Influence of Axial Boundary Conditions on Free Spanning Pipeline Natural Frequencies

2013 ◽  
Author(s):  
Gareth L. Forbes ◽  
Ahmed M. Reda
Keyword(s):  
Boundary Conditions ◽  
Exact Solutions ◽  
Theoretical Calculation ◽  
Natural Frequency ◽  
Natural Frequencies ◽  
Axial Stiffness ◽  
Simple Boundary ◽  
Complex Boundary

The effect of axial restraint (boundary conditions) on the natural frequency of a free spanning pipeline is examined in this paper. Theoretical calculation of the natural frequency of a straight pipeline with simple boundary conditions is a trivial task with exact solutions being available. A pipeline lying on the seabed however is neither completely straight and the interaction with the soil at the span shoulders create more complex boundary conditions. DNV-RP-F105 provides guidance on the calculation of free span boundary conditions with these increased complexities. The DNV recommended practice does not however take into account the effect of the axial restraint on the natural frequency. Results are presented in this paper for a range of axial stiffness combined with span out of straightness for a free spanning pipeline. The results presented show that the effect of axial restraint for moderately out of straight free spans can cause significant deviation in the calculation of the span natural frequency.

scholarly journals Identification of Corrosion on a Hollow Tube Using Vibration

2014 ◽  
Vol 564 ◽  
pp. 176-181
Author(s):  
S.T. Cheng ◽  
Nawal Aswan Abdul Jalil ◽  
Zamir A. Zulkefli
Keyword(s):  
Free Boundary ◽  
Boundary Conditions ◽  
Natural Frequency ◽  
Impact Loading ◽  
Structural Damage ◽  
Natural Frequencies ◽  
Localized Corrosion ◽  
Free Boundary Conditions ◽  
The Impact ◽  
Impact Vibration

Vibration based technique have so far been focused on the identification of structural damage. However, not many studies have been conducted on the corrosion identification on pipes. The objective of this paper is to identify corrosion on pipes from vibration measurements. A hollow pipe, 500 mm in length with 63.5 mm in diameter was subjected to impact loading using an impact hammer to identify the natural frequency of the tube in two conditions i) without any corrosion and ii) with an induced localized 40 mm by 40 mm corrosion at the middle of the pipe. The shift of natural frequencies of the structures under free boundary conditions was examined for each node of excitation. The results showed that there is a shift in natural frequency of the pipe, between 3 and 4 Hz near to the corrosion area. It can suggested that that the impact vibration is capable of identifying of localized corrosion on a hollow tube.

scholarly journals Analysis of Timoshenko beam with Koch snowflake cross-section and variable properties in different boundary conditions using finite element method

2021 ◽  
Vol 13 (11) ◽  
pp. 168781402110609
Author(s):  
Hossein Talebi Rostami ◽  
Maryam Fallah Najafabadi ◽  
Davood Domiri Ganji
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Boundary Conditions ◽  
Natural Frequency ◽  
Cross Section ◽  
Timoshenko Beam ◽  
Natural Frequencies ◽  
Variable Properties ◽  
The Third ◽  
Koch Snowflake

This study analyzed a Timoshenko beam with Koch snowflake cross-section in different boundary conditions and for variable properties. The equation of motion was solved by the finite element method and verified by Solidworks simulation in a way that the maximum error was about 2.9% for natural frequencies. Displacement and natural frequency for each case presented and compared to other cases. Significant research achievements illustrate that if we change the Koch snowflake cross-section of the beam from the first iteration to the second, the area and moment of inertia will increase, and we have a 5.2% rise in the first natural frequency. Similarly, by changing the cross-section from the second iteration to the third, a 10.2% growth is observed. Also, the hollow cross-section is considered, which can enlarge the natural frequency by about 26.37% compared to a solid one. Moreover, all the clamped-clamped, hinged-hinged, clamped-free, and free-free boundary conditions have the highest natural frequency for the Timoshenko beam with the third iteration of the Koch snowflake cross-section in solid mode. Finally, examining important physical parameters demonstrates that variable density from a minimum value to the standard value along the beam increases the natural frequencies, while variable elastic modulus decreases it.

Vibration Characteristic Analysis of V-Shaped Electrothermal Microactuator

2012 ◽  
Vol 503 ◽  
pp. 118-121
Author(s):  
Zhen Lu Wang ◽  
Xue Jin Shen ◽  
Ling Zhou ◽  
Xiao Yang Chen
Keyword(s):  
Theoretical Calculation ◽  
Natural Frequency ◽  
Mechanical Model ◽  
Natural Frequencies ◽  
Maximum Error ◽  
Vibration Characteristic ◽  
Characteristic Analysis ◽  
Element Analysis ◽  
The Finite Element Analysis

This paper is focused on the finite element analysis (FEA) and theoretical calculation of vibration characterization of V-shaped electrothermal microactuator. A vibration mechanical model about V-shaped electrothermal microactuator is presented. By having a comparison between FEA and theoretical calculation about natural frequencies of V-shaped electrothermal microactuator, the maximum error is within 0.19 %. This paper also analyzes the influences of microactuator geometric parameters on natural frequency. The length and thickness have larger effect on the natural frequency of the actuator, while the angle and width have less effect on the natural frequency.

Integral Solution of Diffusion Equation: Part 2—Boundary Conditions of Second and Third Kinds

1987 ◽  
Vol 109 (3) ◽  
pp. 557-562 ◽  
Author(s):  
A. Haji-Sheikh ◽  
R. Lakshminarayanan
Keyword(s):  
Diffusion Equation ◽  
Boundary Conditions ◽  
Exact Solutions ◽  
Green’S Function ◽  
Green's Function ◽  
Buried Pipe ◽  
Square Enclosure ◽  
Complex Boundary ◽  
The Galerkin Method ◽  
Numerical Complexity

An analytical solution of the diffusion equation using the Galerkin method to calculate the eigenvalues is currently available for boundary conditions of the first kind. This paper includes algebraic techniques to accommodate boundary conditions of the second and third kinds. Several case studies are presented to illustrate the utility and accuracy of the procedure. Selected examples either have no exact solutions or their exact solutions have not been cited because of the mathematical or numerical complexity. The illustrations include transient conduction in hemielliptical solids with either external convective surfaces or convective bases, and buried pipe in a square enclosure. Whenever possible, symbolic programming is used to carry out the differentiations and integrations. In some cases, however, the integrations must be strictly numerical. It is also demonstrated that a Green’s function can be defined to accommodate many geometries with nonorthogonal boundaries subject to more complex boundary conditions for which an exact Green’s function does not exist.

Orthogonal Bases for Eigenvalue Sensitivities—Torsional Vibration

1995 ◽  
Author(s):  
S. A. Nayfeh ◽  
H. Asada
Keyword(s):  
Boundary Conditions ◽  
Natural Frequency ◽  
Torsional Vibration ◽  
Natural Frequencies ◽  
General Boundary ◽  
General Boundary Conditions ◽  
Orthogonal Bases ◽  
Design Changes

Abstract The sensitivity of the natural frequencies of torsional vibration of an initially uniform shaft to nonuniform changes in its radius is studied. For the particular example of a fixed-fixed shaft, a set of design changes are found that modify a single natural frequency without modifying any of the others. The possibility of finding such a set of design changes for general boundary conditions is then investigated, and conditions for the existence of such a set are determined.

Free Vibrations of Symmetric Arch: Boundary Conditions of Stress Resultants Revisited

2020 ◽  
Vol 20 (09) ◽  
pp. 2071008
Author(s):  
Joon Kyu Lee ◽  
Byoung Koo Lee
Keyword(s):  
Boundary Conditions ◽  
Natural Frequency ◽  
Mode Shape ◽  
Natural Frequencies ◽  
Free Vibrations ◽  
Mode Shapes ◽  
All Solutions

This paper deals with analyzing free vibrations of the symmetric arch. The boundary conditions of the stress resultants are newly derived, which can be replaced by the conventional boundary conditions of the deflections. All solutions of the natural frequency with the mode shape, using the new boundary conditions, are the same as those of the conventional deflections. The boundary conditions mixed with new and conventional conditions act correctly to calculate natural frequencies. The mode shapes of the stress resultants using the new boundary conditions are reported in two types: symmetric and anti-symmetric modes.

scholarly journals Analysis of Fiberglass Winding Angle on Natural Frequency of Free Vibration of Cylindrical Shell with Asymmetric Boundary Conditions

2013 ◽  
Vol 274 ◽  
pp. 65-69 ◽  
Author(s):  
Zhi Wei Wang ◽  
Bo Wu ◽  
Yan Fu Wang ◽  
S.M. Bosiakov
Keyword(s):  
Cylindrical Shell ◽  
Free Vibration ◽  
Boundary Conditions ◽  
Natural Frequency ◽  
Natural Frequencies ◽  
Circular Cylindrical Shell ◽  
Geometrical Parameters ◽  
Glass Fiber Reinforced Plastic ◽  
Glass Fiber Reinforced ◽  
Winding Angle

In order to obtain approximate solution of natural frequencies for the free vibration of anisotropic circular cylindrical shells made of GFRP (glass fiber-reinforced plastic) with asymmetric boundary conditions, Love’s theory and energy method are used. Computation results show that the fundamental natural frequency comes from different vibration modes while the winding angle varies, the effect of number of axial half waves is stronger than number of circumferential waves on natural frequency of free vibration of anisotropic circular cylindrical shell. The effect of shell’s geometrical parameters is also investigated on natural frequencies.

scholarly journals A continuous model of a standing human body in vertical vibration

2019 ◽  
Vol 39 (2) ◽  
pp. 132-140
Author(s):  
Qingwen Zhang ◽  
Yu Zhang ◽  
Tianjian Ji
Keyword(s):  
Natural Frequency ◽  
Mass Distribution ◽  
Human Body ◽  
Natural Frequencies ◽  
Continuous Model ◽  
Vertical Vibration ◽  
The Body ◽  
Discrete Models ◽  
Mode Shapes ◽  
Axial Stiffness

This paper develops a continuous standing human body model in the vertical vibration based on an anthropomorphic model, two measured natural frequencies of a biomechanics model, and structural dynamics methods. The mass distribution of a standing body is formed using the mass distribution of fifteen body segments in the anthropomorphic model. The axial stiffness of the model is determined based on the best matching to the two natural frequencies of the biomechanics model which were obtained using shaking table tests. Four similar models are assessed using finite element parametric analysis. The best of the four models has seven uniform mass segments with two stiffnesses and the same fundamental natural frequency as that of the biomechanics model, but its second natural frequency is 10% higher. The mode shapes of the continuous model are presented to demonstrate the relative magnitude of vibration throughout the height of the body. Finally the modal mass and stiffness of the continuous model are evaluated, which are related to some simple discrete models.

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