Static instability of an elastically restrained cantilever under a partial follower force

AIAA Journal ◽  
1985 ◽  
Vol 23 (10) ◽  
pp. 1637-1639 ◽  
Author(s):  
Lech Tomski ◽  
Jacek Przybylski
Keyword(s):  
Follower Force ◽  
Static Instability ◽  
Elastically Restrained

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.

A Study of the Hydroelastic Instabilities of Supercavitating Hydrofoils

1960 ◽  
Vol 4 (04) ◽  
pp. 28-38
Author(s):  
Paul Kaplan ◽  
C. J. Henry
Keyword(s):  
Dynamic Instability ◽  
Experimental Studies ◽  
Surface Flow ◽  
Small Range ◽  
Equal Importance ◽  
Static Instability ◽  
Elastically Restrained ◽  
Density Ratios ◽  
Oscillating Foil ◽  
Stream Direction

Presented herein are the results of a theoretical study of the static and dynamic hydroelastic instabilities of rigid supercavitating hydrofoils on elastic supports. A two-dimensional theory is used to define the unsteady hydrodynamic force and moment acting on the oscillating foil, which is assumed to be elastically restrained in translation normal to the free-stream direction and in rotation about a prescribed axis which is normal to the plane of flow. All other motions are neglected. The effects of variation in the elastic and inertial properties, as well as the effect of varying the position of the upper surface flow-separation point on the possibility of either form of instability, are determined. Also, the effect of cavitation number over a small range near zero is hypothesized. The theory predicts that dynamic instability (bending-torsion flutter) is possible at the density ratios typical of supercavitating operation. This is in contrast to the results for fully-wetted flow, where the occurrence of flutter is unlikely at the structural-to-fluid density ratios typical of hydrodynamic operation. The flutter possible in supercavitated operation is also more severe than that indicated for fully-wetted flow. Furthermore, it is shown that for the supercavitating hydrofoil, static instability (torsional divergence) and dynamic instability are of equal importance which again differs from the results in fully-wetted flow where static instability was shown to be the more important practical problem. Recommendations are made for experimental studies to verify these theoretical results.

ACTIVE CONTROL OF AN FGM BEAM UNDER FOLLOWER FORCE WITH PIEZOELECTRIC SENSORS/ACTUATORS

2014 ◽  
Vol 14 (02) ◽  
pp. 1350063 ◽  
Author(s):  
VAHID AZADI ◽  
MOHAMMAD AZADI ◽  
S. AHMAD FAZELZADEH ◽  
EMAD AZADI
Keyword(s):  
Volume Fraction ◽  
Functionally Graded ◽  
Follower Force ◽  
Generalized Function ◽  
Power Law Distribution ◽  
Lumped Mass ◽  
Sensors And Actuators ◽  
Generalized Function Theory ◽  
Graded Material ◽  
Elastically Restrained

In this paper, an active controller is used to suppress the flutter vibration of a beam. The beam is made of Functionally Graded Material (FGM) and subjected to a follower force and arbitrary lumped mass. The properties of the FGM layer are functionally graded in the thickness direction according to the volume fraction power law distribution. The piezoelectric layers, which are attached to both sides of the beam, are used as sensors and actuators. The beam is fixed from one end and elastically restrained by a spring at the other end. To investigate the effect of the controller on the vibration response of the beam, parameters such as the follower force, spring stiffness, mass ratio and attachment location are included in the analysis based on the generalized function theory and Lagrange–Rayleigh–Ritz technique. The vibration responses of the system are presented in the simulation results, where excellent agreement of the controller scheme is observed.

BUCKLING AND FLUTTER OF A COLUMN ENHANCED BY PIEZOELECTRIC LAYERS AND LUMPED MASS UNDER A FOLLOWER FORCE

2010 ◽  
Vol 10 (05) ◽  
pp. 1083-1097 ◽  
Author(s):  
S. A. FAZELZADEH ◽  
M. EGHTESAD ◽  
M. AZADI
Keyword(s):  
Function Theory ◽  
Follower Force ◽  
Design Parameters ◽  
Generalized Function ◽  
Spring Stiffness ◽  
Mass Ratio ◽  
Lumped Mass ◽  
Generalized Function Theory ◽  
Piezoelectric Layers ◽  
Elastically Restrained

In this paper, enhancement of the buckling and flutter capacities of a column by the attachment of an arbitrary lumped mass and a pair of piezoelectric layers on the column sides are studied. The column is subjected to a follower force, with one end fixed and the other end elastically restrained by a spring. To investigate the effects of the piezoelectric layers on the column instability capacity and frequency, parameters such as the follower force, spring stiffness, and mass ratio and attachment location are included in the analysis based on the generalized function theory and Lagrange–Rayleigh–Ritz technique. The numerical results reveal that if each of the design parameters of the piezoelectric layers, follower force, spring stiffness, or external mass exceeds a certain critical value, the column will undergo buckling and flutter instabilities. Besides, comparisons are made with available results in the literature and excellent agreement is observed.

Dynamic stability of a free-free cylindrical shell under a follower force

AIAA Journal ◽  
2000 ◽  
Vol 38 ◽  
pp. 1070-1077
Author(s):  
Si-Hyoung Park ◽  
Ji-Hwan Kim
Keyword(s):  
Cylindrical Shell ◽  
Dynamic Stability ◽  
Follower Force

Shape‐optimized Cantilevered Columns under a Rocket‐based Follower Force

2021 ◽  
pp. 201-227
Author(s):  
Yoshihiko Sugiyama ◽  
Mikael A. Langthjem ◽  
Kazuo Katayama
Keyword(s):  
Follower Force
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