FREE VIBRATION OF A STRING WITH MOVING BOUNDARY CONDITIONS BY THE METHOD OF DISTORTED IMAGES

1996 ◽  
Vol 194 (1) ◽  
pp. 35-47 ◽  
Author(s):  
Y.M. Ram ◽  
J. Caldwell
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Moving Boundary ◽  
Vibration Of A String

A New Wave Technique for Free Vibration of a String With Time-Varying Length

2001 ◽  
Vol 69 (1) ◽  
pp. 83-87 ◽  
Author(s):  
S.-Y. Lee ◽  
M. Lee
Keyword(s):  
Free Vibration ◽  
Traveling Waves ◽  
Moving Boundary ◽  
Transverse Velocity ◽  
Vibration Energy ◽  
Time Varying ◽  
New Wave ◽  
Wave Technique ◽  
Varying Length ◽  
Vibration Of A String

We introduce a new technique to analyze free vibration of a string with time-varying length by dealing with traveling waves. When the string length is varied, the natural frequencies and vibration energy are not constant. Thus, free response is not represented by discrete standing waves but by traveling waves, and a given phase of oscillation travels along the string. String tension and nonzero instantaneous transverse velocity at the moving boundary results in energy variation. When the string undergoes retraction, free vibration energy increases exponentially with time, causing dynamic instability. The new wave technique gives the time-varying natural frequency and the exact amount of energy transferred into the vibrating string at the moving boundary.

Axisymmetric flow near the critical point on the moving boundary

2010 ◽  
Vol 7 ◽  
pp. 182-190
Author(s):  
I.Sh. Nasibullayev ◽  
E.Sh. Nasibullaeva
Keyword(s):  
Fluid Flow ◽  
Finite Difference ◽  
Boundary Conditions ◽  
Numerical Solution ◽  
Axial Velocity ◽  
Moving Boundary ◽  
Axisymmetric Flow ◽  
Boundary Motion ◽  
Newton Raphson ◽  
Raphson Method

In this paper the investigation of the axisymmetric flow of a liquid with a boundary perpendicular to the flow is considered. Analytical equations are derived for the radial and axial velocity and pressure components of fluid flow in a pipe of finite length with a movable right boundary, and boundary conditions on the moving boundary are also defined. A numerical solution of the problem on a finite-difference grid by the iterative Newton-Raphson method for various velocities of the boundary motion is obtained.

Analysis of vibration in rotating pretwisted functionally graded graphene platelets reinforced nanocomposite laminated blades with an attached point mass

2021 ◽  
pp. 095440622110084
Author(s):  
Amin Ghorbani Shenas ◽  
Parviz Malekzadeh ◽  
Sima Ziaee
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Polymer Matrix ◽  
Natural Frequencies ◽  
Weight Fraction ◽  
Functionally Graded ◽  
Point Mass ◽  
Attached Mass ◽  
Graphene Platelets ◽  
Twisted Beam

This work presents an investigation on the free vibration behavior of rotating pre-twisted functionally graded graphene platelets reinforced composite (FG-GPLRC) laminated blades/beams with an attached point mass. The considered beams are constituted of [Formula: see text] layers which are bonded perfectly and made of a mixture of isotropic polymer matrix and graphene platelets (GPLs). The weight fraction of GPLs changes in a layer-wise manner. The effective material properties of FG-GPLRC layers are computed by using the modified Halpin-Tsai model together with rule of mixture. The free vibration eigenvalue equations are developed based on the Reddy’s third-order shear deformation theory (TSDT) using the Chebyshev–Ritz method under different boundary conditions. After validating the approach, the influences of the GPLs distribution pattern, GPLs weight fraction, angular velocity, the variation of the angle of twist along the beam axis, the ratio of attached mass to the beam mass, boundary conditions, position of attached mass, and geometry on the vibration behavior are investigated. The findings demonstrate that the natural frequencies of the rotating pre-twisted FG-GPLRC laminated beams significantly increases by adding a very small amount of GPLs into polymer matrix. It is shown that placing more GPLs near the top and bottom surfaces of the pre-twisted beam is an effective way to strengthen the pre-twisted beam stiffness and increase the natural frequencies.

scholarly journals Free Vibration Analysis of a Graphene-Reinforced Porous Composite Plate with Different Boundary Conditions

Materials ◽  
2021 ◽  
Vol 14 (14) ◽  
pp. 3879
Author(s):  
Hong-Gang Pan ◽  
Yun-Shi Wu ◽  
Jian-Nan Zhou ◽  
Yan-Ming Fu ◽  
Xin Liang ◽  
...  
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Composite Plate ◽  
Porous Plate ◽  
Micromechanical Model ◽  
Value Added ◽  
Porous Composite ◽  
Finite Element Software ◽  
Free Vibration Frequency ◽  
Graphene Platelets

Plates are commonly used in many engineering disciplines, including aerospace. With the continuous improvement in the capacity of high value-added airplanes, large transport aircrafts, and fighter planes that have high strength, high toughness, and corrosion resistance have gradually become the development direction of airplane plate structure production and research. The strength and stability of metal plate structures can be improved by adding reinforced materials. This paper studies graphene platelets (GPLs) reinforced with a free vibration porous composite plate. The porous plate is constructed with a multi-layer model in a metal matrix containing uniform or non-uniformly distributed open-cell internal pores. Considering the random and directional arrangement of graphene platelets in the matrix, the elastic modulus of graphene composites was estimated using the Halpin–Tsai micromechanical model, and the vibration frequencies of graphene composite were calculated using the differential quadrature method. The effects of the total number of layers, GPL distribution pattern, porosity coefficient, GPL weight fraction, and boundary conditions on the free vibration frequency of GPLs reinforced porous composite plates are studied, and the accuracy of the conclusions are verified by the finite element software.

scholarly journals Out-of-Plane Vibration of Curved Uniform and Tapered Beams with Additional Mass

2017 ◽  
Vol 2017 ◽  
pp. 1-8 ◽  
Author(s):  
Hamdi Alper Özyiğit ◽  
Mehmet Yetmez ◽  
Utku Uzun
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Boundary Conditions ◽  
Natural Frequencies ◽  
Variable Cross ◽  
Additional Mass ◽  
Inertia Effects ◽  
Tapered Beam ◽  
Out Of Plane ◽  
Good Agreement

As there is a gap in literature about out-of-plane vibrations of curved and variable cross-sectioned beams, the aim of this study is to analyze the free out-of-plane vibrations of curved beams which are symmetrically and nonsymmetrically tapered. Out-of-plane free vibration of curved uniform and tapered beams with additional mass is also investigated. Finite element method is used for all analyses. Curvature type is assumed to be circular. For the different boundary conditions, natural frequencies of both symmetrical and unsymmetrical tapered beams are given together with that of uniform tapered beam. Bending, torsional, and rotary inertia effects are considered with respect to no-shear effect. Variations of natural frequencies with additional mass and the mass location are examined. Results are given in tabular form. It is concluded that (i) for the uniform tapered beam there is a good agreement between the results of this study and that of literature and (ii) for the symmetrical curved tapered beam there is also a good agreement between the results of this study and that of a finite element model by using MSC.Marc. Results of out-of-plane free vibration of symmetrically tapered beams for specified boundary conditions are addressed.

NUMERICAL AND EXPERIMENTAL STUDY ON FREE VIBRATION OF DELAMINATED WOVEN FIBER GLASS/EPOXY COMPOSITE PLATES

2012 ◽  
Vol 12 (02) ◽  
pp. 377-394 ◽  
Author(s):  
J. MOHANTY ◽  
S. K. SAHU ◽  
P. K. PARHI
Keyword(s):  
Experimental Study ◽  
Aspect Ratio ◽  
Free Vibration ◽  
Boundary Conditions ◽  
Natural Frequencies ◽  
Numerical Study ◽  
Shear Deformation Theory ◽  
Composite Plates ◽  
Fiber Glass ◽  
Number Of Layers

This paper presents a combined experimental and numerical study of free vibration of industry-driven woven fiber glass/epoxy (G/E) composite plates with delamination. Using the first-order shear deformation theory, an eight-noded two-dimensional quadratic isoparametric element was developed, which has five degrees of freedom per node. In the experimental study, the influence of various parameters such as the delamination size, boundary conditions, fiber orientations, number of layers, and aspect ratio on the natural frequencies of delaminated composite plates are investigated. Comparison of the numerical results with experimental ones shows good agreement. Fundamental natural frequencies are found to decrease with the increase in the delamination size and fiber orientation and increases with the increase in the number of layers and aspect ratio of delaminated composite plates. The natural frequency of the delaminated composite plate varies significantly for different boundary conditions.

Free Vibration Energy and Period of a String With Time-Varying Length

2000 ◽  
Author(s):  
Seung-Yop Lee
Keyword(s):  
Free Vibration ◽  
Traveling Waves ◽  
Moving Boundary ◽  
String Tension ◽  
New Technique ◽  
Vibration Energy ◽  
Time Varying ◽  
Constant Rate ◽  
Varying Length ◽  
A New Technique

Abstract We introduce a new technique to analyze free vibration energy and natural frequencies of a string with time-varying length by dealing with traveling waves. One of boundaries is vertically fixed but it moves axially at a constant rate. When the string length is varied, the free vibration energy and period also change with time. String tension and non-zero instantaneous vertical velocity at the moving boundary results in the energy variation. When the string undergoes retraction, the vibration energy increases with time. The new technique using traveling waves gives the exact amount of energy transferred into the vibrating system at the moving boundary. The free vibration energy are compared with previous results using the perturbation method and Kotera’s approach.

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