scholarly journals Vibrational Energy Flow Analysis of Corrected Flexural Waves in Timoshenko Beam – Part I: Theory of an Energetic Model

2006 ◽  
Vol 13 (3) ◽  
pp. 137-165 ◽  
Author(s):  
Young-Ho Park ◽  
Suk-Yoon Hong
Keyword(s):  
Timoshenko Beam ◽  
Energy Flow ◽  
Flow Model ◽  
Vibrational Energy ◽  
Classical Solutions ◽  
Timoshenko Beams ◽  
Governing Equations ◽  
Bernoulli Beam ◽  
Vibrational Energy Flow ◽  
Euler Bernoulli Beam

In this paper, an energy flow model is developed to analyze transverse vibration including the effects of rotatory inertia as well as shear distortion, which are very important in the Timoshenko beam transversely vibrating in the medium-to-high frequency ranges. The energy governing equations for this energy flow model are newly derived by using classical displacement solutions of the flexural motion for the Timoshenko beam, in detail. The derived energy governing equations are in the general form incorporating not only the Euler-Bernoulli beam theory used for the conventional energy flow model but also the Rayleigh, shear, and Timoshenko beam theories. Finally, to verify the validity and accuracy of the derived model, numerical analyses for simple finite Timoshenko beams were performed. The results obtained by the derived energy flow model for simple finite Timoshenko beams are compared with those of the classical solutions for the Timoshenko beam, the energy flow solution, and the classical solution for the Euler-Bernoulli beam with various excitation frequencies and damping loss factors of the beam. In addition, the vibrational energy flow analyses of coupled Timoshenko beams are described in the other companion paper.

Mechanical Characters of Six Engineering Timoshenko Beams

2014 ◽  
Vol 668-669 ◽  
pp. 201-204
Author(s):  
Hong Liang Tian
Keyword(s):  
Timoshenko Beam ◽  
Analytic Solutions ◽  
Timoshenko Beams ◽  
Bernoulli Beam ◽  
Simply Supported ◽  
Normality Assumption ◽  
Length Direction ◽  
The Right ◽  
Euler Bernoulli Beam ◽  
Mechanical Characters

Timoshenko beam is an extension of Euler-Bernoulli beam to interpret the transverse shear impact. The more refined Timoshenko beam relaxes the normality assumption of plane section that remains plane and normal to the deformed centerline. The manuscript presents some exact concise analytic solutions on deflection and stress resultants of NET single-span Timoshenko beam with general distributed force and 6 kinds of standard boundary conditions, adopting its counterpart Euler-Bernoulli beam solutions. Engineering example shows that scale impact would not unveil itself for micro structure with micrometer μm-order length, yet will be prominent for nanostructure with nanometer nm-order length. When simply supported CNTs is undergone to a concentrative force at the median and complete bend moment, scale action is observed along the ensemble CNTs, while it unfurls itself the most at the position of the concentrated strength. When a clamped-free CNTs is exposed to a centralized force at the mesial and distributed force, there is no scale impact about the deflection at all positions on the left border of the concentrated strength position, while such operation inspires at once at all positions on the right margin of the concentrated strength position. When a clamped-clamped CNTs is lain under a concentrative strength at the middle, the deflection of NET Euler-Bernoulli CNTs reflects scale effect completely. Notable differences between the deflection of Euler-Bernoulli CNTs and that of Timoshenko CNTs are reflected at large ratio of diameter versus length. The deflection of NET clamped-free and simply supported Timoshenko beam doesn’t introduce surplus scale process in terms of its counterpart, NET Euler-Bernoulli beam. However, the deflection of NET clamped-clamped Timoshenko beam does involve additional scale impact solely including the method when the concentrated strength position is at the midway in the beam-length direction.

scholarly journals On the Equivalence between Static and Dynamic Railway Track Response and on the Euler-Bernoulli and Timoshenko Beams Analogy

2017 ◽  
Vol 2017 ◽  
pp. 1-13 ◽  
Author(s):  
Wlodzimierz Czyczula ◽  
Piotr Koziol ◽  
Dorota Blaszkiewicz
Keyword(s):  
Axial Force ◽  
Timoshenko Beam ◽  
Linear Models ◽  
Moving Load ◽  
Railway Track ◽  
Variable Load ◽  
Static Case ◽  
Timoshenko Beams ◽  
Bernoulli Beam ◽  
Euler Bernoulli Beam

The paper tries to clarify the problem of solution and interpretation of railway track dynamics equations for linear models. Set of theorems is introduced in the paper describing two types of equivalence: between static and dynamic track response under moving load and between the dynamic response of track described by both the Euler-Bernoulli and Timoshenko beams. The equivalence is clarified in terms of mathematical method of solution. It is shown that inertia element of rail equation for the Euler-Bernoulli beam and constant distributed load can be considered as a substitute axial force multiplied by second derivative of displacement. Damping properties can be treated as additional substitute load in the static case taking into account this substitute axial force. When one considers the Timoshenko beam, the substitute axial force depends additionally on shear properties of rail section, rail bending stiffness, and subgrade stiffness. It is also proved that Timoshenko beam, described by a single equation, from the point of view of solution, is an analogy of the Euler-Bernoulli beam for both constant and variable load. Certain numerical examples are presented and practical interpretation of proved theorems is shown.

scholarly journals Vibrational Energy Flow Analysis of Corrected Flexural Waves in Timoshenko Beam – Part II: Application to Coupled Timoshenko Beams

2006 ◽  
Vol 13 (3) ◽  
pp. 167-196 ◽  
Author(s):  
Young-Ho Park ◽  
Suk-Yoon Hong
Keyword(s):  
Timoshenko Beam ◽  
Energy Flow ◽  
Vibrational Energy ◽  
Flow Analysis ◽  
Companion Paper ◽  
Wave Transmission ◽  
Classical Solutions ◽  
Flexural Waves ◽  
Beam Structures ◽  
Energy Flow Analysis

This paper presents the methodology for the energy flow analysis of coupled Timoshenko beam structures and various numerical applications to verify the developed methodology. To extend the application of the energy flow model for corrected flexural waves in the Timoshenko beam, which is developed in the other companion paper, to coupled structures, the wave transmission analyses of general coupled Timoshenko beam systems are performed. First, power transmission and reflection coefficients for all kinds of propagating waves in the general, coupled Timoshenko beam structures are derived by the wave transmission approach. In numerical applications, the energy flow solutions using the derived coefficients agree well with the classical solutions for various exciting frequencies, damping loss factors, and coupled Timoshenko beam structures. Additionally, the numerical results for the Timoshenko beam are compared with those for the Euler-Bernoulli beam.

Direct Observation of Vibrational Energy Flow in Cytochromec

2011 ◽  
Vol 115 (44) ◽  
pp. 13057-13064 ◽  
Author(s):  
Naoki Fujii ◽  
Misao Mizuno ◽  
Yasuhisa Mizutani
Keyword(s):  
Direct Observation ◽  
Energy Flow ◽  
Vibrational Energy ◽  
Vibrational Energy Flow

Medium Frequency Vibration Analysis of Beam Structures Modeled by the Timoshenko Beam Theory

2020 ◽  
Author(s):  
Yichi Zhang ◽  
Bingen Yang
Keyword(s):  
Shear Deformation ◽  
Timoshenko Beam ◽  
Vibration Analysis ◽  
Beam Theory ◽  
Timoshenko Beam Theory ◽  
Bernoulli Beam ◽  
Beam Structure ◽  
Medium Frequency ◽  
Beam Structures ◽  
Euler Bernoulli Beam

Abstract Vibration analysis of complex structures at medium frequencies plays an important role in automotive engineering. Flexible beam structures modeled by the classical Euler-Bernoulli beam theory have been widely used in many engineering problems. A kinematic hypothesis in the Euler-Bernoulli beam theory is that plane sections of a beam normal to its neutral axis remain normal when the beam experiences bending deformation, which neglects the shear deformation of the beam. However, as observed by researchers, the shear deformation of a beam component becomes noticeable in high-frequency vibrations. In this sense, the Timoshenko beam theory, which describes both bending deformation and shear deformation, may be more suitable for medium-frequency vibration analysis of beam structures. This paper presents an analytical method for medium-frequency vibration analysis of beam structures, with components modeled by the Timoshenko beam theory. The proposed method is developed based on the augmented Distributed Transfer Function Method (DTFM), which has been shown to be useful in various vibration problems. The proposed method models a Timoshenko beam structure by a spatial state-space formulation in the s-domain, without any discretization. With the state-space formulation, the frequency response of a beam structure, in any frequency region (from low to very high frequencies), can be obtained in an exact and analytical form. One advantage of the proposed method is that the local information of a beam structure, such as displacements, bending moment and shear force at any location, can be directly obtained from the space-state formulation, which otherwise would be very difficult with energy-based methods. The medium-frequency analysis by the augmented DTFM is validated with the FEA in numerical examples, where the efficiency and accuracy of the proposed method is present. Also, the effects of shear deformation on the dynamic behaviors of a beam structure at medium frequencies are illustrated through comparison of the Timoshenko beam theory and the Euler-Bernoulli beam theory.

Vibrational energy flow across heme–cytochrome c and cytochrome c–water interfaces

2015 ◽  
pp. 129-138
Author(s):  
Johnson K. Agbo ◽  
Yao Xu ◽  
Ping Zhang ◽  
John E. Straub ◽  
David M. Leitner
Keyword(s):  
Cytochrome C ◽  
Energy Flow ◽  
Vibrational Energy ◽  
Vibrational Energy Flow

scholarly journals Intramolecular vibrational energy redistribution and the quantum ergodicity transition: a phase space perspective

2020 ◽  
Vol 22 (20) ◽  
pp. 11139-11173 ◽  
Author(s):  
Sourav Karmakar ◽  
Srihari Keshavamurthy
Keyword(s):  
Phase Space ◽  
Energy Flow ◽  
Vibrational Energy ◽  
Energy Redistribution ◽  
Quantum Ergodicity ◽  
Connected Network ◽  
Intramolecular Vibrational Energy Redistribution ◽  
Vibrational Energy Flow ◽  
Classical Phase Space

The onset of facile intramolecular vibrational energy flow can be related to features in the connected network of anharmonic resonances in the classical phase space.

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