scholarly journals Dynamic Model of a Rotating Flexible Arm-Flexible Root Mechanism Driven by a Shaft Flexible in Torsion

2006 ◽  
Vol 13 (6) ◽  
pp. 577-593 ◽  
Author(s):  
S.Z. Ismail ◽  
A.A. Al-Qaisia ◽  
B.O. Al-Bedoor
Keyword(s):  
Dynamic Model ◽  
Equations Of Motion ◽  
Beam Theory ◽  
Small Deformation ◽  
Coupled System ◽  
Practical Implementation ◽  
Flexible Beam ◽  
Nonlinear Coupled System ◽  
Linearized System ◽  
Euler Bernoulli Beam

This paper presents a dynamic model of a rotating flexible beam carrying a payload at its tip. The model accounts for the driving shaft and the arm root flexibilities. The finite element method and the Lagrangian dynamics are used in deriving the equations of motion with the small deformation theory assumptions and the Euler-Bernoulli beam theory. The obtained model is a nonlinear-coupled system of differential equations. The model is simulated for different combinations of shaft and root flexibilities and arm properties. The simulation results showed that the root flexibility is an important factor that should be considered in association with the arm and shaft flexibilities, as its dynamics influence the motor motion. Moreover, the effect of system non-linearity on the dynamic behavior is investigated by simulating the equivalent linearized system and it was found to be an important factor that should be considered, particularly when designing a control strategy for practical implementation.

scholarly journals Dynamics of a rotating beam with intermittent contact

2021 ◽  
Author(s):  
Mary Ann Ieropoli
Keyword(s):  
Equations Of Motion ◽  
Beam Theory ◽  
Momentum Balance ◽  
Flexible Beam ◽  
Constrained Motion ◽  
Lagrange Equations ◽  
Depth Of Penetration ◽  
Initial Beam ◽  
Intermittent Contact ◽  
Euler Bernoulli Beam

A flexible beam that is attached to a rotating hub, and whose tip encounters intermittent contact with a flat rigid surface is modelled. The beam is modelled using Euler-Bernoulli beam theory. Lagrange Equations are used to develop the system governing equations of motion, impact is modelled using the momentum balance method and contact is represented via a Lagrange multiplier and Coulomb friction. The model does not allow penetration of the surface to occur by enforcing a geometric constraint throughout contact. Both flexible and rigid initial beam assumptions before impact were analyzed. The effects of angular velocity, depth of penetration and the friction coefficient were examined. A numerical algorithm is outlined and Matlab software is used to implement the procedure. The results show compliance with expected trends and they show smoother transition from unconstrained to constrained motion for the flexible initial beam configuration compared to the rigid configuration.

scholarly journals Dynamics of a rotating beam with intermittent contact

2021 ◽  
Author(s):  
Mary Ann Ieropoli
Keyword(s):  
Equations Of Motion ◽  
Beam Theory ◽  
Momentum Balance ◽  
Flexible Beam ◽  
Constrained Motion ◽  
Lagrange Equations ◽  
Depth Of Penetration ◽  
Initial Beam ◽  
Intermittent Contact ◽  
Euler Bernoulli Beam

A flexible beam that is attached to a rotating hub, and whose tip encounters intermittent contact with a flat rigid surface is modelled. The beam is modelled using Euler-Bernoulli beam theory. Lagrange Equations are used to develop the system governing equations of motion, impact is modelled using the momentum balance method and contact is represented via a Lagrange multiplier and Coulomb friction. The model does not allow penetration of the surface to occur by enforcing a geometric constraint throughout contact. Both flexible and rigid initial beam assumptions before impact were analyzed. The effects of angular velocity, depth of penetration and the friction coefficient were examined. A numerical algorithm is outlined and Matlab software is used to implement the procedure. The results show compliance with expected trends and they show smoother transition from unconstrained to constrained motion for the flexible initial beam configuration compared to the rigid configuration.

An Exact Solution for the Natural Frequencies of Flexible Beams Undergoing Overall Motions

2003 ◽  
Vol 9 (11) ◽  
pp. 1221-1229 ◽  
Author(s):  
Ali H Nayfeh ◽  
S.A. Emam ◽  
Sergio Preidikman ◽  
D.T. Mook
Keyword(s):  
Exact Solution ◽  
Natural Frequencies ◽  
Three Dimensional ◽  
Beam Theory ◽  
Free Vibrations ◽  
Mode Shapes ◽  
Flexible Beam ◽  
Bernoulli Beam ◽  
Flexible Beams ◽  
Euler Bernoulli Beam

We investigate the free vibrations of a flexible beam undergoing an overall two-dimensional motion. The beam is modeled using the Euler-Bernoulli beam theory. An exact solution for the natural frequencies and corresponding mode shapes of the beam is obtained. The model can be extended to beams undergoing three-dimensional motions.

The elastochrone: the descent time of a sphere on a flexible beam

2009 ◽  
Vol 465 (2107) ◽  
pp. 2293-2311 ◽  
Author(s):  
Jeffrey M. Aristoff ◽  
Christophe Clanet ◽  
John W.M. Bush
Keyword(s):  
Gravitational Field ◽  
Theoretical Model ◽  
Elastic Beam ◽  
Beam Theory ◽  
Flexible Beam ◽  
Bernoulli Beam ◽  
Horizontal Beam ◽  
Theoretical Predictions ◽  
Static Regime ◽  
Euler Bernoulli Beam

We present the results of a combined experimental and theoretical investigation of the motion of a sphere on an inclined flexible beam. A theoretical model based on Euler–Bernoulli beam theory is developed to describe the dynamics, and in the limit where the beam reacts instantaneously to the loading, we obtain exact solutions for the load trajectory and descent time. For the case of an initially horizontal beam, we calculate the period of the resulting oscillations. Theoretical predictions compare favourably with our experimental observations in this quasi-static regime. The time taken for descent along an elastic beam, the elastochrone, is shown to exceed the classical brachistochrone, the shortest time between two points in a gravitational field.

Dynamic Behavior of Vehicles Travelling on Bridges

1993 ◽  
Author(s):  
Ebrahim Esmailzadeh ◽  
Mehrdaad Ghorashi
Keyword(s):  
Boundary Conditions ◽  
Dynamic Behavior ◽  
Numerical Solutions ◽  
Equations Of Motion ◽  
Beam Theory ◽  
Parameter System ◽  
Moving Vehicle ◽  
Lumped Parameter ◽  
Euler Bernoulli Beam ◽  
Two Degree Of Freedom

Abstract An investigation into the dynamic behavior of a bridge with simply supported boundary conditions, carrying a moving vehicle, is performed. The vehicle has been modelled as a two degree of freedom lumped-parameter system travelling at a uniform speed. Furthermore, the bridge is assumed to obey the Euler-Bernoulli beam theory of vibration. This analysis may well be applied to a beam with different boundary conditions, but the computer simulation results given in this paper are set for only the case of freely hinged ends. Numerical solutions for the derived differential equations of motion are obtained and their close agreement, in some extreme cases, with those reported earlier by the authors are observed. Finally, the effect of speed on the maximum dynamic deflection of bridge is shown to be of much importance and hence an estimation for the critical speed of the vehicle is presented.

scholarly journals Differential Equations of Motion for Naturally Curved and Twisted Composite Space Beams

2018 ◽  
Vol 2018 ◽  
pp. 1-12
Author(s):  
Ying Hao ◽  
Wei He ◽  
Yanke Shi
Keyword(s):  
Differential Equations ◽  
Cross Section ◽  
Cross Sections ◽  
Design Principle ◽  
Equations Of Motion ◽  
Beam Theory ◽  
Coupled System ◽  
Variable Coefficients ◽  
Curve Beam ◽  
Design Factor

The differential equations of motion for naturally curved and twisted elastic space beams made of anisotropic materials with noncircular cross sections, being a coupled system consisting of 14 second-order partial differential equations with variable coefficients, are derived theoretically. The warping deformation of beam’s cross section, as a new design factor, is incorporated into the differential equations in addition to the anisotropy of material, the curvatures of the rod axis, the initial twist of the cross section, the rotary inertia, and the shear and axial deformations. Numerical examples show that the effect of warping deformation on the natural frequencies of the beam is significant under certain geometric and boundary conditions. This study focuses on improving and consummating the traditional theories to build a general curve beam theory, thereby providing new scientific research reference and design principle for curve beam designers.

Dynamic Analysis of a Beam-Type Resonator With Off-Axis Attached Mass

2012 ◽  
Author(s):  
Pezhman A. Hassanpour ◽  
Kamran Behdinan
Keyword(s):  
Equations Of Motion ◽  
Center Of Mass ◽  
Beam Theory ◽  
Numerical Approach ◽  
Governing Equations ◽  
Bernoulli Beam ◽  
Comb Drive ◽  
Comb Drives ◽  
Beam Type ◽  
Euler Bernoulli Beam

In this paper, the model of a micro-machined beam-type resonator is presented. The resonator is a micro-bridge which is modeled using Euler-Bernoulli beam theory. A comb-drive electrostatic actuator is attached to the micro-bridge for the excitation/detection of vibrations. In the models presented in the literature, it is assumed that the center of mass of the comb-drive is located on the neutral axis of the beam. In this paper, it is demonstrated that this assumption can not be applied for asymmetric-shaped comb-drives. Furthermore, the governing equations of motion are derived by relaxing the above assumption. It has been shown that the off-axis center of mass of the comb-drive generates an amplitude-dependent transverse force in the beam, which is essentially a nonlinear effect. The governing equations of motion are solved using a hybrid analytical-numerical approach. The end application of the structure under investigation is in resonant sensing and energy harvesting applications.

Nonlinear Free Vibration of a Beam With Off-Axis Attached Mass

2013 ◽  
Author(s):  
Pezhman A. Hassanpour
Keyword(s):  
Free Vibration ◽  
Multiple Scales ◽  
Equations Of Motion ◽  
Center Of Mass ◽  
Beam Theory ◽  
Governing Equations ◽  
Attached Mass ◽  
Lumped Mass ◽  
Nonlinear Free Vibration ◽  
Euler Bernoulli Beam

A model of a clamped-clamped beam with an attached lumped mass is presented in this paper. The system is modeled using the Euler-Bernoulli beam theory. In the models presented in literature, it is assumed that the center of mass of the attached mass is located on the neutral axis of the beam. In this paper, this assumption is relaxed. The governing equations of motion are derived. It has been shown that the off-axis center of mass of the attached mass generates an amplitude-dependent transverse force in the beam, which introduces a quadratic nonlinearity. The nonlinear governing equations of motion are solved using the Multiple Scales method. The nonlinear free vibration frequencies are determined.

Dynamic Modeling of Bottomhole Assembly

2014 ◽  
Author(s):  
Madhu Vadali ◽  
Zhijie Sun ◽  
Yuzhen Xue ◽  
Jason Dykstra
Keyword(s):  
Dynamic Model ◽  
Oil And Gas ◽  
System Development ◽  
Beam Theory ◽  
Flexible Beam ◽  
Fluid Mud ◽  
Directional Drilling ◽  
Lumped Mass ◽  
Stick Slip ◽  
Drilling System

This paper presents a comprehensive 4D dynamic model of a bottomhole assembly (BHA) used for directional drilling of oil and gas wells. Although directional drilling has been in practice for some time, it still poses several challenges, particularly related to building an autonomous drilling system. The difficulty with drilling automation derives from the complexity of the process that includes interaction with the borehole and fluid (mud) flow and complex downhole vibrations, such as bit-bounce (axial), whirl (lateral), and stick/slip (torsional). Moreover, the measurements from a limited number of downhole sensors are usually contaminated with high noise levels, and can only be transmitted at low rates with long transmission delays using mud pulsing, or at a high cost using wired pipe. Therefore, it is preferable that the directional drilling system work autonomously with limited communication to the surface. To facilitate this, a compressive physics-based model of the BHA behavior was created to be used in control system development. In this work, the 4D dynamic model of the BHA accounts for the dynamics in rotation, axial motion, and bending along two lateral directions. The model uses a lumped mass-spring system and the system parameters (mass and stiffness) are derived from the shear beam theory of a flexible beam under certain boundary conditions. Simulation results of the model were successful in qualitatively replicating the three types of downhole vibrations, namely bit-bounce, whirl, and stick/slip, and are discussed in this paper. The model is shown to qualitatively replicate downhole conditions and can be implemented in real-time, thereby making it suitable for autonomous directional drilling control.

Dynamic Modeling of a Compliant Tail-Propelled Robotic Fish

2013 ◽  
Author(s):  
Vladislav Kopman ◽  
Jeffrey Laut ◽  
Maurizio Porfiri ◽  
Francesco Acquaviva ◽  
Alessandro Rizzo
Keyword(s):  
Equations Of Motion ◽  
Beam Theory ◽  
The Body ◽  
Robotic Fish ◽  
Body Dynamics ◽  
Flexible Fin ◽  
Optimization And Control ◽  
Rigid Component ◽  
And Control ◽  
Euler Bernoulli Beam

This paper presents a dynamic model for a class of robotic fish propelled by a tail with a flexible fin. The robot is comprised of a rigid frontal link acting as a body and a rear link serving as the tail. The tail includes a rigid component, hinged to the body through a servomotor, which is connected to a compliant caudal fin whose underwater vibration induces the propulsion. The robot’s body dynamics is modeled using Kirchhoff’s equations of motion of bodies in quiescent fluids, while its tail motion is described with Euler-Bernoulli beam theory, accounting for the effect of the encompassing fluid through the Morison equation. Simulation data of the model is compared with experimental data. Applications of the model include simulation, prediction, design optimization, and control.

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