The Instability of a Cantilever on an Elastic Foundation under the Influence of a Follower Force

1975 ◽  
Vol 17 (4) ◽  
pp. 219-222 ◽  
Author(s):  
I. F. A. Wahed
Keyword(s):  
Differential Equation ◽  
Elastic Foundation ◽  
Critical Frequency ◽  
Critical Force ◽  
Follower Force ◽  
Damping Coefficient ◽  
Viscous Damping ◽  
Lateral Vibration ◽  
Galerkin’S Method ◽  
Instability Boundary

The instability of a uniform cantilever compressed by a follower force at its free tip is investigated. The cantilever is supported on an elastic foundation and subjected to external viscous damping. The differential equation of lateral vibration of the cantilever is solved simply by Galerkin's method and the instability boundary is determined by applying Routh's criterion. It is found that the cantilever becomes unstable by flutter and that the critical force and the critical frequency depend on both damping coefficient and foundation modulus. Only with no damping is the critical force independent of foundation modulus, a phenomenon reported by other investigators.

Critical Force Analysis of a Cantilever Column Subjected to a Subtangential Follower Force and a Vertical Force

2011 ◽  
Vol 138-139 ◽  
pp. 3-8 ◽  
Author(s):  
Z.C. Su ◽  
Yan Xia Xue ◽  
Cheng Bin Du
Keyword(s):  
Differential Equation ◽  
Exact Solution ◽  
Critical Force ◽  
Follower Force ◽  
Vertical Force ◽  
Force Parameter ◽  
Force Analysis ◽  
Influence Curves ◽  
Governing Differential Equation ◽  
The Stability

The stability of a cantilever column subjected to a subtangential follower force and a vertical force is discussed for investigating the effects of these factors on the critical force. The governing differential equation of the system and the corresponding boundary conditions are established, and the exact solution is found out by integrating the differential equation. Based on the exact solution, the effects of the parameters relating to the subtangential follower force and the vertical force on the critical force are analyzed, and discussions for these results are performed， the influence curves of the subtangential follower force parameter and the vertical force parameter to the critical force are plotted. The results show that the parameter of a subtangential follower force can be bigger than 1/2, even equal to 1.0, with taking into account of the effect of the vertical force.

Stability of Cracked Fluid-Conveying Pipeline on Elastic Foundation under Distributed Follower Forces

2014 ◽  
Vol 1065-1069 ◽  
pp. 2076-2079
Author(s):  
Ye Zhou Sheng ◽  
Chang Qing Guo ◽  
Wei Bin Hong
Keyword(s):  
Differential Equation ◽  
Elastic Foundation ◽  
Bending Moment ◽  
Follower Force ◽  
Crack Location ◽  
Characteristic Values ◽  
Transfer Method ◽  
Distributed Follower Force ◽  
The Stability ◽  
Fluid Conveying Pipes

The differential equation of fluid-conveying pipes considering distributed follower force and elastic foundation is established. The equation is discreted and solved by Galerkin method and the frequency characteristic values are solved by bending moment transfer method. The effects of crack location and elastic foundation stiffness to the form of instability of the pipes under the distributed follower force are analyzed. Results show that the elastic foundation stiffness can enforce the stability of the pipes effectively, and the effects are more obvious when the crack location is closer to the middle of the pipe.

Static Instability of a Restrained Cantilever Column with a Tip Mass Subjected to a Subtangential Follower Force

2013 ◽  
Vol 345 ◽  
pp. 341-344
Author(s):  
Zhen Chao Su ◽  
Yan Xia Xue
Keyword(s):  
Differential Equation ◽  
Mass Parameter ◽  
Follower Force ◽  
Force Parameter ◽  
Euler Beam ◽  
Numerical Computations ◽  
Divergence Instability ◽  
Static Instability ◽  
Tip Mass

Based on the theory of Bernoulli-Euler beam, the differential equation of a restrained cantilever column with a tip mass subjected to a subtangential follower force is constructed, the solution of the differential equation is found, and the existence of regions of divergence instability of the system is discussed. The influence of the follower force parameter η, the tip mass parameter β and an end elastic end support on the divergence instability of the column is investigated. Several numerical computations of some cases have completed.

Impact of a Mass on a Damped Elastically Supported Beam

1948 ◽  
Vol 15 (2) ◽  
pp. 125-136
Author(s):  
W. H. Hoppmann
Keyword(s):  
Differential Equation ◽  
Elastic Foundation ◽  
Forced Vibration ◽  
Numerical Solutions ◽  
Coefficient Of Restitution ◽  
Tabular Form ◽  
Single Degree Of Freedom ◽  
Simply Supported ◽  
Single Degree ◽  
Elastically Supported

Abstract In this paper a study is made of the problem of the central impact of a mass on a simply supported beam on an elastic foundation with considerations of internal and external damping. The differential equation for the forced vibration of the beam is developed. It is solved for the case in which the force is a function of time and is concentrated at the center of the beam. Formulas are obtained for the deflections. An expression is developed for the coefficient of restitution which is essential in determining the deflections and the strains. Criteria are devised for determining the cases in which the beam may be considered as a single-degree-of-freedom system when damping and an elastic foundation are considered. The importance of these criteria is discussed. A numerical example illustrating the theory developed in the paper is worked out in detail. Results of computations for several numerical solutions are given in tabular form.

scholarly journals Electromagnetic simulation of an external rotor PM hub motor power device for distributed driving electric vehicle

2020 ◽  
Vol 12 (10) ◽  
pp. 168781402096652
Author(s):  
Qiping Chen ◽  
Yue Tian ◽  
Chuanjie Liao ◽  
Sheng Kang ◽  
Ning Wang
Keyword(s):  
Electric Vehicle ◽  
Damping Coefficient ◽  
Power Device ◽  
Viscous Damping ◽  
Motor Power ◽  
Analysis Model ◽  
Performance Requirements ◽  
Split Ratio ◽  
Steady State Simulation ◽  
External Rotor

In order to increase efficiency and reliability of hub motor power device for distributed driving electric vehicle, a novel hub motor with an external rotor PM (permanent magnet) is designed and optimized. The performance parameters of hub motor are computed and selected based on vehicle dynamics indicators and the driving equations. This paper determines the optimum primary size of hub motor by choosing appropriate magnetic circuit structure and integrating three key parameters, including as stator split ratio, electromagnetic load and viscous damping coefficient. This paper has built the analysis model of external rotor PM hub motor, and simulated and analyzed the transient magnetic field of hub motor under no-load and load transient or steady state. Simulation results indicate that the external rotor PM hub motor designed by combining stator split ratio, electromagnetic load and viscous damping coefficient has satisfactory electromagnetic performance, which can satisfy the performance requirements and indicators of hub motor power device for distributed driving electric vehicles.

scholarly journals Damping Force and Loading Position Dependence of Mass Sensitivity of Magnetoelastic Biosensors in Viscous Liquid

Sensors ◽  
2018 ◽  
Vol 19 (1) ◽  
pp. 67
Author(s):  
Kewei Zhang ◽  
Zhe Chen ◽  
Qianke Zhu ◽  
Yong Jiang ◽  
Wenfeng Liu ◽  
...  
Keyword(s):  
Numerical Simulation ◽  
Damping Coefficient ◽  
Viscous Damping ◽  
Simulation Approach ◽  
Damping Force ◽  
Mass Sensitivity ◽  
High Order Resonance ◽  
Target Loading ◽  
Position Dependence ◽  
Different Order

We established the vibration governing equation for a magnetoelastic (ME) biosensor with target loading in liquid. Based on the equation, a numerical simulation approach was used to determine the effect of the target loading position and viscous damping coefficient on the node (“blind points”) and mass sensitivity (Sm) of an ME biosensor under different order resonances. The results indicate that viscous damping force causes the specific nodes shift but does not affect the overall variation trend of Sm as the change of target loading position and the effect on Sm gradually reduces when the target approaches to the node. In addition, Sm decreases with the increase of viscous damping coefficient but the tendency becomes weak at high-order resonance. Moreover, the effect of target loading position on Sm decreases with the increase of viscous damping coefficient. Finally, the results provide certain guidance on improving the mass sensitivity of an ME biosensor in liquid by controlling the target loading position.

Analysis of the Influences of Drilling Fluid Flow Velocity inside and outside the Drilling String on Drilling String Lateral Vibration Frequency

2013 ◽  
Vol 821-822 ◽  
pp. 1418-1421
Author(s):  
Tie Yan ◽  
Li Wang ◽  
Xiao Feng Sun ◽  
Jun Bo Qu
Keyword(s):  
Differential Equation ◽  
Fluid Flow ◽  
Flow Velocity ◽  
Vibration Frequency ◽  
Drilling Fluid ◽  
Euler Method ◽  
Lateral Vibration ◽  
Fluid Flow Velocity ◽  
Drilling String ◽  
Mass Coefficient

Drilling string lateral vibration is a severe damage,which is influenced by many complex factors. This paper makes a theoretical analysis of the drilling string lateral vibration frequency caused by drilling fluid flow velocity inside and outside the drilling string, which supplies some evidence for calculating rotation speed of rotary table and reduces the times of drill string resonance. The influence of drilling fluid flow velocity inside the drilling string on lateral vibration frequency is analyzed by Euler method. Besides,through the use of mechanical analysis method and the introduction of additional mass coefficient. A differential equation of drilling string lateral vibration with the consideration of drilling fluid flow velocity inside and outside the drilling string is built up, and a mathematical model of drilling string lateral vibration under the influence of drilling fluid flow velocity is obtained. Field applications indicate that this model is in agreement with the field condition. Key words: mass coefficient;differential equation; drilling fluid flow velocity; lateral vibration frequency;

Force Behavior of Parallel Double Coupling Beams with Different Width

2014 ◽  
Vol 578-579 ◽  
pp. 707-710
Author(s):  
Ming Li ◽  
Ji Guang Chen ◽  
Wei Jian Zhao ◽  
Li Guo Wang
Keyword(s):  
Finite Element ◽  
Energy Dissipation ◽  
Damping Coefficient ◽  
Viscous Damping ◽  
Coupling Beams ◽  
Equivalent Viscous Damping ◽  
Dissipation Coefficient ◽  
Finite Element Software ◽  
Double Coupling ◽  
Energy Dissipation Coefficient

The force behavior of parallel double coupling beams (PDCB) with different width is analyzed, based on which the feasibility of this kind of beams is discussed. The loading process of the PDCB is simulated by using finite element software ABAQUS. By analyzing the hysteretic loops, skeleton curves, energy dissipation coefficient, equivalent viscous damping coefficient and ductility coefficient,the bearing capacity and seismic performance of the PDCB is studied. Through simulation, it shows that the hysteretic loops is plump, and the energy dissipation coefficient, equivalent viscous damping coefficient and ductility coefficient of this double beams is high. It can be concluded that the PDCB has good force behavior, and the beams of PDCB can work in coordination.

NONDIMENSIONAL ANALYSIS OF ANNULAR DUCT FLOW IN MAGNETORHEOLOGICAL/ELECTRORHEOLOGICAL DAMPERS

2005 ◽  
Vol 19 (07n09) ◽  
pp. 1577-1583 ◽  
Author(s):  
JIN-HYEONG YOO ◽  
NORMAN M. WERELEY
Keyword(s):  
Quadratic Equation ◽  
Damping Coefficient ◽  
Viscous Damping ◽  
Uniform Field ◽  
Duct Flow ◽  
Equivalent Viscous Damping ◽  
Performance Metric ◽  
Annular Duct ◽  
Er Damper ◽  
Analytical Expressions

Approximate analytical expressions describing MR/ER damper performance for an axisymmetric annular duct under the assumption of uniform field are presented. The key performance metric is the damping coefficient, which is the ratio of the equivalent viscous damping constant, Ceq, to the Newtonian viscous damping constant, C. To develop these approximations, a quadratic equation was used to approximate the center of the plug location in the annular duct. This equation simplified the calculation of the annular duct solution without resorting to numerical methods to solve the boundary value problem. Approximations for the damping coefficient are developed on this basis.

Sign in / Sign up

Export Citation Format

Share Document