scholarly journals Natural Vibration of a Beam with a Breathing Oblique Crack

2017 ◽  
Vol 2017 ◽  
pp. 1-13 ◽  
Author(s):  
Yijiang Ma ◽  
Guoping Chen
Keyword(s):  
Natural Frequency ◽  
Analytical Method ◽  
Bending Moment ◽  
Fem Analysis ◽  
Maximum Error ◽  
Computational Accuracy ◽  
Cracked Beam ◽  
Fem Method ◽  
Oblique Crack ◽  
The Galerkin Method

An analytical method is proposed to calculate the natural frequency of a cantilever beam with a breathing oblique crack. A double-linear-springs-model is developed in the modal analysis process to describe the breathing oblique crack, and the breathing behaviour of the oblique crack is objectively simulated. The finite element method (FEM) analysis software ABAQUS is used to calculate the geometric correction factors when the cracked plate is subjected to a pure bending moment at different oblique crack angles and relative depths. The Galerkin method is applied to simplify the cracked beam to a single degree of freedom system, allowing the natural frequency of the beam with the breathing oblique crack to be calculated. Compared with the natural frequencies of the breathing oblique cracked beam obtained using the ABAQUS FEM method, the proposed analytical method exhibits a high computational accuracy, with a maximum error of only 4.65%.

scholarly journals Analytical Method for Geometric Nonlinear Problems Based on Offshore Derricks

Mathematics ◽  
2021 ◽  
Vol 9 (6) ◽  
pp. 610
Author(s):  
Chunbao Li ◽  
Hui Cao ◽  
Mengxin Han ◽  
Pengju Qin ◽  
Xiaohui Liu
Keyword(s):  
Analytical Method ◽  
Bending Moment ◽  
Nonlinear Problems ◽  
Weather Conditions ◽  
Order Effect ◽  
Practical Calculation ◽  
Geometrically Nonlinear ◽  
Uniform Load ◽  
Safety Research ◽  
Calculation Results

The marine derrick sometimes operates under extreme weather conditions, especially wind; therefore, the buckling analysis of the components in the derrick is one of the critical contents of engineering safety research. This paper aimed to study the local stability of marine derrick and propose an analytical method for geometrically nonlinear problems. The rod in the derrick is simplified as a compression rod with simply supported ends, which is subjected to transverse uniform load. Considering the second-order effect, the differential equations were used to establish the deflection, rotation angle, and bending moment equations of the derrick rod under the lateral uniform load. This method was defined as a geometrically nonlinear analytical method. Moreover, the deflection deformation and stability of the derrick members were analyzed, and the practical calculation formula was obtained. The Ansys analysis results were compared with the calculation results in this paper.

scholarly journals Vibrational Analysis on Hemp and Okra Fibres Mixed Glass Fiber Polyester Composite

2021 ◽  
Vol 8 (11) ◽  
pp. 55-62
Author(s):  
Putti Venkata Siva Teja ◽  
Badatala Ooha ◽  
Kondeti Sravanth
Keyword(s):  
Glass Fiber ◽  
Natural Frequency ◽  
Natural Frequencies ◽  
Fiber Composite ◽  
Fem Analysis ◽  
Vibration Characteristics ◽  
Mode Shapes ◽  
Machine Component ◽  
Free System ◽  
Glass Fiber Composite

In transverse vibrations the element moves to and fro in a direction perpendicular to the direction of the advance of the wave. To determine the vibration characteristics i.e., natural frequencies and mode shapes, modal analysis is a process for a structure or a machine component while is being designed. In real life, aero planes, missiles, rockets, space vehicles, satellites, sub marines etc are modeled as free-free mechanical systems. In this paper an attempt was made to compare natural frequency for two composite materials- ladies finger with Glass fiber composite and Hemp with Glass fiber composite by taking as cantilever beams. The cantilever beam which is fixed at one end is vibrated to obtain the natural frequency, mode shapes at four different modes. A simple low cost demonstration experiment is performed in this paper by using common apparatus in order to compare theoretical, numerical (FEM analysis) profiles of two free-free thin two rectangular composite beams of dimensions 305*49.5* 7 in mm. Keywords: Natural frequencies, Mode shapes, Vibration characteristics, Ladies finger fiber, Hemp fiber, Glass fiber, FEM analysis, Free-Free system.

scholarly journals Influence of the phase difference between kinematic and inertial loads on seismic behaviour of pile foundations in layered soils

2020 ◽  
Author(s):  
Thejesh Kumar Garala ◽  
Gopal Madabhushi
Keyword(s):  
Natural Frequency ◽  
Free Field ◽  
Phase Relationship ◽  
Phase Variation ◽  
Bending Moment ◽  
Pile Group ◽  
Pile Foundations ◽  
Single Pile ◽  
Seismic Behaviour ◽  
Soil Layers

A series of dynamic centrifuge experiments was conducted on model pile foundations embedded in a two-layered soil profile consisted of soft-clay layer underlain by dense sand. These experiments were specifically designed to investigate the individual effect of kinematic and inertial loads on a single pile and a 3×1 row pile group during model earthquakes. It was observed that the ratio of free-field soil natural frequency to the natural frequency of structure might not govern the phase relationship between the kinematic and inertial loads for pile foundations as reported in some previous research. The phase relationship obtained in this study agrees well with the conventional phase variation between the force and displacement of a viscously damped simple oscillator subjected to a harmonic force. Further, as expected, the pile accelerations and bending moments can be smaller when the kinematic and inertial loads act against each other compared to the case when they act together on the pile foundations. This study also revealed that the peak kinematic pile bending moment will be at the interface of soil layers for both single pile and pile group. However, in the presence of both kinematic and inertial loads, the peak pile bending moment can occur either at the shallower depths or at the interface of soil layers depending on the pile cap rotational constraint.

scholarly journals An Improved Analytical Method for Vibration Analysis of Variable Section Beam

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Jingjing Feng ◽  
Zhengneng Chen ◽  
Shuying Hao ◽  
Kunpeng Zhang
Keyword(s):  
Natural Frequency ◽  
Analytical Method ◽  
Adomian Decomposition Method ◽  
Theoretical Method ◽  
Element Simulation ◽  
Adomian Decomposition ◽  
Variable Section ◽  
Vibration Problems ◽  
Section Structure ◽  
Section Function

The variable section structure could be the physical model of many vibration problems, and its analysis becomes more complicated either. It is very important to know how to obtain the exact solution of the modal function and the natural frequency effectively. In this paper, a general analytical method, based on segmentation view and iteration calculation, is proposed to obtain the modal function and natural frequency of the beam with an arbitrary variable section. In the calculation, the section function of the beam is considered as an arbitrary function directly, and then the result is obtained by the proposed method that could have high precision. In addition, the total amount of calculation caused by high-order Taylor expansion is reduced greatly by comparing with the original Adomian decomposition method (ADM). Several examples of the typical beam with different variable sections are calculated to show the excellent calculation accuracy and convergence of the proposed method. The correctness and effectiveness of the proposed method are verified also by comparing the results of the several kinds of the theoretical method, finite element simulation, and experimental method.

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.

FEM Stress Analysis and Sealing Performance in Pipe Flange Connections With Adhesive Subjected to Internal Pressure and External Bending Moments

2005 ◽  
Author(s):  
Masahide Katsuo ◽  
Toshiyuki Sawa ◽  
Yuki Kikuchi
Keyword(s):  
Internal Pressure ◽  
Stress Analysis ◽  
Bending Moment ◽  
Fem Analysis ◽  
Bending Moments ◽  
3 Dimensional ◽  
Leakage Test ◽  
Sealing Performance ◽  
Flange Thickness ◽  
Good Agreement

This study deals with the stress analysis and the estimation of sealing performance of the pipe flange connections with an adhesive under an internal pressure and an external bending moment are analyzed by using the 3-dimensional elastic finite element method (FEM). The experiment of the leakage test of the connections with an adhesive was carried out by applying the above loads to the connections. From the FEM analysis, the following results were obtained; (1) when an internal pressure is applied to the flange connections, the compressive stress at the interface between a flange and an adhesive increases proportionally from the inner side of the interface to outside, and (2) when an internal pressure and a bending moment apply to the flange connections, the stress distribution at the half part of the interface increases as the external bending moments increase and also Young’s modulus of the adhesive increases. From the experiments, the following results were obtained: (1) sealing performance of the pipe flange connections with an adhesive under an internal pressure and an external bending moment increases as the flange thickness and an initial clamping force of bolts increases and (2) the sealing performances were not found between the connections with an adhesive and that with a gasket combining an adhesive. Furthermore, the numerical results are in fairly good agreement with the experimental results.

An Analytical Method for Expansion Chambers With Continuously Varying Cross-Sectional Area

2004 ◽  
Vol 126 (2) ◽  
pp. 173-183
Author(s):  
M. Utsumi
Keyword(s):  
Analytical Method ◽  
Broadband Noise ◽  
Cross Sectional Area ◽  
Characteristic Functions ◽  
Sectional Area ◽  
Algebraic Equations ◽  
Expansion Chamber ◽  
Cross Sectional ◽  
Linear Algebraic Equations ◽  
The Galerkin Method

An analytical method is applied to predict the acoustic attenuation performance of expansion chambers with continuously varying cross-sectional area. A feature of the present method is the use of spherical coordinates whose origin is at the top of the cone that is tangent to the wall of the expansion chamber. By this means, the characteristic functions can be analytically determined despite the non-uniform geometry of the expansion chamber. Using the Galerkin method, a variational principle is transformed into linear algebraic equations that are solved to determine the transmission coefficient of the expansion chamber. Numerical results are provided for the case where broadband noise attenuation is achieved.

FEM analysis of conventional and square bird-beak SHS joint subject to in-plane bending moment — experimental study

2007 ◽  
Vol 63 (10) ◽  
pp. 1361-1372 ◽  
Author(s):  
A.D. Christitsas ◽  
D.T. Pachoumis ◽  
C.N. Kalfas ◽  
E.G. Galoussis
Keyword(s):  
Experimental Study ◽  
Bending Moment ◽  
Fem Analysis ◽  
Bird Beak ◽  
Plane Bending

scholarly journals Simplified Analytical Method for Optimized Initial Shape Analysis of Self-Anchored Suspension Bridges and Its Verification

2015 ◽  
Vol 2015 ◽  
pp. 1-14 ◽  
Author(s):  
Myung-Rag Jung ◽  
Dong-Ju Min ◽  
Moon-Young Kim
Keyword(s):  
Analytical Method ◽  
Bending Moment ◽  
Suspension Bridge ◽  
Suspension Bridges ◽  
Equilibrium Equations ◽  
Initial State ◽  
Initial Shape ◽  
Main Cable ◽  
Initial Shape Analysis ◽  
Bridge Models

A simplified analytical method providing accurate unstrained lengths of all structural elements is proposed to find the optimized initial state of self-anchored suspension bridges under dead loads. For this, equilibrium equations of the main girder and the main cable system are derived and solved by evaluating the self-weights of cable members using unstrained cable lengths and iteratively updating both the horizontal tension component and the vertical profile of the main cable. Furthermore, to demonstrate the validity of the simplified analytical method, the unstrained element length method (ULM) is applied to suspension bridge models based on the unstressed lengths of both cable and frame members calculated from the analytical method. Through numerical examples, it is demonstrated that the proposed analytical method can indeed provide an optimized initial solution by showing that both the simplified method and the nonlinear FE procedure lead to practically identical initial configurations with only localized small bending moment distributions.

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