Estimation of the severity of damage produced by a transverse crack

2020 ◽  
Vol 65 (1) ◽  
pp. 137-144
Author(s):  
Marius-Vasile Pop
Keyword(s):  
Transverse Crack ◽  
Bending Moment ◽  
Cantilever Beams ◽  
Trend Line ◽  
The Real ◽  
Symmetrical Deformation ◽  
Frequency Drop ◽  
Equidistant Points ◽  
Fixed End ◽  
Crack Position

This paper presents a method to find the severity of a crack for cantilever beams that can be used to estimate the frequency drop due to the crack. The severity is found for the crack located at the location where the biggest curvature (or bending moment) is achieved. Because the fixing condition does not permit a symmetrical deformation around the crack, the apparent severity is smaller as the real one. The latter is found by the estimated value of the trend-line at the fixed end, it being constructed on points that consider the crack position (equidistant points in the proximity of the fixed end) and the resulted deflections.

Dynamic Rate Effects on Timoshenko Beam Response

1985 ◽  
Vol 52 (2) ◽  
pp. 439-445 ◽  
Author(s):  
T. J. Ross
Keyword(s):  
Timoshenko Beam ◽  
Bending Moment ◽  
Laplace Transform Method ◽  
Transform Method ◽  
Rate Effects ◽  
The Laplace Transform ◽  
Step Loading ◽  
Fixed End ◽  
Constitutive Formulation ◽  
Viscoelastic Timoshenko Beam

The problem of a viscoelastic Timoshenko beam subjected to a transversely applied step-loading is solved using the Laplace transform method. It is established that the support shear force is amplified more than the support bending moment for a fixed-end beam when strain rate influences are accounted for implicitly in the viscoelastic constitutive formulation.

scholarly journals Flexural-Torsional Vibration of Thin-Walled Beams Subjected to Combined Initial Axial Load and End Bending Moment: Application to the Design of Saw Tooth Blades

2019 ◽  
Vol 2019 ◽  
pp. 1-11
Author(s):  
Van Binh Phung ◽  
Anh Tuan Nguyen ◽  
Hoang Minh Dang ◽  
Thanh-Phong Dao ◽  
V. N. Duc
Keyword(s):  
Boundary Conditions ◽  
Axial Load ◽  
Stability Boundary ◽  
Bending Moment ◽  
Element Analysis ◽  
The Finite Element Analysis ◽  
Rayleigh Method ◽  
Thin Walled ◽  
The Stability ◽  
Fixed End

The present paper analyzes the vibration issue of thin-walled beams under combined initial axial load and end moment in two cases with different boundary conditions, specifically the simply supported-end and the laterally fixed-end boundary conditions. The analytical expressions for the first natural frequencies of thin-walled beams were derived by two methods that are a method based on the existence of the roots theorem of differential equation systems and the Rayleigh method. In particular, the stability boundary of a beam can be determined directly from its first natural frequency expression. The analytical results are in good agreement with those from the finite element analysis software ANSYS Mechanical APDL. The research results obtained here are useful for those creating tooth blade designs of innovative frame saw machines.

Effect of Dielectric-Layer on the Stress Field of Micro Cantilever Beams at the Onset of Pull-In Instability

2013 ◽  
Vol 30 (1) ◽  
pp. 49-56 ◽  
Author(s):  
E. Yazdanpanahi ◽  
A. Noghrehabadi ◽  
M. Ghalambaz
Keyword(s):  
Stress Distribution ◽  
Dielectric Layer ◽  
Adomian Decomposition Method ◽  
Bending Moment ◽  
Distributed Parameter ◽  
Cantilever Beams ◽  
Layer Parameter ◽  
Adomian Decomposition ◽  
Micro Cantilever ◽  
Good Agreement

ABSTRACTIn this paper, stress distribution of micro cantilever beams in the presence of a dielectric-layer is studied using an analytic method. The Modified Adomian Decomposition Method (MADM) is applied to obtain a semi-analytical solution for a distributed parameter model of the micro cantilever beam. The important parameters for designing and manufacturing micro-actuators such as shear force, bending moment and stress distribution along the cantilevers are computed for different values of the dielectric-layer parameter. The results of MADM are compared with the numerical results, and they found in good agreement. It is found that increase of the dielectric-layer parameter increases the dimensionless pull-in voltage, tip deflection, internal stress and bending moment of the micro cantilever actuators at the onset of pull-in instability.

Elastic Analysis of Beam-Support Impact

1985 ◽  
Vol 107 (1) ◽  
pp. 64-67 ◽  
Author(s):  
M. A. Salmon ◽  
V. K. Verma ◽  
T. G. Youtsos
Keyword(s):  
Analytical Solutions ◽  
Beam Theory ◽  
Bending Moment ◽  
General Purpose ◽  
Euler Beam ◽  
Piping Systems ◽  
Euler Beam Theory ◽  
Impact Problems ◽  
Fixed End ◽  
Spring Support

The effect of gaps present in the seismic supports of nuclear piping systems has been studied with the use of such large general-purpose analysis codes as ANSYS. Exact analytical solutions to two simple beam-impact problems are obtained to serve as benchmarks for the evaluation of the ability of such codes to model impact between beam elements and their supports. Bernoulli-Euler beam theory and modal analysis are used to obtain analytical solutions for the motion of simply supported and fixed-end beams after impact with a spring support at midspan. The solutions are valid up to the time the beam loses contact with the spring support. Numerical results are obtained which show that convergence for both contact force and bending moment at the point of impact is slower as spring stiffness is increased. Finite element solutions obtained with ANSYS are compared to analytical results and good agreement is obtained.

The Vibrational Behavior of a Turbine Rotor Containing a Transverse Crack

1980 ◽  
Vol 102 (1) ◽  
pp. 140-146 ◽  
Author(s):  
B. Grabowski
Keyword(s):  
Theoretical Model ◽  
Modal Analysis ◽  
Transverse Crack ◽  
Strong Dependence ◽  
Turbine Rotor ◽  
Time Variable ◽  
Vibrational Behavior ◽  
Variable System ◽  
Crack Position

A modal formulation is used to investigate the vibrational behavior of flexible single or coupled rotors containing a transverse crack. A theoretical model has been developed to simulate the crack mechanism. The transformed time variable system is numerically integrated. The modal analysis shows particularly the strong dependence of the vibrational behavior on the crack position. The vibrations, excited by the crack, are independent of the unbalance.

scholarly journals Identifying the cause of cutting tool failure by using simulation software

2018 ◽  
Vol 157 ◽  
pp. 02057
Author(s):  
Andrej Zrak ◽  
Radoslav Koňár
Keyword(s):  
Opposite Direction ◽  
Cutting Tool ◽  
Cutting Tools ◽  
Bending Moment ◽  
Simulation Software ◽  
Tool Failure ◽  
The Real

The article is focused on the construction problems of cutting tools designed for manufacturing components in high numbers. Analysis of the tool with low lifetime is provided with the use of simulation software to detect the causes of the tool failure. Parameters of the simulation are close to the real conditions of the tool in production. The results from the simulation indicate that the bending moment occurs in the tool because of forces which have opposite direction on different areas. On these basis technological adjustments are made. These adjustments are also analysed by using simulation software.

The Best Position to Determine the Hinge in the Cantilever Bridge

2014 ◽  
Vol 578-579 ◽  
pp. 814-817
Author(s):  
Chun Lei Liu ◽  
Su Juan Dai
Keyword(s):  
Optimum Design ◽  
Bending Moment ◽  
Internal Force ◽  
Cantilever Beams ◽  
Structure Form ◽  
Absolute Value ◽  
Large Span ◽  
Common Structure ◽  
Negative Bending ◽  
Beam Bridge

The simple-supported beam bridge is a common structure form widely used in small and medium span bridges. When the span is longer, the maximum bending moment is accordingly bigger. The maximum positive and negative bending moment numerical of beam decreases obviously because of cantilever bridge with cantilever beams to reduce the amount of materials. This article analyzes the current commonly used cantilever bridge with large span. The two-span cantilever bridge is analyzed under various loads about the internal force according to the condition of the absolute value of the maximum positive and negative bending moment being equal. It carries on the contrast and analysis about simple-supported beam bridges and obtains the best location of the hinge in the cantilever bridge. Moreover, it provides some reference for the optimum design of similar bridges and projects.

Investigation of stresses at the fixed end of deep cantilever beams

1998 ◽  
Vol 69 (3) ◽  
pp. 329-338 ◽  
Author(s):  
S.R. Ahmed ◽  
M.R. Khan ◽  
K.M.S. Islam ◽  
Md.W. Uddin
Keyword(s):  
Cantilever Beams ◽  
Fixed End

Crack Position and Depth Identification in Rotating Shafts: Part 1— Theoretical Model

2005 ◽  
Author(s):  
Nicolo` Bachschmid ◽  
Paolo Pennacchi ◽  
Andrea Vania
Keyword(s):  
Finite Element ◽  
Transverse Crack ◽  
Crack Identification ◽  
Finite Element Models ◽  
Equivalent System ◽  
Identification Method ◽  
Rotating Shafts ◽  
Breathing Mechanism ◽  
Crack Position ◽  
Relative Theory

This paper presents a model based transverse crack identification method in rotating shafts suitable for industrial machines. The identification method and the relative theory is fully discussed, by presenting the breathing mechanism of the crack, the equivalent system of forces, which excites the vibrations of rotating shafts, the way to localize the crack position along the shaft and finally to identify the depth of the crack. This is obtained by using standard finite element models of the machine and the vibration measured in the bearings only, as usual in industrial machines. The proposed method will be validated by means of experimental results which are described in detail in the second part of the paper.

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