scholarly journals Dynamic Behavior of Externally Prestressed Continuous Beam considering Second-Order Effect

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
De-Ping Fang
Keyword(s):  
Analytical Solution ◽  
Dynamic Behavior ◽  
Energy Method ◽  
Natural Frequencies ◽  
Order Effect ◽  
Second Order ◽  
Influence Coefficient ◽  
Continuous Beam ◽  
Order Deformation ◽  
Zero Effect

Considering precisely the second-order deformation of external tendon, the analytical solution of natural frequencies of 2-span externally prestressed continuous beam was obtained by the energy method. The effect of external prestress compression softening is between the zero effect of unbonded prestress compression and the effect of axial outside compression and is determined by the influence coefficient ranging within 0∼1. The influence coefficient is mainly related to the number of deviators and slightly related to tendon layout. Without deviator, the influence coefficient is 1, and the effect of external prestress compression softening is the same as the effect of axial outside compression. As the number of deviators increases, the influence coefficient gradually decreases from 1 to near 0, and the effect of external prestress compression softening is close to zero effect of unbonded prestress compression. With one or more deviators, the effect of external prestress compression softening is negligible. As the eccentricity and area of tendon increase, only the first symmetric frequency increases obviously, and other frequencies almost remain unchanged. The influence of tendon layout linear transformation on the frequency is negligible.

Vibration of Spring-Supported Massless Beams with Discrete Masses

2010 ◽  
Vol 38 (2) ◽  
pp. 117-131
Author(s):  
Kui Fu Chen ◽  
Lin Nan Zhang ◽  
Zhe Zhou
Keyword(s):  
Energy Method ◽  
Arbitrary Number ◽  
Natural Frequencies ◽  
Degree Of Freedom ◽  
Influence Coefficient ◽  
Vibration Equation ◽  
Engineering Vibration ◽  
Mass Spring

Versatile examples are essential on any engineering vibration course. However, most examples in current textbooks, especially those of multi-degree-of-freedom systems, are based on mass–spring systems. The system of spring-supported beams is explored in this report with the purpose of developing enriching examples. Firstly, the method using the stiffness influence coefficient is illustrated in order to establish a vibration equation for a beam with three discrete masses. This is followed by methods using the flexibility influence coefficient. Then we analyze a general case, with an arbitrary number of springs and masses, using the energy method. Finally, a reduced case with repeated natural frequencies is explored.

An Influence Analysis of Second-Order Effect to the Vibration Control of Piezoelectric Beam by the Spline Finite Point Method

2012 ◽  
Vol 166-169 ◽  
pp. 3124-3130 ◽  
Author(s):  
Shuang Bei Li ◽  
Lin Jie Jiang ◽  
Chun Xia Gu ◽  
Rong Qin
Keyword(s):  
Control Theory ◽  
Vibration Control ◽  
Axial Force ◽  
Natural Frequencies ◽  
Order Effect ◽  
Second Order ◽  
Modal Control ◽  
Finite Point ◽  
Axial Forces ◽  
Piezoelectric Beam

The field functions of the spline finite point (SFP) method were constructed by the linear combination of B-spline basis function, and the higher-precision results would be obtained with less discrete nodes by the SFP method. In this paper, based on Reddy's third order beam theory, a motion equation was developed by the SFP method to analyze the first five natural frequencies of piezoelectric laminated beam under different axial forces. The influence of second-order effect caused by the axial force on vibration control was discussed based on the modal control theory and the Linear Quadratic Regulator (LQR) optimal control method. It can be concluded that the SFP method is suitable for the dynamic analysis of piezoelectric beam which needs less computational cost and has high accuracy. The vibration of the structure can be effectively inhibited by the LQR method and modal control theory. And the axial force has significant impact on the natural frequencies and control voltage of piezoelectric beam.

Electromagnetism as a second order effect

1961 ◽  
Vol 3 (1) ◽  
pp. 28-44 ◽  
Author(s):  
W. G. V. Rosser
Keyword(s):  
Order Effect ◽  
Second Order

Studies on Determination of Natural Frequencies of Industrial Turbine Blades

1995 ◽  
Author(s):  
Mahesh M. Bhat ◽  
V. Ramamurti ◽  
C. Sujatha
Keyword(s):  
Steam Turbine ◽  
Dynamic Behavior ◽  
Turbine Blade ◽  
Natural Frequencies ◽  
Complex Structure ◽  
Turbine Blades ◽  
Blade Root ◽  
Steam Turbine Blade ◽  
Manufacturing Tolerances

Abstract Steam turbine blade is a very complex structure. It has geometric complexities like variation of twist, taper, width and thickness along its length. Most of the time these variations are not uniform. Apart from these geometric complexities, the blades are coupled by means of lacing wire, lacing rod or shroud. Blades are attached to a flexible disc which contributes to the dynamic behavior of the blade. Root fixity also plays an important role in this behavior. There is a considerable variation in the frequencies of blades of newly assembled turbine and frequencies after some hours of running. Again because of manufacturing tolerances there can be some variation in the blade to blade frequencies. Determination of natural frequencies of the blade is therefore a very critical job. Problems associated with typical industrial turbine bladed discs of a 235 MW steam turbine are highlighted in this paper.

Exakte posenabhängige Strukurmodelle*/Accurate virtual machine tool structures - Online-identification of the general model of a lightweight machine tool structure with pose-dependent dynamic behavior

2017 ◽  
Vol 107 (05) ◽  
pp. 323-328
Author(s):  
S. Apprich ◽  
F. Wulle ◽  
A. Prof. Pott ◽  
A. Prof. Verl
Keyword(s):  
Machine Tool ◽  
Least Squares ◽  
Dynamic Behavior ◽  
Natural Frequencies ◽  
Recursive Least Squares ◽  
Machine Model ◽  
Online Identification ◽  
Working Space ◽  
Machine Tool Structure ◽  
Machine Tool Structures

Serielle Werkzeugmaschinenstrukturen weisen ein posenabhängiges, dynamisches Verhalten auf, wobei die Eigenfrequenzen um mehrere Hertz im Arbeitsraum variieren können. Die genaue Kenntnis dieses Verhaltens gestattet eine verbesserte Regelung der Strukturen. Ein generelles parametrisches Maschinenmodell, dessen Parameter online durch einen Recursive-Least-Squares-Algorithmus an das reale Maschinenverhalten angepasst werden, stellt Informationen über dieses Maschinenverhalten bereit.   Serial machine tool structures feature a pose-dependent dynamic behavior with natural frequencies varying by serveral hertz within the working space. The accurate knowledge of this behavior allows an improved control of the structures. A general parametric machine model, whose parameters are adapted online to the actual machine tool behavior by a Recursive Least Squares algorithm, provides information about the pose-dependent dynamic behavior.

scholarly journals Effect of intermediate supports location on natural frequencies of multiple cracked continuous beams

2018 ◽  
Author(s):  
Do Nam ◽  
Nguyen Tien Khiem ◽  
Le Khanh Toan ◽  
Nguyen Thi Thao ◽  
Pham Thi Ba Lien
Keyword(s):  
General Solution ◽  
Free Vibration ◽  
Natural Frequencies ◽  
Continuous Beam ◽  
Cracked Beam ◽  
Continuous Beams ◽  
Simplified Method ◽  
Rigid Supports ◽  
Natural Frequency Analysis ◽  
Eigenfrequency Spectrum

The present paper deals with free vibration of multiple cracked continuous beams with intermediate rigid supports. A simplified method is proposed to obtain general solution of free vibration in cracked beam with intermediate supports that is then used for natural frequency analysis of the beam in dependence upon cracks and support locations. Numerical results show that the support location or ratio of span lengths in combination with cracks makes a significant effect on eigenfrequency spectrum of beam. The discovered effects of support locations on eigenfrequency spectrum of cracked continuous beam are useful for detecting not only cracks but also positions of vanishing deflection on the beam.

scholarly journals Analysis of Dynamic Characteristics of a Propeller Blade Subjected to Large Material Removal in Milling

2020 ◽  
pp. 10-14
Author(s):  
Luyi Han ◽  
◽  
Riliang Liu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Dynamic Behavior ◽  
Dynamic Characteristics ◽  
Material Removal ◽  
Natural Frequencies ◽  
Machining Process ◽  
Time Varying ◽  
Propeller Blade ◽  
Large Material

A propeller blade, as a typical example of low-rigidity components, is prone to chatter and deformation in machining process, especially when large material removal is applied. In order to foresee the problems and then optimize the process, identification of the dynamic behavior of the workpiece is of great importance. This paper studies the dynamic characteristics of the workpiece in the machining process from plate to propeller blade using Finite Element Method. The results show that the time-varying natural frequencies of the workpiece decrease gradually at the beginning steps of the process due to the influence of material removal, and increases afterwards influenced by the geometry of the blade.

Study on the Method of the Damage Identification for Frame Structure

2012 ◽  
Vol 204-208 ◽  
pp. 2824-2831
Author(s):  
You Fa Yang ◽  
Shuai Li ◽  
Ling Ling
Keyword(s):  
Analytical Solution ◽  
Iterative Algorithm ◽  
Taylor Series ◽  
Structural Damage ◽  
Damage Identification ◽  
Second Order ◽  
Bias Error ◽  
Dynamic Data ◽  
First Order ◽  
Sensitivity Equations

First order iterative algorithm, mixed iterative algorithm, structural damage identification using static and dynamic data were put forward. The first and second order sensitivity matrixes of modal parameters that respect to the damage member were derived, and the modal truncation error which produced during the derivation of modal mode sensitivity was improved. The first and second order sensitivity equations were established respectively based on the principle of Taylor series expansion. And the solving method of these sensitivity equations was studied. Mixed iterative algorithm took up the second order nonlinear analytical solution as the first substituting value, and then the first substituting value was modified based on the Taylor series bias error using the solution of the first order sensitivity equation. It showed that the mixed iterative algorithm in this paper had a better convergence and a faster iteration speed because the higher precision second order nonlinear analytical solution was adopted. Because the method using static and dynamic data combined the static information and dynamic information of the structure, it could react the inside information of the structure more comprehensively, the result of damage identification was more accurate and it would be adapted more widely.

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