Topic
Timoshenko beam theory
About: Timoshenko beam theory is a research topic. Over the lifetime, 9426 publications have been published within this topic receiving 200570 citations.
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TL;DR: In this paper, the coupling between longitudinal, lateral and torsional vibrations is studied together for a rotating cracked shaft with a response-dependent non-linear breathing crack model and the coupling mechanisms have been studied with a nonlinear breathing-crack model.
211 citations
TL;DR: In this paper, an analytical method that uses Timoshenko beam theory for calculating the tool point FRF of a given combination by using the receptance coupling and structural modification methods is presented.
Abstract: Regenerative chatter is a well-known machining problem that results in unstable cutting process, poor surface quality and reduced material removal rate. This undesired self-excited vibration problem is one of the main obstacles in utilizing the total capacity of a machine tool in production. In order to obtain a chatter-free process on a machining center, stability diagrams can be used. Numerically or analytically, constructing the stability lobe diagram for a certain spindle–holder–tool combination implies knowing the system dynamics at the tool tip; i.e., the point frequency response function (FRF) that relates the dynamic displacement and force at that point. This study presents an analytical method that uses Timoshenko beam theory for calculating the tool point FRF of a given combination by using the receptance coupling and structural modification methods. The objective of the study is two fold. Firstly, it is aimed to develop a reliable mathematical model to predict tool point FRF in a machining center so that chatter stability analysis can be done, and secondly to make use of this model in studying the effects of individual bearing and contact parameters on tool point FRF so that better approaches can be found in predicting contact parameters from experimental measurements. The model can also be used to study the effects of several spindle, holder and tool parameters on chatter stability. In this paper, the mathematical model, as well as the details of obtaining the system component (spindle, holder and tool) dynamics and coupling them to obtain the tool point FRF are given. The model suggested is verified by comparing the natural frequencies of an example spindle–holder–tool assembly obtained from the model with those obtained from a finite element software. r 2006 Elsevier Ltd. All rights reserved.
208 citations
TL;DR: In this article, the buckling analysis of embedded functionally graded (FG) microbeams is performed based on sinusoidal shear deformation beam and modified couple stress theories.
208 citations
TL;DR: In this article, it was shown that if a consistent expression for the shear coefficient, such as those given by Cowper [1] or Stephen [2], is used in Timoshenko's beam theory, then very high accuracies can be expected for the natural frequencies, even for wavelengths of the same magnitude as the transverse dimension of the beam.
205 citations
Book•
17 Nov 2005
TL;DR: In this article, the Equations of Motion of Open/Closed Cross-Section Beams and Linear Beam Theory have been studied in the context of thin-walled beams.
Abstract: Kinematics of Thin Walled Beams.- The Equations of Motion of Open/Closed Cross-Section Beams.- Additional Equations of the Linear Beam Theory.- Several Theorems in Linear Thin-Walled Beam Theory.- Free Vibration.- Dynamic Response to Time-Dependent External Excitation.- Thin-Walled Beams Carrying Stores.- Rotating Thin-Walled Anisotropic Beams.- Spinning Thin-Walled Anisotropic Beams.- Thermally Induced Vibration and Control of Spacecraft Booms.- Aeroelasticity of Thin-Walled Aircraft Wings.- Open-Section Beams.
204 citations