The Fundamental Flexural Vibration of a Cantilever Beam of Rectangular Cross Section with Uniform Taper

1965 ◽  
Vol 16 (2) ◽  
pp. 139-144 ◽  
Author(s):  
J. S. Rao
Keyword(s):  
Galerkin Method ◽  
Natural Frequency ◽  
Cantilever Beam ◽  
Cross Section ◽  
Rectangular Cross Section ◽  
Flexural Vibration ◽  
The Other ◽  
Correction Factors ◽  
Flexural Mode ◽  
The Galerkin Method

SummaryAn attempt has been made to determine the natural frequency of fundamental flexural mode of a cantilever beam with uniform taper by the Galerkin method. The method suggested considerably reduces the calculations as compared with the other methods available and the results are checked with the correction factors derived by Martin.

scholarly journals Estimation of Reduced Stiffness under the Influence of Crack in a Beam

2019 ◽  
Vol 9 (1) ◽  
pp. 711-714
Keyword(s):  
Natural Frequency ◽  
Cantilever Beam ◽  
Cross Section ◽  
Loading Condition ◽  
Dynamic Behaviour ◽  
Rectangular Cross Section ◽  
Fatigue Loading ◽  
Stiffness Reduction ◽  
Modes Of Vibration ◽  
The Relationship

Machine components with cantilever boundary conditions are most prominently used in mechanical engineering applications. When such components are subjected to fatigue loading, crack may get initiated and failure may occur. In order to prevent catastrophic failure and safe guard these components one has to condition monitor the dynamic behavior under fatigue loading condition. Vibration based condition monitoring is one of the most effective method to assess the fatigue failure of the component. In this paper, a cantilever beam is analyzed for its dynamic behaviour under the influence of crack. The cantilever beam considered for the analysis is of rectangular cross section and is uniform throughout its length. The characteristic equation was derived for the Euler-Bernoulli cantilever beam to obtain the relationship between the location of the crack and stiffness of the beam because the stiffness of the beam influences the natural frequency. It is found that the stiffness of the cantilever beam is varying for varying locations of the crack in different modes of vibration. It is clearly understood from the analysis that the vibration response of the cracked cantilever beam in its modes of vibration is affected by the corresponding stiffness reduction based upon the location of the crack. So, it can be inferred that the natural frequency of the cracked cantilever beam may have different values for different locations of the crack.

scholarly journals Behavior of reinforced concrete columns strenghtened by partial jacketing

2016 ◽  
Vol 9 (1) ◽  
pp. 1-21 ◽  
Author(s):  
D. B. FERREIRA ◽  
R. B. GOMES ◽  
A. L. CARVALHO ◽  
G. N. GUIMARÃES
Keyword(s):  
Reinforced Concrete ◽  
Cross Section ◽  
Rectangular Cross Section ◽  
Concrete Columns ◽  
The Other ◽  
Self Compacting Concrete ◽  
Reinforced Concrete Columns ◽  
Compressive Stresses ◽  
Concrete Layer ◽  
Ultimate Resistance

This article presents the study of reinforced concrete columns strengthened using a partial jacket consisting of a 35mm self-compacting concrete layer added to its most compressed face and tested in combined compression and uniaxial bending until rupture. Wedge bolt connectors were used to increase bond at the interface between the two concrete layers of different ages. Seven 2000 mm long columns were tested. Two columns were cast monolithically and named PO (original column) e PR (reference column). The other five columns were strengthened using a new 35 mm thick self-compacting concrete layer attached to the column face subjected to highest compressive stresses. Column PO had a 120mm by 250 mm rectangular cross section and other columns had a 155 mm by 250mm cross section after the strengthening procedure. Results show that the ultimate resistance of the strengthened columns was more than three times the ultimate resistance of the original column PO, indicating the effectiveness of the strengthening procedure. Detachment of the new concrete layer with concrete crushing and steel yielding occurred in the strengthened columns.

Experimental Analysis of Vortex Induced Vibration in the Bladeless Small Wind Turbine

2019 ◽  
Author(s):  
Micha Premkumar Thomai ◽  
Lasoodawanki Kharsati ◽  
Nakandhrakumar Rama Samy ◽  
Seralathan Sivamani ◽  
Hariram Venkatesan
Keyword(s):  
Energy Conversion ◽  
Wind Turbine ◽  
Natural Frequency ◽  
Cross Section ◽  
Vortex Shedding ◽  
Rectangular Cross Section ◽  
The Body ◽  
Test Facility ◽  
Vortex Induced Vibration ◽  
Small Wind Turbine

Abstract Vortex-induced vibration is one of the predominant fundamental concepts for forced oscillation which attracts considerable practical engineering application for energy conversion. In this work, an oscillation of a mast arising as a result of wind force is utilized for energy conversion. The paradigm for energy conversion from vortex-induced vibration in the mast is the bladeless wind turbine. It consists of a rigid mass known as a mast, fixed in the spring of stiffness (k) and allowed to oscillate along the direction of the flow. In this work, four different types of mast have been fabricated and tested. The first is uniform tapered hollow conical mast (MAST1), the cross-section of the second is uniform tapered plus symbol (MAST2), the third is uniform tapered inversed plus symbol (MAST3) and the fourth is uniform tapered simple rectangular cross-section (MAST4). All the masts were fabricated using fiber carbon. The experiments were conducted in a versatile small wind turbine testing facility of Hindustan Institute of Technology and Science, Chennai. This test facility contained an open jet wind tunnel with variable frequency drive and other measuring instruments. The vibration sensor was located in the mast where it experienced a large oscillation in a free stream. In this experiment, an increase in wind velocity led to a terrible change in the amplitude of vibration. A vigorous oscillation was experienced in this mast at this critical frequency, when the natural frequency of the mast was synchronized with the frequency of the vortex shedding and the frequency of the oscillation of the mast. The total force in this oscillation was a summation of the body force due to the mass of the mast and vorticity force that is mainly which was the result of the shedding of the vortices. In this work, extensive studies have been carried out for Reynolds number ranging from 2.5 × 105 to 5.0 × 105. The mast length to diameter ratio of 13 was exposed to various speeds of wind and response was measured. The occurrence of the maximum oscillation in a simple rectangular mast was seen where vortex shedding due to the bluff body was large for constant mass and spring stiffness. The frequency of the oscillation at maximum amplitude of the rectangular cross-section mast was equal to the natural frequency, due to vortices shedding at critical velocity. This demonstrated the appropriateness of the simple rectangular cross-section for harnessing the low rated wind energy and its suitability for renewable energy conversion in the small bladeless wind turbine.

Dynamics of a Cantilever Beam With Attached Pendulum

2001 ◽  
Author(s):  
Danuta Sado
Keyword(s):  
Differential Equations ◽  
Galerkin Method ◽  
Cantilever Beam ◽  
Weakly Nonlinear ◽  
Second Mode ◽  
Linear Viscoelastic ◽  
Nonlinear Pendulum ◽  
Analysis Of Dynamics ◽  
The Galerkin Method ◽  
Euler Bernoulli Beam

Abstract This work draws attention to the to the analysis of dynamics of a nonlinear coupled cantilever beam-pendulum oscillator. Dynamical systems of this type have important technical applications, because many mechanical components consist of linear or weakly nonlinear continuos substructures such as beam coupled to nonlinear oscillators. The present paper is a continuation of the author’s previous work where in applying the Galerkin method the modal series was truncated at the first mode. In this work it is assumed that the cantilever beam behaves like an Euler-Bernoulli beam and to its end pendulum is attached. The integro-differential equations are transformed into an ordinary differential equations with the use of Galerkin procedure with beam functions. In this study, in applying the Galerkin method the modal series was truncated at the second mode. Next these equations were solved numerically and there was studied the effect of the internal friction on energy transfer in a coupled structure that consist of a linear viscoelastic beam supporting at its tip a nonlinear pendulum.

Mechanics of magnetic robots akin to soft beams supported at unanchored contacts

2021 ◽  
pp. 1-39
Author(s):  
Amanda De Oliveira Barros ◽  
Sukalyan Bhattacharya ◽  
James Yang
Keyword(s):  
Cross Section ◽  
Mathematical Theory ◽  
Numerical Scheme ◽  
Rectangular Cross Section ◽  
The Other ◽  
Theoretical Simulation ◽  
Multiple Contacts ◽  
Dimensional Parameters ◽  
Novel Algorithm ◽  
Single Contact

Abstract This article presents a novel algorithm to predict the shape and the support configurations of a magnetic robot acting like a supple beam which deforms due to an imposed magnetic field. The soft magnet loosely rests on a flat horizontal surface which provides the pivoting supports to the robot to attain its deformed shape. The key difficulty in analysis of the mechanics is the lack of any prior knowledge about the location of the contacts where the distorted beam finds support from the ground. This paper outlines an algorithm in which different possibilities referred to as modes are checked systematically to locate the placement and the nature of such supports. Consequently, the 2D shape of the soft beam can be determined without any heuristic assumption about where the magnetic robot is touching the solid surface. This work focuses on single contact sections although the algorithm idea is valid for multiple contacts as well. The mathematical theory and the numerical scheme are validated by comparing the simulated results with existing experimentally obtained configurations. Also, the parametric space of system-defining non-dimensional parameters is explored to determine when a transition happens from one mode to another, and which magnetization methods are desirable for higher stability. Through theoretical simulation the results show that a thin rectangular cross-section provides higher deformation when compared to the other two tested shapes (circular and equilateral triangle cross-section).

The NAVMI Factor and Natural Frequency of a Circular Plate Exposed to Water in Flexural Vibration

2011 ◽  
Vol 199-200 ◽  
pp. 1445-1450
Author(s):  
Hui Juan Ren ◽  
Mei Ping Sheng
Keyword(s):  
Boundary Condition ◽  
Natural Frequency ◽  
Circular Plate ◽  
Natural Frequencies ◽  
Integration Method ◽  
Flexural Vibration ◽  
The Other ◽  
Additional Mass ◽  
Simply Supported ◽  
Higher Order Modes

The expression of NAVMI factor and the natural frequency of a circular plate, which is placed in a hole of an infinite grid wall with one side exposed to water, are derived from the viewpoint of the additional mass. 10 Nodes Gauss-Legender integration method and the iteration method are employed to obtain the numerical results of the NAVMI factors, AVMI factors and the natural frequencies. It can be found from the results that NAVMI factors of the first two order modes are far bigger than those of the other modes when the boundary condition of a circular plate is certain. The first two order modal NAVMI factors of the circular plate with clamped and simply supported boundary conditions are far bigger than those of the circular plate with free-edged boundary condition, and the NAVMI factors are almost the same for the three order or much higher order modes regardless of the boundary condition. It is also observed that the natural frequencies of the circular plate exposed to water are smaller than those exposed to air, and the natural frequencies of the circular plate exposed to water with both sides are smaller than those of the circular plate exposed to water with one side.

Numerical Computation of Flow in Rotating Ducts

1977 ◽  
Vol 99 (1) ◽  
pp. 148-153 ◽  
Author(s):  
A. K. Majumdar ◽  
V. S. Pratap ◽  
D. B. Spalding
Keyword(s):  
Experimental Data ◽  
Kinetic Energy ◽  
Finite Difference ◽  
Numerical Computation ◽  
Cross Section ◽  
Dissipation Rate ◽  
Rectangular Cross Section ◽  
Longitudinal Direction ◽  
The Other ◽  
Constant Area

A finite-difference procedure is employed to predict the turbulent flow in ducts of rectangular cross-section, rotating about an axis normal to the longitudinal direction. The flows were treated as “parabolic” and the turbulence model used involved the solution of two differential equations, one for the kinetic energy of the turbulence and the other for its dissipation rate. Agreement with experimental data is good for a constant-area duct at low rotation, but less satisfactory for a divergent duct at larger rotation. It is argued that a “partially-parabolic” procedure will be needed to predict the latter flow correctly.

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