scholarly journals Forced Vibration of a Timoshenko Beam Subjected to Stationary and Moving Loads Using the Modal Analysis Method

2017 ◽  
Vol 2017 ◽  
pp. 1-26 ◽  
Author(s):  
Taehyun Kim ◽  
Ilwook Park ◽  
Usik Lee
Keyword(s):  
Modal Analysis ◽  
Timoshenko Beam ◽  
Forced Vibration ◽  
Natural Frequencies ◽  
Dynamic Responses ◽  
Mode Shapes ◽  
Timoshenko Beams ◽  
Moving Loads ◽  
Analysis Method ◽  
Simply Supported

The modal analysis method (MAM) is very useful for obtaining the dynamic responses of a structure in analytical closed forms. In order to use the MAM, accurate information is needed on the natural frequencies, mode shapes, and orthogonality of the mode shapes a priori. A thorough literature survey reveals that the necessary information reported in the existing literature is sometimes very limited or incomplete, even for simple beam models such as Timoshenko beams. Thus, we present complete information on the natural frequencies, three types of mode shapes, and the orthogonality of the mode shapes for simply supported Timoshenko beams. Based on this information, we use the MAM to derive the forced vibration responses of a simply supported Timoshenko beam subjected to arbitrary initial conditions and to stationary or moving loads (a point transverse force and a point bending moment) in analytical closed form. We then conduct numerical studies to investigate the effects of each type of mode shape on the long-term dynamic responses (vibrations), the short-term dynamic responses (waves), and the deformed shapes of an example Timoshenko beam subjected to stationary or moving point loads.

Wave-Induced Vibrations of an Axial-Loaded Immersed Timoshenko Beam Carrying an Eccentric Tip Mass with Rotary Inertia

2010 ◽  
Vol 54 (01) ◽  
pp. 15-33
Author(s):  
Jong-Shyong Wu ◽  
Chin-Tzu Chen
Keyword(s):  
Closed Form ◽  
Timoshenko Beam ◽  
Forced Vibration ◽  
Natural Frequencies ◽  
Closed Form Solution ◽  
Form Solution ◽  
Rotary Inertia ◽  
Mode Shapes ◽  
Mode Superposition Method ◽  
Tip Mass

Under the specified assumptions for the equation of motion, the closed-form solution for the natural frequencies and associated mode shapes of an immersed "Euler-Bernoulli" beam carrying an eccentric tip mass possessing rotary inertia has been reported in the existing literature. However, this is not true for the immersed "Timoshenko" beam, particularly for the case with effect of axial load considered. Furthermore, the information concerning the forced vibration analysis of the foregoing Timoshenko beam caused by wave excitations is also rare. Therefore, the first purpose of this paper is to present a technique to obtain the closed-form solution for the natural frequencies and associated mode shapes of an axial-loaded immersed "Timoshenko" beam carrying eccentric tip mass with rotary inertia by using the continuous-mass model. The second purpose is to determine the forced vibration responses of the latter resulting from excitations of regular waves by using the mode superposition method incorporated with the last closed-form solution for the natural frequencies and associated mode shapes of the beam. Because the determination of normal mode shapes of the axial-loaded immersed "Timoshenko" beam is one of the main tasks for achieving the second purpose and the existing literature concerned is scarce, the details about the derivation of orthogonality conditions are also presented. Good agreements between the results obtained from the presented technique and those obtained from the existing literature or conventional finite element method (FEM) confirm the reliability of the presented theories and the developed computer programs for this paper.

Modal Analysis and Dynamic Responses of a Hysteretically Damped Axle Shaft With a Transverse Crack

2019 ◽  
Author(s):  
C. Shravankumar ◽  
Yash K. Sarda ◽  
V. Thamarai Selvan
Keyword(s):  
Modal Analysis ◽  
Condition Monitoring ◽  
Crack Detection ◽  
Natural Frequencies ◽  
Fatigue Cracks ◽  
Dynamic Responses ◽  
Mode Shapes ◽  
Fast Fourier Transformation ◽  
Transverse Loads ◽  
Eigen Value

Abstract An axle shaft supports rotating elements, and is fitted to the housing by means of bearings. It mostly does not transmit torque, with exceptions such as in train axles. Non-rotating axles are subjected to bending moments due to dynamic transverse loads. Axles such as in automobiles are marked with occasional failures due to fatigue cracks, which can prove serious, if the cracks are not detected early. Vibration based condition monitoring is the field concerned with crack detection based on the dynamic responses of the system. In this light, the present paper discusses the vibration analysis of a cracked axle. The cracked shaft is modelled using finite element method, for transverse vibration conditions. The shaft is modelled based on Euler-Bernoulli theory for bending, while the crack is modelled based on fracture mechanics approach. After modelling, modal analysis of the system is carried out, with the consideration of proportional hysteretic damping. The Eigen value problem provides the natural frequencies and mode shapes. The Frequency Response Functions (FRF’s) magnitude and phase plots are obtained, from which the natural frequencies and structural damping loss factors can be calculated. Further, the free vibration and forced vibration system time responses are obtained, using numerical integration methods. The corresponding responses in frequency domain are obtained using Fast Fourier Transformation (FFT). The FRF’s and dynamic responses of the shaft without and with crack are comparatively studied. The study provides the platform for condition monitoring of shaft cracks.

Experimental and Numerical Investigation of Residual Stress Stiffening Influence on Dynamic Response of Welded Structures

2019 ◽  
Author(s):  
AmirHossein MajidiRad ◽  
Yimesker S. Yihun
Keyword(s):  
Residual Stress ◽  
Finite Element ◽  
Modal Analysis ◽  
Natural Frequencies ◽  
Model Updating ◽  
Experimental Modal Analysis ◽  
Experimental Results ◽  
Welding Residual Stress ◽  
Dynamic Responses ◽  
Mode Shapes

Abstract This paper presents the study of welding residual stress-stiffening effect on the dynamic responses and vibrational parameters of welded aluminum parts through an experimental modal analysis and Center Hole Drilling (CHD) residual stress measurement methods. Having a great corrosion resistance, AA5056 was utilized in this research that has been used in aircraft and ship structures; making the welding assesment of crucial. Natural frequencies and damping factors of several specimens are compared before and after the welding along with verification of experimental modal analysis integrity using Euler-Bernoulli relations. Finite element modeling of welding, cutting and modal/stress analysis of samples are also done to compare the experimental results. The results obtained from the precise modal analysis of all samples show that welding made the structure harder leading to 2% increase in natural frequencies and changing damping factors of different mode shapes. Cutting also reduced the level of residual stresses up to 34%. A good agreement is shown between the modal analysis and the experimental results. The technique used in the experiment and finite element simulation along with modeling assumptions are beneficial to other applications where model updating is required or a prediction of residual stress stiffening influence on modal responses is important.

Assessment of Serviceability of the Footbridge Across Opatovska Street

2016 ◽  
Vol 827 ◽  
pp. 263-266
Author(s):  
Vladimír Sana
Keyword(s):  
Theoretical Analysis ◽  
Modal Analysis ◽  
Forced Vibration ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Three Dimensional ◽  
Mode Shapes ◽  
Fe Model ◽  
Matlab Code ◽  
Forced Vibration Analysis

This paper is focused on the assessment of serviceability of the footbridge structure, which has been excited by pedestrians and vandals. The three dimensional FE model of the footbridge structure was created for the necessities of theoretical modal analysis. Computed mode shapes and natural frequencies were subsequently used for the forced vibration analysis as an input files into MATLAB code. Results obtained by the theoretical analysis were compared with the experimental results. At the end of this paper, the comfort criterion of crossing pedestrians has been evaluated.

Modal Analysis of Aeroengine Turbine Blade-Disc System

2012 ◽  
Vol 487 ◽  
pp. 889-893
Author(s):  
Wei Qiang Zhao ◽  
Yong Xian Liu ◽  
Mo Wu Lu ◽  
Qing Jun Guo
Keyword(s):  
Optimal Design ◽  
Modal Analysis ◽  
Turbine Blade ◽  
Natural Frequencies ◽  
Dynamical Analysis ◽  
Mode Shapes ◽  
Analysis Method ◽  
Safety Verification ◽  
Aero Engine ◽  
Free Status

This paper introduces the FEA method for modal analysis of aero-engine turbine blade-disc system. Natural modal analysis for dynamical analysis and the result can be used as criterion of many dynamics characteristics and further analysis. In this paper, the natural modal of an aero-engine turbine blade-disc system with the turbine joint hole fully constrained and in free status is calculated respectively. And the first ten natural frequencies and mode shapes are obtained. Also, vibration characteristics of each natural modal and the corresponding influence on turbine blade-disc system and other structure are discussed. The analysis method and results in this paper can be used for further study on optimal design and vibration safety verification for the blade-disc system.

Dynamic Response of the Spectral Element Model by Using the FFT

2007 ◽  
Vol 345-346 ◽  
pp. 845-848
Author(s):  
Joo Yong Cho ◽  
Han Suk Go ◽  
Usik Lee
Keyword(s):  
Fourier Transforms ◽  
Initial Conditions ◽  
Element Model ◽  
Spectral Element ◽  
Dynamic Responses ◽  
Analysis Method ◽  
Euler Beam ◽  
Exact Analytical Solutions ◽  
Simply Supported ◽  
Spectral Analysis Method

In this paper, a fast Fourier transforms (FFT)-based spectral analysis method (SAM) is proposed for the dynamic analysis of spectral element models subjected to the non-zero initial conditions. To evaluate the proposed SAM, the spectral element model for the simply supported Bernoulli-Euler beam is considered as an example problem. The accuracy of the proposed SAM is evaluated by comparing the dynamic responses obtained by SAM with the exact analytical solutions.

scholarly journals Modal Perturbation Method for the Dynamic Characteristics of Timoshenko Beams

2005 ◽  
Vol 12 (6) ◽  
pp. 425-434 ◽  
Author(s):  
Menglin Lou ◽  
Qiuhua Duan ◽  
Genda Chen
Keyword(s):  
Perturbation Method ◽  
Dynamic Characteristics ◽  
Timoshenko Beam ◽  
Natural Frequencies ◽  
Solution Process ◽  
Equation Of Motion ◽  
Timoshenko Beams ◽  
Algebraic Equations ◽  
Nonlinear Algebraic Equations ◽  
Shear Distortion

Timoshenko beams have been widely used in structural and mechanical systems. Under dynamic loading, the analytical solution of a Timoshenko beam is often difficult to obtain due to the complexity involved in the equation of motion. In this paper, a modal perturbation method is introduced to approximately determine the dynamic characteristics of a Timoshenko beam. In this approach, the differential equation of motion describing the dynamic behavior of the Timoshenko beam can be transformed into a set of nonlinear algebraic equations. Therefore, the solution process can be simplified significantly for the Timoshenko beam with arbitrary boundaries. Several examples are given to illustrate the application of the proposed method. Numerical results have shown that the modal perturbation method is effective in determining the modal characteristics of Timoshenko beams with high accuracy. The effects of shear distortion and moment of inertia on the natural frequencies of Timoshenko beams are discussed in detail.

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.

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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