scholarly journals Nonlinear Vibration Analysis of a Beam with a Breathing Crack

2019 ◽  
Vol 9 (18) ◽  
pp. 3874 ◽  
Author(s):  
Hui Long ◽  
Yilun Liu ◽  
Kefu Liu
Keyword(s):  
Nonlinear Vibration ◽  
Structural Parameters ◽  
Multiple Scale ◽  
Element Model ◽  
Harmonic Excitation ◽  
Breathing Crack ◽  
Cracked Beam ◽  
Nonlinear Responses ◽  
Stiffness Model ◽  
Stiffness Variation

The phenomena of sub- and super-harmonic responses make up one of the prominent nonlinear characteristics of a beam with a breathing crack. In order to fully understand the behaviors of sub- and super-harmonic resonances, it is necessary to analyze the nonlinear vibration of a beam-like structure with a breathing crack. In this study, a new stiffness model that considers the influence of the partial crack closure is proposed to model the stiffness variation of the cracked beam. Based on the finite element model of a beam with a breathing crack, the multiple-scale method is proposed to analyze the nonlinear vibration of a cracked beam subjected to harmonic excitation, and the relation between the nonlinear vibration of the cracked beam and the system parameters is obtained. An experiment is conducted to validate the analytical results. The study shows that the nonlinear responses of a beam with a breathing crack are affected by both the structural parameters and the crack parameters.

scholarly journals Modelling a Cracked Beam Structure Using the Finite Element Displacement Method

2019 ◽  
Vol 2019 ◽  
pp. 1-13
Author(s):  
Hui Long ◽  
Yilun Liu ◽  
Changzheng Huang ◽  
Weihui Wu ◽  
Zhaojun Li
Keyword(s):  
Finite Element ◽  
Dynamic Model ◽  
Structural Parameters ◽  
Element Model ◽  
Beam Element ◽  
The Finite Element Method ◽  
Displacement Method ◽  
Beam Structure ◽  
Cracked Beam ◽  
Local Flexibility

A new model is presented for studying the effects of crack parameters on the dynamics of a cracked beam structure. The model is established by the finite element displacement method. In particular, the stiffness matrix of the cracked beam element is firstly derived by the displacement method, which does not need the flexibility matrix inversion calculation compared with the previous local flexibility approaches based on the force method. Starting with a finite element model of cracked beam element, the equation of strain energy of a cracked beam element is formed by the displacement method combined with the linear fracture mechanics. Then, based on the finite element method, the dynamic model of the cracked beam structure is obtained. The results show that the dynamic model discovers the internal relation between the dynamic characteristics of cracked beam structure and structural parameters, material parameters, and crack parameters. Finally, an example is presented to validate the proposed dynamic model.

Nonlinear Features in the Dynamic Response of a Cracked Beam Under Harmonic Forcing

2005 ◽  
Author(s):  
Ugo Andreaus ◽  
Paolo Casini ◽  
Fabrizio Vestroni
Keyword(s):  
Nonlinear Response ◽  
Damage Identification ◽  
Period Doubling ◽  
Element Model ◽  
Breathing Crack ◽  
Cracked Beam ◽  
Response Characteristics ◽  
Harmonic Forcing ◽  
Dimensional Finite Element ◽  
Nonlinear Features

Detection of damage in beam structures is usually pursued by means of methods based on the measured variations of modal quantities, like frequencies and eigenmodes. The drawback of these methods is the small sensitivity of modal quantities to concentrated damage. Since a crack introduces nonlinearities in the system, the use of nonlinear techniques of damage detection merits to be investigated. With this aim the present paper is devoted to analyze the peculiar features of the nonlinear response of a cracked beam. The problem of a cantilever beam with an asymmetric edge crack subjected to a harmonic forcing at the tip is considered as a plane problem and is solved by using two-dimensional finite element model; the behaviour of the breathing crack is simulated as a frictionless contact problem. The modification of the response with respect to the linear one is outlined: in particular, excitation of sub- and super-harmonics, period doubling, quasi-impulsive behaviour at crack interfaces are the main achievements. These response characteristics can be used in nonlinear techniques of damage identification.

scholarly journals Dynamic and Stability Analysis of Multibolt Plane Joints under Normal Forces

2019 ◽  
Vol 9 (24) ◽  
pp. 5521
Author(s):  
Zhenyuan Li ◽  
Yimin Zhang ◽  
Changyou Li ◽  
Zhi Tan
Keyword(s):  
Structural Parameters ◽  
Three Dimensional ◽  
Harmonic Excitation ◽  
Design Parameters ◽  
Tightening Force ◽  
Normal Forces ◽  
Stiffness Characteristic ◽  
Stiffness Model ◽  
Fractal Parameters ◽  
Contact Surfaces

In this paper, a stiffness model of contact surfaces based on a modified three-dimensional fractal contact model is built, which is in accordance with the experiment results. Additionally, the static, dynamic, and stable behaviors of the bolt joint between the spindle box and the machine bed are analyzed. The mathematical relationship between fractal parameters of the surface topography and the stiffness of the system was established to accurately study its static behaviors. Asymmetric curves are observed from the load–deflection results and the nonlinear stiffness characteristic is also presented. It is shown that both the stress and the stiffness increase with the increase of the displacement near the static equilibrium position. Meanwhile, a simplified model without the consideration of roughness is compared with joint interfaces composed from milling, scraping, and grinding surfaces. Numerical calculation was employed to investigate effects of design parameters on the system under harmonic excitation when the processing method, excitation force, bolt pre-tightening force, topography parameters, and other structural parameters, i.e., nominal contact area, joint thickness and bolt number, are eventually regarded as the control parameters. The aim of the article is to analysis the influence of these parameters, including surface morphology, on nonlinear characteristics of the bolt interface with fractal contact surfaces andto provide some references to improve the characteristics.

scholarly journals Nonlinear vibration of knitted spacer fabric under harmonic excitation

2020 ◽  
Vol 15 ◽  
pp. 155892502098356
Author(s):  
Fuxing Chen ◽  
Hong Hu
Keyword(s):  
Nonlinear Vibration ◽  
Harmonic Balance Method ◽  
Harmonic Excitation ◽  
Polyurethane Foams ◽  
Excitation Level ◽  
Harmonic Amplitude ◽  
Damping Force ◽  
Spacer Fabric ◽  
Fabric System ◽  
Quadratic Stiffness

Knitted spacer fabrics can be an alternative material to typical rubber sponges and polyurethane foams for the protection of the human body from vibration exposure, such as automotive seat cushions and anti-vibration gloves. To provide a theoretical basis for the understanding of the nonlinear vibration behavior of the mass-spacer fabric system under harmonic excitation, experimental, analytical and numerical methods are used. Different from a linear mass-spring-damper vibration model, this study builds a phenomenological model with the asymmetric elastic force and the fractional derivative damping force to describe the periodic solution of the mass-spacer fabric system under harmonic excitation. Mathematical expression of the harmonic amplitude versus frequency response curve (FRC) is obtained using the harmonic balance method (HBM) to solve the equation of motion of the system. Parameter values in the model are estimated by performing curve fit between the modeled FRC and the experimental data of acceleration transmissibility. Theoretical analysis concerning the influence of varying excitation level on the FRCs is carried out, showing that nonlinear softening resonance turns into nonlinear hardening resonance with the increase of excitation level, due to the quadratic stiffness term and the cubic stiffness term in the model, respectively. The quadratic stiffness term also results in biased vibration response and causes an even order harmonic distortion. Besides, the increase of excitation level also results in elevated peak transmissibility at resonance.

Dynamic Characteristics Analysis of Cable-Rib Tension Deployable Antenna

2016 ◽  
Author(s):  
Liu Ruiwei ◽  
Hongwei Guo ◽  
Zhang Qinghua ◽  
Rongqiang Liu ◽  
Tang Dewei
Keyword(s):  
Dynamic Characteristics ◽  
Structural Parameters ◽  
Element Model ◽  
Structure Design ◽  
Antenna Structure ◽  
Characteristics Analysis ◽  
New Type ◽  
Dynamic Characteristics Analysis ◽  
The Finite Element Model ◽  
Weight Dynamic

Balancing stiffness and weight is of substantial importance for antenna structure design. Conventional fold-rib antennas need sufficient weight to meet stiffness requirements. To address this issue, this paper proposes a new type of cable-rib tension deployable antenna that consists of six radial rib deployment mechanisms, numerous tensioned cables, and a mesh reflective surface. The primary innovation of this study is the application of numerous tensioned cables instead of metal materials to enhance the stiffness of the entire antenna while ensuring relatively less weight. Dynamic characteristics were analyzed to optimize the weight and stiffness of the antenna with the finite element model by subspace method. The first six orders of natural frequencies and corresponding vibration modes of the antenna structure are obtained. In addition, the effects of structural parameters on natural frequency are studied, and a method to improve the rigidity of the deployable antenna structure is proposed.

Structural Optimization of the Telescopic Boom of a Certain Type of Truck-Mounted Crane

2014 ◽  
Vol 548-549 ◽  
pp. 383-388
Author(s):  
Zhi Wei Chen ◽  
Zhe Cui ◽  
Yi Jin Fu ◽  
Wen Ping Cui ◽  
Li Juan Dong ◽  
...  
Keyword(s):  
Finite Element ◽  
Static Analysis ◽  
Cross Sections ◽  
Optimization Design ◽  
Structural Parameters ◽  
Vertical Direction ◽  
Element Model ◽  
Shape Parameters ◽  
Conventional Design ◽  
Design Variables

Parametric finite element model for a commonly used telescopic boom structure of a certain type of truck-mounted crane has been established. Static analysis of the conventional design configuration was performed first. And then an optimization process has been carried out to minimize the total weight of the telescopic structures. The design variables include the geometric shape parameters of the cross-sections and the integrated structural parameters of the telescopic boom. The constraints include the maximum allowable equivalent stresses and the flexure displacements at the tip of the assembled boom structure in both the vertical direction and the circumferential direction of the rotating plane. Compared with the conventional design, the optimization design has achieved a significant weight reduction of up to 24.3%.

Parametric Instability in Metallic Bellows Subjected to Seismic Excitation

2010 ◽  
Author(s):  
Nobuyuki Kobayashi ◽  
Keisaku Kitada ◽  
Yoshiki Sugawara
Keyword(s):  
Parametric Instability ◽  
Fluid Pressure ◽  
Element Model ◽  
Frequency Component ◽  
Seismic Excitation ◽  
Axial Stiffness ◽  
Predominant Frequency ◽  
Earthquake Motion ◽  
Static Fluid ◽  
Stiffness Variation

This paper investigates the parametric instability of a metallic bellows filled with fluid and subjected to the variance of dynamic internal pressure due to an earthquake. The axial stiffness of the bellows varies due to the variation in internal static fluid pressure, and this stiffness variation induces a parametric instability in the bellows. A finite element model describing a bellows connected to a pipe is developed to examine the question of whether parametric instability is excited in such bellows by earthquake motion, which is not the harmonic vibration. Numerical simulations and experiments were carried out using the acceleration recorded by past recorded actual earthquakes. We find that indeed parametric instability may appear in the bellows when the natural frequency of the pipe is close to the predominant frequency component of the earthquake, though the earthquake motion is not harmonic.

scholarly journals Sensitivity Analysis of the Influence of Structural Parameters on Dynamic Behaviour of Highly Redundant Cable-Stayed Bridges

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
B. Asgari ◽  
S. A. Osman ◽  
A. Adnan
Keyword(s):  
Sensitivity Analysis ◽  
Finite Element ◽  
Finite Element Model ◽  
Model Updating ◽  
Structural Parameters ◽  
Element Model ◽  
Structural Behavior ◽  
Model Tuning ◽  
The Finite Element Model ◽  
Cable Stayed Bridges

The model tuning through sensitivity analysis is a prominent procedure to assess the structural behavior and dynamic characteristics of cable-stayed bridges. Most of the previous sensitivity-based model tuning methods are automatic iterative processes; however, the results of recent studies show that the most reasonable results are achievable by applying the manual methods to update the analytical model of cable-stayed bridges. This paper presents a model updating algorithm for highly redundant cable-stayed bridges that can be used as an iterative manual procedure. The updating parameters are selected through the sensitivity analysis which helps to better understand the structural behavior of the bridge. The finite element model of Tatara Bridge is considered for the numerical studies. The results of the simulations indicate the efficiency and applicability of the presented manual tuning method for updating the finite element model of cable-stayed bridges. The new aspects regarding effective material and structural parameters and model tuning procedure presented in this paper will be useful for analyzing and model updating of cable-stayed bridges.

scholarly journals Comparison of Galerkin, POD and Nonlinear-Normal-Modes Models for Nonlinear Vibrations of Circular Cylindrical Shells

2006 ◽  
Author(s):  
M. Amabili ◽  
C. Touze´ ◽  
O. Thomas
Keyword(s):  
Nonlinear Vibrations ◽  
Circular Cylindrical Shell ◽  
Equations Of Motion ◽  
Normal Modes ◽  
Nonlinear Normal Modes ◽  
Harmonic Excitation ◽  
Nonlinear Responses ◽  
Nonlinear Normal ◽  
The Galerkin Method ◽  
Proper Orthogonal

The aim of the present paper is to compare two different methods available to reduce the complicated dynamics exhibited by large amplitude, geometrically nonlinear vibrations of a thin shell. The two methods are: the proper orthogonal decomposition (POD) and an asymptotic approximation of the Nonlinear Normal Modes (NNMs) of the system. The structure used to perform comparisons is a water-filled, simply supported circular cylindrical shell subjected to harmonic excitation in the spectral neighbourhood of the fundamental natural frequency. A reference solution is obtained by discretizing the Partial Differential Equations (PDEs) of motion with a Galerkin expansion containing 16 eigenmodes. The POD model is built by using responses computed with the Galerkin model; the NNM model is built by using the discretized equations of motion obtained with the Galerkin method, and taking into account also the transformation of damping terms. Both the POD and NNMs allow to reduce significantly the dimension of the original Galerkin model. The computed nonlinear responses are compared in order to verify the accuracy and the limits of these two methods. For vibration amplitudes equal to 1.5 times the shell thickness, the two methods give very close results to the original Galerkin model. By increasing the excitation and vibration amplitude, significant differences are observed and discussed.

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