLSM as wearing surface layer. The Young's moduli of CLSM are obtained from laboratory tests for two different binder mixtures, marked as CLSM-B80/30% and CLSM-B130/30%. Two-dimensional planar strain assumption is employed in the FE formulation of steady-state elasto-dynamic analysis of four-layered flexible pavements in which four kinds of different base materials are considered: graded crushed stone, CLSM-B80/30%, CLSM-B130/30% and AC. Comparison study on computed natural frequencies and mode shapes of the flexible pavement using different bases materials will be conducted. Results show that CLSM pavement bases depict higher natural frequencies as compared with graded crushed stone bases and can be suitable sustainable materials employed for pavement design and construction in highway engineering.

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.

Forced Vibration of Several Bladed Discs on the Shaft

2006 ◽  
Author(s):  
Romuald Rza¸dkowski ◽  
Marcin Drewczynski
Keyword(s):  
Finite Element ◽  
Forced Vibration ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Free Vibrations ◽  
Mode Shapes ◽  
Coupling Effects ◽  
Centrifugal Stiffening ◽  
Shaft Deflection ◽  
Forced Vibration Analysis

The effect of multistage coupling on the dynamics of a rotor consisting of eight bladed discs on a solid shaft is considered. Free vibrations are examined using finite element representations of rotating single blades, bladed discs, and the complete rotor. In this study, the global rotating mode shapes of flexible tuned bladed discs-shaft assemblies are calculated. Rotational effects, such as centrifugal stiffening are accounted for. The calculated natural frequencies obtained from the blade, the shaft, the bladed disc, and the complete shaft with discs are carefully examined to discover resonance conditions and the coupling effects. It was found that the flexible modes of the tuned bladed discs affected by shaft motion are those with zero, one and two nodal diameters. In these modes the shaft deflection is clearly visible. Different EO excitation is applied for particular stages in forced vibration analysis.

Free Vibration Analysis of an Inflated Toroidal Shell

2002 ◽  
Vol 124 (3) ◽  
pp. 387-396 ◽  
Author(s):  
Akhilesh K. Jha ◽  
Daniel J. Inman ◽  
Raymond H. Plaut
Keyword(s):  
Differential Equations ◽  
Free Vibration ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Circular Cross Section ◽  
Free Vibration Analysis ◽  
Longitudinal Direction ◽  
Variable Coefficients ◽  
Mode Shapes ◽  
Toroidal Shell

Free vibration analysis of a free inflated torus of circular cross-section is presented. The shell theory of Sanders, including the effect of pressure, is used in formulating the governing equations. These partial differential equations are reduced to ordinary differential equations with variable coefficients using complete waves in the form of trigonometric functions in the longitudinal direction. The assumed mode shapes are divided into symmetric and antisymmetric groups, each given by a Fourier series in the meridional coordinate. The solutions (natural frequencies and mode shapes) are obtained using Galerkin’s method and verified with published results. The natural frequencies are also obtained for a circular cylinder with shear diaphragm boundary condition as a special case of the toroidal shell. Finally, the effects of aspect ratio, pressure, and thickness on the natural frequencies of the inflated torus are studied.

scholarly journals Free vibration analysis of a DST-0285 truck crane considering changes in the system load configuration

2018 ◽  
Vol 157 ◽  
pp. 03005
Author(s):  
Tomasz Geisler
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Free Vibration ◽  
Vibration Analysis ◽  
Free Vibration Analysis ◽  
Free Vibrations ◽  
The Finite Element Method ◽  
System Load ◽  
Load Location ◽  
Fundamental Units

A model of a truck crane, consisting of the fundamental units of the crane, is presented in this paper. The finite element method and a COSMOS/M package were applied to perform the modelling. Research into the influence of a change in the crane radius and load location on changes in the chosen free vibrations was carried out using the built models. Diagrams containing changes in the frequency of vibrations for chosen values of the crane radius and the load are presented and conclusions are drawn.

Free Vibration Analysis of Circular FGM Plate Having Variable Thickness Under Axisymmetric Condition by Finite Element Method

2005 ◽  
Author(s):  
M. Nikkhah-Bahrami ◽  
Abazar Shamekhi
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Free Vibration ◽  
Variable Thickness ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Free Vibration Analysis ◽  
Thickness Variation ◽  
Simply Supported ◽  
Element Method

This study presents the free vibration analysis of circular plate having variable thickness made of functionally-graded material. The boundary conditions of the plate is either simply supported or clamped. Dynamic equations were obtained using energy method based on Love-Kichhoff hypothesis and Sander’s non-linear strain-displacement relation for thin plates. The finite element method is used to determine the natural frequencies. The results obtained show good agreement with known analytical data. The effects of thickness variation and Poisson’s ratio are investigated by calculating the natural frequencies. These effects are found not to be the same for simply supported and clamped plates.

Free vibration analysis of a single edge cracked symmetric functionally graded stepped beams

2020 ◽  
Vol 23 (16) ◽  
pp. 3415-3428
Author(s):  
Yusuf Cunedioglu ◽  
Shkelzen Shabani
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Crack Depth ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Mode Shapes ◽  
Single Edge ◽  
Functionally Graded Beam ◽  
Cross Sectional

Free vibration analysis of a single edge cracked multi-layered symmetric sandwich stepped Timoshenko beams, made of functionally graded materials, is studied using finite element method and linear elastic fracture mechanic theory. The cantilever functionally graded beam consists of 50 layers, assumed that the second stage of the beam (step part) is created by machining. Thus, providing the material continuity between the two beam stages. It is assumed that material properties vary continuously, along the thickness direction according to the exponential and power laws. A developed MATLAB code is used to find the natural frequencies of three types of the stepped beam, concluding a good agreement with the known data from the literature, supported also by ANSYS software in data verification. In the study, the effects of the crack location, crack depth, power law gradient index, different material distributions, different stepped length, different cross-sectional geometries on natural frequencies and mode shapes are analysed in detail.

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