scholarly journals Finite Element Modeling of the Dynamic Properties of Composite Steel–Polymer Concrete Beams

Materials ◽  
2020 ◽  
Vol 13 (7) ◽  
pp. 1630
Author(s):  
Paweł Dunaj ◽  
Stefan Berczyński ◽  
Marcin Chodźko ◽  
Beata Niesterowicz
Keyword(s):  
Finite Element ◽  
Frequency Response ◽  
Natural Frequencies ◽  
Concrete Beams ◽  
Dynamic Properties ◽  
Mode Shapes ◽  
Polymer Concrete ◽  
Response Functions ◽  
Full Agreement ◽  
High Agreement

This paper presents a method for modeling the dynamic properties of steel–polymer concrete beams, the basic structural components of machine tools, assembly lines, vibratory machines, and other structures subjected to time-varying loads during operation. The presented method of modeling steel–polymer concrete beams was developed using the finite element method. Three models of beams differing in cross-sectional dimensions showed high agreement with experimental data: relative error in the case of natural frequencies did not exceed 5% (2.2% on average), the models were characterized by the full agreement of mode shapes and high agreement of frequency response functions with the results of experimental tests. Additionally, the developed beam models supported the reliable description of complex structures, as demonstrated on a spatial frame, obtaining a relative error for natural frequencies of less than 3% (on average 1.7%). Full agreement with the mode shapes and high agreement with the frequency response functions were achieved in the analyzed frequency range.

scholarly journals Rigid Finite Element Method in Modeling Composite Steel-Polymer Concrete Machine Tool Frames

Materials ◽  
2020 ◽  
Vol 13 (14) ◽  
pp. 3151 ◽  
Author(s):  
Paweł Dunaj ◽  
Krzysztof Marchelek ◽  
Stefan Berczyński ◽  
Berkay Mizrak
Keyword(s):  
Finite Element ◽  
Machine Tool ◽  
Experimental Verification ◽  
Natural Frequencies ◽  
Dynamic Properties ◽  
High Accuracy ◽  
Mode Shapes ◽  
Polymer Concrete ◽  
Beam Model ◽  
Low Dimensional

At the stage of designing a special machine tool, it is necessary to analyze many variants of structural solutions of frames and load-bearing systems and to choose the best solution in terms of dynamic properties, in particular considering its resistance to chatter. For this reason, it is preferred to adopt a low-dimensional calculation model, which allows the user to reduce the necessary calculation time while maintaining a high accuracy. The paper presents the methodology of modeling the natural frequencies, mode shapes, and receptance functions of machine tool steel welded frames filled with strongly heterogenous polymer concrete, using low-dimensional models developed by the rigid finite elements method (RigFEM). In the presented study, a RigFEM model of a simple steel beam filled with polymer concrete and a frame composed of such beams were built. Then, the dynamic properties obtained on the basis of the developed RigFEM models were compared with the experimental results and the 1D and 3D finite element models (FEM) in terms of accuracy and dimensionality. As a result of the experimental verification, the full structural compliance of the RigFEM models (for beam and frame) was obtained, which was manifested by the agreement of the mode shapes. Additionally, experimental verification showed a high accuracy of the RigFEM models, obtaining for the beam model a relative error for natural frequencies of less than 4% and on average 2.2%, and for the frame model at a level not exceeding 11% and on average 5.5%. Comparing the RigFEM and FEM models, it was found that the RigFEM models have a slightly worse accuracy, with a dimensionality significantly reduced by 95% for the beam and 99.8% for the frame.

Detection of Damage Extension in Cantilever Beams Using Change Ratio of Frequency Response Functions

2011 ◽  
Vol 50-51 ◽  
pp. 875-879
Author(s):  
Hai Lei Jia ◽  
Yin Zhao
Keyword(s):  
Frequency Response ◽  
Natural Frequencies ◽  
Dynamic Properties ◽  
Damage Index ◽  
High Sensitivity ◽  
Cantilever Beams ◽  
Response Functions ◽  
Full Spectrum ◽  
Structural Dynamic ◽  
Low Dimensional

Frequency response function (FRF) is a fundamental dynamic index, which is capable of reflecting structural dynamic properties using full-spectrum information. In spite of distinct merits over conventional modal parameters, the FRF has an observable drawback of multi-dimensionality, unsuited for damage characterization. Such a situation motivates an interesting subject, i.e., extracting low-dimensional, high-sensitivity damage index from the FRF. This study focuses on developing a valid damage index, called FRF change ratio, to detect extension of damage. An experiment towards cantilever beams is systemically conducted. The results show that the FRF change ratio can effectively reflects damage extension, and it is more sensitive than conventional natural frequencies. This new damage index holds promise for practical damage detection in beam-like structures.

scholarly journals On Solving One-Dimensional Partial Differential Equations With Spatially Dependent Variables Using the Wavelet-Galerkin Method

2013 ◽  
Vol 80 (6) ◽  
Author(s):  
Simon Jones ◽  
Mathias Legrand
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Galerkin Method ◽  
Frequency Response ◽  
Natural Frequencies ◽  
Basis Functions ◽  
Mode Shapes ◽  
Response Functions ◽  
Partial Differential ◽  
Frequency Response Functions

The discrete orthogonal wavelet-Galerkin method is illustrated as an effective method for solving partial differential equations (PDE's) with spatially varying parameters on a bounded interval. Daubechies scaling functions provide a concise but adaptable set of basis functions and allow for implementation of varied loading and boundary conditions. These basis functions can also effectively describe C0 continuous parameter spatial dependence on bounded domains. Doing so allows the PDE to be discretized as a set of linear equations composed of known inner products which can be stored for efficient parametric analyses. Solution schemes for both free and forced PDE's are developed; natural frequencies, mode shapes, and frequency response functions for an Euler–Bernoulli beam with piecewise varying thickness are calculated. The wavelet-Galerkin approach is shown to converge to the first four natural frequencies at a rate greater than that of the linear finite element approach; mode shapes and frequency response functions converge similarly.

Dynamic Characteristics Analysis and Topology Optimization of Column Based on Finite Element Method

2013 ◽  
Vol 721 ◽  
pp. 541-544
Author(s):  
Jing Chen ◽  
Ze Long Yang ◽  
Xian Xuan Li
Keyword(s):  
Finite Element ◽  
Topology Optimization ◽  
Frequency Response ◽  
Dynamic Characteristics ◽  
Natural Frequencies ◽  
Mode Shapes ◽  
Response Analysis ◽  
Response Curves ◽  
Element Analysis ◽  
Column Structure

Aiming to improve the dynamic and static characteristics of a type of machining center column, the finite element modal analysis and harmonic response analysis of the column are performed, and this paper analyzes the dynamic characteristics of the column based on the first five mode shapes and natural frequencies of the column and the displacement - frequency response curves of the column. Topology optimization analysis of the column is performed with ANSYS, and the finite element analysis is performed on the column again after the column structure is improved based on the optimal distribution of material of the column structure and the design experience of column. The result shows that the first five natural frequencies of the column increase, the peak of the displacement - frequency response of the column decrease, and the dynamic characteristics are improved significantly.

Finite Element Analysis on Modal Parameters of Anisotropic Laminated Plates

1988 ◽  
Vol 110 (4) ◽  
pp. 473-477 ◽  
Author(s):  
C. Z. Xiao ◽  
D. X. Lin ◽  
F. Ju
Keyword(s):  
Finite Element ◽  
Shear Deformation ◽  
Transverse Shear ◽  
Natural Frequencies ◽  
Dynamic Properties ◽  
Shear Deformation Theory ◽  
Laminated Plates ◽  
Mode Shapes ◽  
Transverse Shear Deformation ◽  
Element Technique

This paper is concerned with the finite element technique for predicting the dynamic properties of anisotropic fiber-reinforced composite laminated plates. Considering the effect of transverse shear deformation, a higher order shear deformation theory which satisifes the zero shear stress conditions at the upper and bottom surfaces is assumed. The natural frequencies and mode shapes of a rectangular plate with all free edges are obtained by finite element method and the modal damping values by finite damped element technique. An equivalent stiffness method is introduced to reduce computation time. Four different theoretical predictions of natural frequencies and damped values of a laminated plate are compared with experimental results. Discussions on the effect of transverse shear deformation to the dynamic properties of composite plates are given.

scholarly journals Research on the dynamics of railway car construction

2019 ◽  
Vol 20 (1-2) ◽  
pp. 142-146
Author(s):  
Jarosław Bednarz
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Structural Model ◽  
Natural Frequencies ◽  
Dynamic Properties ◽  
Structural Models ◽  
Transformation Model ◽  
Mode Shapes ◽  
The Finite Element Method ◽  
Modal Model

Nowadays, one of the basic criteria of the design of mechanical structures are dynamic properties of the object. They have a significant effect on the vibration, emitted noise, fatigue strength, controllability and stability of the structure. The structural models are most often use to describe the dynamics of the structures. These models are built in accordance with the principles of the finite element method . Structural model can be used to determine the modal model which is a collection of natural frequencies and corresponding mode shapes by an appropriate coordinate transformation model. The construction pro-cess is called the modal analysis . The article presented a method of conducting the experimental modal studies of railway car. The aim of the study was to identify the dynamic properties including the frequency and mode shapes of the object..

scholarly journals Using Pade´ Approximants and Curve-fitting to Approximate Eigenvalues and Eigenvectors for Large Design Changes

1996 ◽  
Vol 118 (1) ◽  
pp. 151-153 ◽  
Author(s):  
J. M. Vance ◽  
J. E. Bernard
Keyword(s):  
Finite Element ◽  
Natural Frequencies ◽  
Solution Process ◽  
Mode Shapes ◽  
Eigenvalues And Eigenvectors ◽  
Computational Burden ◽  
Design Change ◽  
Design Changes ◽  
Develop Software ◽  
Unique Method

Our overall goal is to develop software that facilitates the interactive participation of the designer in the optimization process. We are focusing this research on problems which use finite element solutions as part of the objective function. One challenge to implementing interactive participation in these types of problems is the high computational burden of computing a finite element solution for each design change. The research presented here focuses on a unique method to develop fast approximations for natural frequencies and mode shapes which can be used to avoid the time-consuming re-solution process and which will facilitate interactive design for systems with even large design changes.

Flexural Vibration of Prestressed Concrete Bridges with Corrugated Steel Webs

2017 ◽  
Vol 17 (02) ◽  
pp. 1750023 ◽  
Author(s):  
Xia-Chun Chen ◽  
Zhen-Hu Li ◽  
Francis T. K. Au ◽  
Rui-Juan Jiang
Keyword(s):  
Finite Element ◽  
Shear Deformation ◽  
Prestressed Concrete ◽  
Natural Frequencies ◽  
Sandwich Beam ◽  
Flexural Vibration ◽  
Concrete Bridges ◽  
Mode Shapes ◽  
Beam Model ◽  
Prestressed Concrete Bridges

Prestressed concrete bridges with corrugated steel webs have emerged as a new form of steel-concrete composite bridges with remarkable advantages compared with the traditional ones. However, the assumption that plane sections remain plane may no longer be valid for such bridges due to the different behavior of the constituents. The sandwich beam theory is extended to predict the flexural vibration behavior of this type of bridges considering the presence of diaphragms, external prestressing tendons and interaction between the web shear deformation and flange local bending. To this end, a [Formula: see text] beam finite element is formulated. The proposed theory and finite element model are verified both numerically and experimentally. A comparison between the analyses based on the sandwich beam model and on the classical Euler–Bernoulli and Timoshenko models reveals the following findings. First of all, the extended sandwich beam model is applicable to the flexural vibration analysis of the bridges considered. By letting [Formula: see text] denote the square root of the ratio of equivalent shear rigidity to the flange local flexural rigidity, and L the span length, the combined parameter [Formula: see text] appears to be more suitable for considering the diaphragm effect and the interaction between the shear deformation and flange local bending. The diaphragms have significant effect on the flexural natural frequencies and mode shapes only when the [Formula: see text] value of the bridge falls below a certain limit. For a bridge with an [Formula: see text] value over a certain limit, the flexural natural frequencies and mode shapes obtained from the sandwich beam model and the classical Euler–Bernoulli and Timoshenko models tend to be the same. In such cases, either of the classical beam theories may be used.

Experimental Study for Extraction of Normal Modes

1995 ◽  
Author(s):  
S. Y. Chen ◽  
M. S. Ju ◽  
Y. G. Tsuei
Keyword(s):  
Frequency Response ◽  
Normal Mode ◽  
Normal Modes ◽  
Measurement Data ◽  
Mode Shapes ◽  
Complex Frequency ◽  
Response Functions ◽  
Frequency Response Functions ◽  
Incomplete System ◽  
Coupled Structures

Abstract A frequency-domain technique to extract the normal mode from the measurement data for highly coupled structures is developed. The relation between the complex frequency response functions and the normal frequency response functions is derived. An algorithm is developed to calculate the normal modes from the complex frequency response functions. In this algorithm, only the magnitude and phase data at the undamped natural frequencies are utilized to extract the normal mode shapes. In addition, the developed technique is independent of the damping types. It is only dependent on the model of analysis. Two experimental examples are employed to illustrate the applicability of the technique. The effects due to different measurement locations are addressed. The results indicate that this technique can successfully extract the normal modes from the noisy frequency response functions of a highly coupled incomplete system.

scholarly journals Dynamics Characteristics of Blast Furnace Shell

2011 ◽  
Vol 2-3 ◽  
pp. 1018-1020
Author(s):  
De Chen Zhang ◽  
Yan Ping Sun
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Blast Furnace ◽  
Modal Analysis ◽  
Natural Frequencies ◽  
Theoretical Foundation ◽  
Structural Mechanics ◽  
Mode Shapes ◽  
The Future ◽  
Element Method

Finite element method and structural mechanics method are used to study the blast furnace shell modal analysis and the natural frequencies and mode shapes have been calculated. The two methods were compared and validated , and the results provide a theoretical foundation for the anti-vibration capabilities design of blast furnace shell in the future .

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