Dynamic Formulations and Energy Analysis of Rotating Flexible-Shaft/Multi-Flexible-Disk System With Eddy-Current Brake

2000 ◽  
Vol 122 (4) ◽  
pp. 365-375 ◽  
Author(s):  
Rong-Fong Fung ◽  
Shih-Ming Hsu
Keyword(s):  
Eddy Current ◽  
Energy Analysis ◽  
Virtual Work ◽  
Beam Theory ◽  
Brake System ◽  
Euler Beam ◽  
Disk System ◽  
Coupling System ◽  
Flexible Disk ◽  
Work Done

In this paper, the rotating flexible-Timoshenko-shaft/flexible-disk coupling system is formulated by introducing the kinetic and strain energies, and the virtual work done by the eddy-current brake system into Hamilton’s principle. The attachment of disk to shaft becomes flexible for Timoshenko-beam theory and rigid for Euler-beam theory. It is found that the eddy-current brake system can be used to decrease speed and suppress flexible and shear vibrations simultaneously. From the dynamic formulations and energy analysis, some important discussions are made. Numerical results are provided to validate the theoretical analysis. [S0739-3717(00)01504-X]

Vibration Control of the Rotating Flexible-Shaft/Multi-Flexible-Disk System With the Eddy-Current Damper

2002 ◽  
Vol 124 (4) ◽  
pp. 519-526 ◽  
Author(s):  
Rong-Fong Fung ◽  
Jung-Hung Sun ◽  
Shih-Ming Hsu
Keyword(s):  
Eddy Current ◽  
Virtual Work ◽  
Equations Of Motion ◽  
Bilinear System ◽  
Optimal Feedback Control ◽  
Disk System ◽  
Control Laws ◽  
Assumed Mode Method ◽  
Eddy Current Damper ◽  
Flexible Disk

In this paper, the rotating flexible-Timoshenko-shaft/flexible-disk coupling system is formulated by applying the assumed-mode method into the kinetic and strain energies, and the virtual work done by the eddy-current damper. From Lagrange’s equations, the resulting discretized equations of motion can be simplified as a bilinear system (BLS). Introducing the control laws, including the quadratic, nonlinear and optimal feedback control laws, into the BLS, it is found that the eddy-current damper can be used to suppress flexible and shear vibrations simultaneously, and the system is globally asymptotically stable. Numerical results are provided to validate the theoretical analysis.

A Laminated Beam Theory With Interlayer Slip

1984 ◽  
Vol 51 (3) ◽  
pp. 551-559 ◽  
Author(s):  
H. Murakami
Keyword(s):  
Virtual Work ◽  
Sandwich Beam ◽  
Beam Theory ◽  
Transverse Shear Strain ◽  
Beam Model ◽  
Euler Beam ◽  
Concentrated Load ◽  
Laminated Beam ◽  
Wide Range ◽  
Interlayer Slip

A Timoshenko beam theory with built-in interlayer slip is developed to facilitate analytical means of simulating the effect of interlayer slip on the stiffness degradation of laminated beam structures. The proposed theory is unique in the sense that any well-structures interlay slip law can be adopted in the beam model. Based on the principle of virtual work, well-posed boundary value problems of the proposed beam theory are defined. It is shown that the proposed theory reduces to the existing Bernoulli-Euler beam theory with interlayer slip by introducing the kinematic constraint of zero transverse shear strain. As a demonstration of the theory the load-deflection curves of a simply supported sandwich beam subjected to a concentrated load at the center are computed for several characteristic interlayer slip laws. It is found that the proposed model has the capability of simulating the deformation of beams with wide range of interlayer bond qualities, from interface with perfect bond to interface without connectors.

scholarly journals Beam Theory of Thermal–Electro-Mechanical Coupling for Single-Wall Carbon Nanotubes

Nanomaterials ◽  
2021 ◽  
Vol 11 (4) ◽  
pp. 923
Author(s):  
Kun Huang ◽  
Ji Yao
Keyword(s):  
Mechanical Properties ◽  
Carbon Nanotubes ◽  
Beam Theory ◽  
Bending Stiffness ◽  
Single Wall Carbon Nanotubes ◽  
Beam Model ◽  
Euler Beam ◽  
New Model ◽  
Mechanical Coupling ◽  
Electrostatic Fields

The potential application field of single-walled carbon nanotubes (SWCNTs) is immense, due to their remarkable mechanical and electrical properties. However, their mechanical properties under combined physical fields have not attracted researchers’ attention. For the first time, the present paper proposes beam theory to model SWCNTs’ mechanical properties under combined temperature and electrostatic fields. Unlike the classical Bernoulli–Euler beam model, this new model has independent extensional stiffness and bending stiffness. Static bending, buckling, and nonlinear vibrations are investigated through the classical beam model and the new model. The results show that the classical beam model significantly underestimates the influence of temperature and electrostatic fields on the mechanical properties of SWCNTs because the model overestimates the bending stiffness. The results also suggest that it may be necessary to re-examine the accuracy of the classical beam model of SWCNTs.

Disk Position Nonlinearity Effects on the Chaotic Behavior of Rotating Flexible Shaft-Disk Systems

2012 ◽  
Vol 28 (3) ◽  
pp. 513-522 ◽  
Author(s):  
H. M. Khanlo ◽  
M. Ghayour ◽  
S. Ziaei-Rad
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Dynamic Behavior ◽  
Chaotic Behavior ◽  
Equations Of Motion ◽  
Beam Theory ◽  
Disk System ◽  
Partial Differential ◽  
Rayleigh Beam ◽  
Flexible Shaft

AbstractThis study investigates the effects of disk position nonlinearities on the nonlinear dynamic behavior of a rotating flexible shaft-disk system. Displacement of the disk on the shaft causes certain nonlinear terms which appears in the equations of motion, which can in turn affect the dynamic behavior of the system. The system is modeled as a continuous shaft with a rigid disk in different locations. Also, the disk gyroscopic moment is considered. The partial differential equations of motion are extracted under the Rayleigh beam theory. The assumed modes method is used to discretize partial differential equations and the resulting equations are solved via numerical methods. The analytical methods used in this work are inclusive of time series, phase plane portrait, power spectrum, Poincaré map, bifurcation diagrams, and Lyapunov exponents. The effect of disk nonlinearities is studied for some disk positions. The results confirm that when the disk is located at mid-span of the shaft, only the regular motion (period one) is observed. However, periodic, sub-harmonic, quasi-periodic, and chaotic states can be observed for situations in which the disk is located at places other than the middle of the shaft. The results show nonlinear effects are negligible in some cases.

scholarly journals Vibration and Instability of Rotating Composite Thin-Walled Shafts with Internal Damping

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Ren Yongsheng ◽  
Zhang Xingqi ◽  
Liu Yanghang ◽  
Chen Xiulong
Keyword(s):  
Virtual Work ◽  
Numerical Study ◽  
Equations Of Motion ◽  
Beam Theory ◽  
Dynamical Analysis ◽  
Design Parameters ◽  
Internal Damping ◽  
Analysis Method ◽  
Governing Equations ◽  
Thin Walled

The dynamical analysis of a rotating thin-walled composite shaft with internal damping is carried out analytically. The equations of motion are derived using the thin-walled composite beam theory and the principle of virtual work. The internal damping of shafts is introduced by adopting the multiscale damping analysis method. Galerkin’s method is used to discretize and solve the governing equations. Numerical study shows the effect of design parameters on the natural frequencies, critical rotating speeds, and instability thresholds of shafts.

scholarly journals Power Train Designing for Formula styled Racing Car

2021 ◽  
Vol 9 (10) ◽  
pp. 1883-1901
Author(s):  
Malav Sevak
Keyword(s):  
Power Transmission ◽  
Suspension System ◽  
Previous Model ◽  
Brake System ◽  
Maximum Acceleration ◽  
Power Train ◽  
The Road ◽  
Work Done

Abstract: A wheel assembly is an integral part of a vehicle’s design that connects the wheel to the suspension system and transfers pressure from the road to the suspension system. It also holds the brake system and facilitates steering. Power transmission is also addressed in the powertrain department. We describe the process and simulation that result in the hub, upright, and differential mounting of a formula student car and the size of the sprocket for maximum acceleration in this report. As a result of the work done on this project, the resulting car has improved acceleration, is easy and reliable to assemble, and has fewer breakdowns than the previous model. The report includes all the calculations that support the simulations and a validating statement about the bearing selection.

Vibration Analysis of a Partially Covered Double Sandwich Cantilever Beam With Concentrated Mass at the Free End

1993 ◽  
Author(s):  
C. Levy ◽  
Q. Chen
Keyword(s):  
Loss Factor ◽  
Equations Of Motion ◽  
Beam Theory ◽  
Physical Parameters ◽  
Mass Ratio ◽  
Euler Beam ◽  
Concentrated Mass ◽  
Sandwich Type ◽  
Euler Beam Theory ◽  
Two Parameters

Abstract The partially covered, sandwich-type cantilever with concentrated mass at the free end is studied. The equations of motion for the system modeled via Euler beam theory are derived and the resonant frequency and loss factor of the system are analyzed. The variations of resonance frequency and system loss factor for different geometrical and physical parameters are also discussed. Variation of these two parameters are found to strongly depend on the geometrical and physical properties of the constraining layers and the mass ratio.

Investigation on Free Vibration of Buckled Beams

2012 ◽  
Vol 433-440 ◽  
pp. 41-44 ◽  
Author(s):  
Ming Hsu Tsai ◽  
Wen Yi Lin ◽  
Kuo Mo Hsiao ◽  
Fu Mio Fujii
Keyword(s):  
Free Vibration ◽  
Virtual Work ◽  
Beam Theory ◽  
Taylor Series Expansion ◽  
Element Formulation ◽  
Governing Equations ◽  
Nonlinear Beam ◽  
Buckled Beams ◽  
Buckled Beam ◽  
D’Alembert Principle

The objective of this study is to investigate the deformed configuration and free vibration around the deformed configuration of clamped buckled beams by co-rotational finite element formulation. The principle of virtual work, d'Alembert principle and the consistent second order linearization of the nonlinear beam theory are used to derive the element equations in current element coordinates. The governing equations for linear vibration are obtained by the first order Taylor series expansion of the equation of motion at the static equilibrium position of the buckled beam. Numerical examples are studied to investigate the natural frequencies of clamped buckled beams with different slenderness ratios under different axial compression.

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