Constrained-Layer Damping of Torsional Vibration of Thin-Walled Tubes

2001 ◽  
Author(s):  
Samir A. Nayfeh
Keyword(s):  
Closed Form ◽  
Torsional Vibration ◽  
Unit Length ◽  
Constrained Layer Damping ◽  
Cross Sectional ◽  
Thin Walled ◽  
Viscoelastic Layers

Abstract In this paper, we take up the problem of damping torsional vibration of thin-walled tubes with closed sections. Assuming that the deformation obeys the Saint-Venant hypotheses, we develop a model suitable for predicting the complex stiffness per unit length in tubes with constrained viscoelastic layers over part or all of their perimeter. For some basic cross-sectional shapes, we solve the warping problem and thence obtain closed-form expressions for the complex stiffness per unit length. Finally, we provide some guidelines for the design of tubes with high damping in torsion.

scholarly journals Sensitivity analysis of free torsional vibration frequencies of thin-walled laminated beams under axial load

2019 ◽  
Vol 32 (5) ◽  
pp. 1347-1356 ◽  
Author(s):  
Czesław Szymczak ◽  
Marcin Kujawa
Keyword(s):  
Sensitivity Analysis ◽  
Cross Section ◽  
Torsional Vibration ◽  
Volume Fraction ◽  
Fibre Volume Fraction ◽  
Vibration Frequencies ◽  
Cross Sectional ◽  
First Order ◽  
Thin Walled ◽  
Frequency Changes

AbstractThe paper addresses sensitivity analysis of free torsional vibration frequencies of thin-walled beams of bisymmetric open cross section made of unidirectional fibre-reinforced laminate. The warping effect and the axial end load are taken into account. The consideration is based upon the classical theory of thin-walled beams of non-deformable cross section. The first-order sensitivity variation of the frequencies is derived with respect to the design variable variations. The beam cross-sectional dimensions and the material properties are assumed the design variables undergoing variations. The paper includes a numerical example related to simply supported I-beams and the distributions of sensitivity functions of frequencies along the beam axis. Accuracy is discussed of the first-order sensitivity analysis in the assessment of frequency changes due to the fibre volume fraction variable variations, and the effect of axial loads is discussed too.

Geometrical Stiffness of Thin-Walled I-Beam Element Based on Rigid-Beam Assemblage Concept

2012 ◽  
Vol 28 (1) ◽  
pp. 97-106 ◽  
Author(s):  
J. D. Yau ◽  
S.-R. Kuo
Keyword(s):  
Stiffness Matrix ◽  
Virtual Work ◽  
Bending Moment ◽  
Beam Element ◽  
Narrow Beam ◽  
Cross Sectional ◽  
Geometric Stiffness ◽  
Buckling Behavior ◽  
Post Buckling ◽  
Thin Walled

ABSTRACTUsing conventional virtual work method to derive geometric stiffness of a thin-walled beam element, researchers usually have to deal with nonlinear strains with high order terms and the induced moments caused by cross sectional stress results under rotations. To simplify the laborious procedure, this study decomposes an I-beam element into three narrow beam components in conjunction with geometrical hypothesis of rigid cross section. Then let us adopt Yanget al.'s simplified geometric stiffness matrix [kg]12×12of a rigid beam element as the basis of geometric stiffness of a narrow beam element. Finally, we can use rigid beam assemblage and stiffness transformation procedure to derivate the geometric stiffness matrix [kg]14×14of an I-beam element, in which two nodal warping deformations are included. From the derived [kg]14×14matrix, it can take into account the nature of various rotational moments, such as semi-tangential (ST) property for St. Venant torque and quasi-tangential (QT) property for both bending moment and warping torque. The applicability of the proposed [kg]14×14matrix to buckling problem and geometric nonlinear analysis of loaded I-shaped beam structures will be verified and compared with the results presented in existing literatures. Moreover, the post-buckling behavior of a centrally-load web-tapered I-beam with warping restraints will be investigated as well.

Modal Loss Factor Predication in Flexible Mechanism Systems With Constrain Viscoelastic Layers

1998 ◽  
Author(s):  
Zhang Xianmin ◽  
Liu Jike
Keyword(s):  
Equations Of Motion ◽  
Sandwich Beam ◽  
Viscoelastic Layer ◽  
Treatment Technique ◽  
Constrained Layer Damping ◽  
Modal Strain Energy ◽  
Frame Element ◽  
Modal Damping ◽  
Flexible Mechanism ◽  
Viscoelastic Layers

Abstract Control of dynamic vibration is critical to the operational success of many flexible mechanism systems. This paper addresses the problem of vibration control of such mechanisms through passive damping, using constrained layer damping treatment technique. A new type of shape function for three layer frame element containing a viscoelastic layer is developed. The equations of motion of the damped flexible mechanism are derived. Modal loss factors of this kind mechanisms are predicated from undamped normal mode by means of the modal strain energy method. Comparisons between the results obtained by this paper and the results obtained by exact solution of the governing equations for a well known sandwich beam demonstrate that the method presented in this paper is correct and reliable. Application of this method in predication of modal damping ratios for damped mechanisms is discussed. It is believed that the method of this paper hold the greatest potential for optimal design of damped flexible mechanism systems.

scholarly journals A Method for the Statistical Evaluation of Crosstalk Effect Between Three Parallel Conductors

1999 ◽  
Vol 22 (2) ◽  
pp. 111-119
Author(s):  
P. T. Trakadas ◽  
C. N. Capsalis
Keyword(s):  
Closed Form ◽  
Uniform Distribution ◽  
Transmission Lines ◽  
Statistical Evaluation ◽  
Unit Length ◽  
Surrounding Medium ◽  
Probabilistic Approach ◽  
Random Variable ◽  
Mutual Inductance ◽  
Theoretical Results

There are several cases at which, in order to evaluate the crosstalk effect among transmission lines carrying useful signals, there is a need for probabilistic approach. This paper considers the problem of crosstalk estimation between transmission lines consisting of three conductors in a homogeneous surrounding medium, where the distance between the conductors is a random variable described by uniform distribution. The transmission lines are considered as electrically short. A closed-form equation is developed for the statistical distribution of the per-unit-length mutual inductance(lm)and an analytical one is described for the evaluation of the per-unit-length capacitance(cm). Theoretical results are compared with simulated ones for validation purposes.

Torsional Stiffness of a Thin-Walled Beam Braced by Pinned or Rigidly Fixed Transverse Diaphragms

1973 ◽  
Vol 15 (5) ◽  
pp. 351-356
Author(s):  
T. Harrison ◽  
J. M. Siddall
Keyword(s):  
Experimental Evidence ◽  
Theoretical Work ◽  
Torsional Stiffness ◽  
Cross Sectional ◽  
Cross Sectional Profile ◽  
Thin Walled ◽  
Sectional Profile ◽  
Good Agreement

The torsional stiffness of a thin-walled beam of open cross-sectional profile braced by evenly spaced transverse diaphragms is studied. Diaphragms rigidly fixed or attached by frictionless pins are treated and it is seen that, in either case, the only effect is to modify the St Venant torsional constant for the thin-walled beam. The theoretical work is supported by experimental evidence from two braced perspex channels which simulate the two assumed methods of attaching the diaphragms. Good agreement is demonstrated.

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