scholarly journals Comparison of the Natural Vibration Frequencies of Timoshenko and Bernoulli Periodic Beams

Materials ◽  
2021 ◽  
Vol 14 (24) ◽  
pp. 7628
Author(s):  
Łukasz Domagalski
Keyword(s):  
Natural Frequencies ◽  
Classical Method ◽  
Mode Shapes ◽  
Periodicity Cell ◽  
The Finite Element Method ◽  
Frequency Spectra ◽  
Constant Weight ◽  
Method Of Solution ◽  
Averaged Models ◽  
Beam Theories

This paper deals with the linear natural vibrations analysis of beams where the geometric and material properties vary periodically along the beam axis. In contrast with homogeneous prismatic beams, the frequency spectra of such beams are irregular as there exist enlarged intervals between some adjacent frequencies. Presented here are two averaged models of beams based on the tolerance modelling approach. The assumptions of classical Euler–Bernoulli and Timoshenko–Ehrenfest beam theories are adopted as the foundations. The resulting mathematical models are systems of differential equations with constant, weight-averaged coefficients. This makes it possible to apply any classical method of solution suitable for homogeneous beams, such as Galerkin orthogonalization. Here, emphasis is placed on the comparison of natural frequencies neighbouring the frequency band-gaps that are obtained from these two theories. Two basic cases of material and geometric property distribution in a periodicity cell are studied, and the natural frequencies and mode shapes are obtained for a simply supported beam. The results are supported by a comparison with the finite element method and partially exact solutions.

scholarly journals Modal analysis of an iced offshore composite wind turbine blade

2021 ◽  
pp. 0309524X2110116
Author(s):  
Oumnia Lagdani ◽  
Mostapha Tarfaoui ◽  
Mourad Nachtane ◽  
Mourad Trihi ◽  
Houda Laaouidi
Keyword(s):  
Wind Turbine ◽  
Modal Analysis ◽  
Turbine Blade ◽  
Natural Frequencies ◽  
Wind Turbine Blade ◽  
Resonance Phenomenon ◽  
Mode Shapes ◽  
The Finite Element Method ◽  
Numerical Work ◽  
Composite Blades

In the far north, low temperatures and atmospheric icing are a major danger for the safe operation of wind turbines. It can cause several problems in fatigue loads, the balance of the rotor and aerodynamics. With the aim of improving the rigidity of the wind turbine blade, composite materials are currently being used. A numerical work aims to evaluate the effect of ice on composite blades and to determine the most adequate material under icing conditions. Different ice thicknesses are considered in the lower part of the blade. In this paper, modal analysis is performed to obtain the natural frequencies and corresponding mode shapes of the structure. This analysis is elaborated using the finite element method (FEM) computer program through ABAQUS software. The results have laid that the natural frequencies of the blade varied according to the material and thickness of ice and that there is no resonance phenomenon.

Effect of Delamination on Natural Frequencies of E-glass and S-glass Epoxy Composite Plates

2021 ◽  
Author(s):  
P. K. Karsh ◽  
Bindi Thakkar ◽  
R. R. Kumar ◽  
Abhijeet Kumar ◽  
Sudip Dey
Keyword(s):  
Natural Frequencies ◽  
Epoxy Composite ◽  
Orientation Angle ◽  
Laminated Composite ◽  
Composite Plates ◽  
Mode Shapes ◽  
Transverse Shear Deformation ◽  
The Finite Element Method ◽  
Modes Of Failure ◽  
Ply Orientation

The delamination is one of the major modes of failure occurring in the laminated composite due to insufficient bonding between the layers. In this paper, the natural frequencies of delaminated S-glass and E-glass epoxy cantilever composite plates are presented by employing the finite element method (FEM) approach. The rotary inertia and transverse shear deformation are considered in the present study. The effect of parameters such as the location of delamination along the length, across the thickness, the percentage of delamination, and ply-orientation angle on first three natural frequencies of the cantilever plates are presented for S-glass and E-glass epoxy composites. The standard eigenvalue problem is solved to obtain the natural frequencies and corresponding mode shapes. First three mode shape of S-Glass and E-Glass epoxy laminated composites are portrayed corresponding to different ply angle of lamina.

A Vibrational Mode Analysis of Free Finite-Length Thick Cylinders Using the Finite Element Method

1998 ◽  
Vol 120 (2) ◽  
pp. 371-377 ◽  
Author(s):  
Huan Wang ◽  
Keith Williams ◽  
Wei Guan
Keyword(s):  
Finite Length ◽  
Natural Frequencies ◽  
Three Dimensional ◽  
Mode Analysis ◽  
Mode Shapes ◽  
Vibrational Modes ◽  
The Finite Element Method ◽  
Cylinder Length ◽  
Radial Thickness ◽  
Thick Cylinder

Based on their three-dimensional mode shapes, the vibrational modes of free finite length thick cylinders can be classified into 6 categories, consisting of pure radial, radial motion with radial shearing, extensional, circumferential, axial bending, and global modes. This classification, together with the numbers of both the circumferential and the longitudinal nodes, is sufficient to identify each mode of a finite length thick cylinder. The mode classification was verified experimentally by measurements on a thick cylinder. According to the displacement distribution ratio in the radial, tangential and longitudinal directions, the effect of varying cylinder length on the vibrational modes is such that all the modes can be broadly categorized as either pure radial modes, or non pure radial modes. The natural frequencies and mode shapes of the former are dependent upon only the radial dimensions of the models, while the natural frequencies and mode shapes of the latter are dependent upon both the axial length and radial thickness.

Dynamic Modeling of a Ball-Screw Drive and Identification of Its Installation Parameters

2020 ◽  
Vol 143 (4) ◽  
Author(s):  
Yu-Jia Hu ◽  
Yaoyu Wang ◽  
Weidong Zhu ◽  
Haolin Li
Keyword(s):  
Dynamic Model ◽  
Natural Frequencies ◽  
Data Fitting ◽  
Ball Screw ◽  
Mode Shapes ◽  
The Finite Element Method ◽  
Screw Drive ◽  
Log Normal ◽  
Ball Screw Drive ◽  
Log Normal Distribution

Abstract Parametric expressions of equivalent stiffnesses of a ball-screw shaft are obtained by derivation of its geometric parameters, the finite element method (FEM), and data fitting based on a modified probability density function of log-normal distribution. A dynamic model of a ball-screw drive that considers effects of bearing stiffnesses, the mass of the nut, and the axial pretension is established based on equivalent stiffnesses of its shaft. With the dynamic model and modal experimental results obtained by Bayesian operational modal analysis (BOMA), installation parameters of the ball-screw drive are identified by a genetic algorithm (GA) with a new comprehensive objective function that considers natural frequencies, mode shapes, and flexibility of the ball-screw drive. The effectiveness of the methodology is experimentally validated.

scholarly journals A Study on the Effect of Carbon Nanotubes’ Distribution and Agglomeration in the Free Vibration of Nanocomposite Plates

2020 ◽  
Vol 6 (4) ◽  
pp. 79
Author(s):  
D. S. Craveiro ◽  
M. A. R. Loja
Keyword(s):  
Carbon Nanotubes ◽  
Elastic Properties ◽  
Natural Frequencies ◽  
Mechanical Performance ◽  
Negative Impact ◽  
Free Vibrations ◽  
Mode Shapes ◽  
The Finite Element Method ◽  
Agglomeration Effect ◽  
Performance Predictions

The present work aimed to characterize the free vibrations’ behaviour of nanocomposite plates obtained by incorporating graded distributions of carbon nanotubes (CNTs) in a polymeric matrix, considering the carbon nanotubes’ agglomeration effect. This effect is known to degrade material properties, therefore being important to predict the consequences it may bring to structures’ mechanical performance. To this purpose, the elastic properties’ estimation is performed according to the two-parameter agglomeration model based on the Eshelby–Mori–Tanaka approach for randomly dispersed nano-inclusions. This approach is implemented in association with the finite element method to determine the natural frequencies and corresponding mode shapes. Three main agglomeration cases were considered, namely, agglomeration absence, complete agglomeration, and partial agglomeration. The results show that the agglomeration effect has a negative impact on the natural frequencies of the plates, regardless the CNTs’ distribution considered. For the corresponding vibrations’ mode shapes, the agglomeration effect was shown in most cases not to have a significant impact, except for two of the cases studied: for a square plate and a rectangular plate with symmetrical and unsymmetrical CNTs’ distribution, respectively. Globally, the results confirm that not accounting for the nanotubes’ agglomeration effect may lead to less accurate elastic properties and less structures’ performance predictions.

scholarly journals Dynamic Characteristics of an Elastic Structure with Thermal Effects

2020 ◽  
Vol 25 (2) ◽  
pp. 200-208
Author(s):  
Guanhua Xu ◽  
Jianzhong Fu ◽  
Wen He ◽  
Yuetong Xu ◽  
Zhiwei Lin ◽  
...  
Keyword(s):  
Modal Analysis ◽  
Dynamic Characteristics ◽  
Thermal Effects ◽  
Natural Frequencies ◽  
Elastic Structure ◽  
Mode Shapes ◽  
The Finite Element Method ◽  
Environmental Testing ◽  
Temperature Changes ◽  
Property Changes

The vibration table in a combination environmental testing device suffers from temperature changes, which cause the dynamic characteristics of the vibration structure to vary. The mechanism of the thermal effect on the dynamic characteristics of an elastic structure is presented, and a modal analysis with thermal effects based on the finite-element method (FEM) is carried out. The results show that the natural frequencies for each order decrease as the temperature increases, while the mode shapes of the vibrator do not change with temperature. Although thermal stress may affect natural frequencies due to the additional initial stress element stiffness, this stress can be neglected in the modal analysis because it is negligible relative to the effect of the material property changes with temperature.

scholarly journals Modal Analysis of Orthotropic Thin Rectangular Plate Based on Analytical and Finite Element Approaches

2020 ◽  
Vol 30 (5-6) ◽  
pp. 217-225
Author(s):  
Samir Deghboudj ◽  
Wafia Boukhedena ◽  
Hamid Satha
Keyword(s):  
Finite Element ◽  
Modal Analysis ◽  
Rectangular Plate ◽  
Analytical Approach ◽  
Natural Frequencies ◽  
Mode Shapes ◽  
Geometrical Parameters ◽  
The Finite Element Method ◽  
Thin Rectangular Plate ◽  
Good Agreement

The present work aims to carry out modal analysis of orthotropic thin rectangular plate to determine its natural frequencies and mode shapes by using analytical method based on Rayleigh-Ritz energy approach. To demonstrate the accuracy of this approach, the same plate is discritisated and analyzed using the finite element method. The natural and angular frequencies were computed and determined analytically and numerically by using ABAQUS finite element code. The convergency and accuracy of the numerical solution was examined. The effects of geometrical parameters and boundary conditions on vibrations are investigated. The results obtained showed a very good agreement between the analytical approach and the numerical simulations. Also, the paper presents simulations results of testing of the plate with passive vibration control.

Free Vibration of a Spinning Stepped Timoshenko Beam

2000 ◽  
Vol 67 (4) ◽  
pp. 839-841 ◽  
Author(s):  
S. D. Yu ◽  
W. L. Cleghorn
Keyword(s):  
Free Vibration ◽  
Timoshenko Beam ◽  
Natural Frequencies ◽  
Equation Of Motion ◽  
Mode Shapes ◽  
The Finite Element Method ◽  
Linear Transformations ◽  
Stepped Beam ◽  
Uniform Cross Section ◽  
Vibration Problems

The finite element method is employed in this paper to investigate free-vibration problems of a spinning stepped Timoshenko beam consisting of a series of uniform segments. Each uniform segment is considered a substructure which may be modeled using beam finite elements of uniform cross section. Assembly of global equation of motion of the entire beam is achieved using Lagrange’s multiplier method. The natural frequencies and mode shapes are subsequently reduced with the help of linear transformations to a standard eigenvalue problem for which a set of natural frequencies and mode shapes may be easily obtained. Numerical results for an overhung stepped beam consisting of three uniform segments are obtained and presented as an illustrative example. [S00021-8936(01)00101-5]

scholarly journals Transverse Vibration of Stiffened Plates with Cutouts Subjected to In-Plane Uniform Edge Loading at the Plate Boundary

2004 ◽  
Vol 11 (1) ◽  
pp. 9-19 ◽  
Author(s):  
A.K.L. Srivastava ◽  
P.K. Datta ◽  
A.H. Sheikh
Keyword(s):  
Natural Frequencies ◽  
Plate Boundary ◽  
Mode Shapes ◽  
Stiffened Plates ◽  
Plate Boundaries ◽  
The Finite Element Method ◽  
Edge Loading ◽  
Plate Width ◽  
Clamped Edge ◽  
Good Agreement

Vibration characteristics of stiffened plates with cutouts subjected to uni-axial in-plane uniform edge loading at the plate boundaries are investigated using the finite element method. The characteristic equations for the natural frequencies, buckling loads and their corresponding mode shapes are obtained from the equation of motion. The vibration frequencies and buckling load parameters for various modes of stiffened plates with cutouts have been determined for simply supported and clamped edge boundary conditions. In the structure modelling, the plate and the stiffeners are treated as separate elements where the compatibility between these two types of elements is maintained. Numerical results are presented for a range of hole to plate width ratios of 0 to 0.8. The correlations of the natural frequencies and buckling parameters obtained by the present approach with those available in the literature are found to show good agreement.

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.

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