scholarly journals Modal analysis of cracked beam with a piezoelectric layer

2021 ◽  
Author(s):  
Duong Thanh Huan ◽  
Luu Quynh Huong ◽  
Nguyen Tien Khiem
Keyword(s):  
Modal Analysis ◽  
Piezoelectric Layer ◽  
Structural Control ◽  
Beam Model ◽  
Vibration Modes ◽  
Governing Equations ◽  
Cracked Beam ◽  
Natural Modes ◽  
Double Beam ◽  
Effective Use

Piezoelectric material was employed first as sensor/actuator for structural control and then it has got an effective use for structural health monitoring and repairing damaged structures. In this report, modal analysis of cracked beam with piezoelectric layer is carried out to investigate effect of crack and piezoelectric layer thickness on natural frequencies of the structure and output charge generated in the piezoelectric layer by vibration modes. Governing equations of the coupled structure are established using the double beam model and two-spring (translational and rotational) representation of crack and solved to obtain the modal parameters including the output charge associated with natural modes acknowledged as modal piezoelectric charge (MPC). Numerical examples have been examined for validation and illustration of the developed theory.

Experimental and Finite Element Analysis of Natural Modes and Frequencies of Hollow Fan Blades

2013 ◽  
Vol 467 ◽  
pp. 306-311 ◽  
Author(s):  
M. Nikhamkin ◽  
B. Bolotov
Keyword(s):  
Finite Element ◽  
Modal Analysis ◽  
Vibration Modes ◽  
Element Analysis ◽  
Turbine Engine ◽  
Natural Modes ◽  
Resonance Vibrations ◽  
Super Plastic ◽  
Fan Blade ◽  
Scanning Laser Vibrometry

Natural modes and frequencies of gas turbine engine hollow fan blades were experimentally investigated. The blades were produced with the method of super-plastic molding and pressure welding combination. Two independent experimental methods were used: three-component scanning laser vibrometry and impact modal analysis. Natural frequencies and vibration modes of a hollow fan blade and stress fields corresponding to the natural modes were got. The finite element modal analysis was carried out. The hollow fan blade was stated to have particular natural vibration modes. The investigation results can be used to detune the resonance vibrations and to verify calculation models.

Coupled Flexural–Longitudinal Vibrations of Timoshenko Double-Beam Systems Induced by Mass Eccentricities

2016 ◽  
Vol 08 (05) ◽  
pp. 1650067
Author(s):  
Jian Wang ◽  
Zhenguo Zhang ◽  
Hongxing Hua
Keyword(s):  
Natural Frequencies ◽  
Flexural Vibration ◽  
Longitudinal Direction ◽  
Forced Response ◽  
Beam Model ◽  
Vertical Force ◽  
Governing Equations ◽  
Longitudinal Vibrations ◽  
Mass Eccentricity ◽  
Double Beam

In many instances, marine vessel may suffer unexpected flexural–longitudinal vibrations as the consequences of the unevenly distribution of the inner structures and equipment. In order to study the dynamic behaviors of the marine vessel with the involvement of the mass unevenness, the whole vessel is modeled as a discretely connected double-beam system in this paper. In this model, the misalignment between geometric and gravitational center are considered as the simplification of the mass unevenness. The governing equations of coupled flexural–longitudinal vibrations of Timoshenko beam due to mass eccentricity are derived. Extending to the double-beam model, the natural frequencies, modal shapes and forced response of the system are obtained analytically by using the modified transfer matrix method. The comparison between the present method and the conventional finite element method shows a great match. The result indicates that the existence of mass eccentricity can cause significant coupled flexural–longitudinal vibrations, thus, even only vertical force is applied, the vibration in longitudinal direction can be excited and controlled by the natural frequencies of the flexural vibration.

scholarly journals Vibration of Rotating and Revolving Planet Rings with Discrete and Partially Distributed Stiffnesses

2020 ◽  
Vol 11 (1) ◽  
pp. 127
Author(s):  
Fuchun Yang ◽  
Dianrui Wang
Keyword(s):  
High Speed ◽  
Differential Operators ◽  
Natural Frequencies ◽  
Rotation Speed ◽  
Distribution Area ◽  
Vibration Modes ◽  
Governing Equations ◽  
Vibration Properties ◽  
Wide Range ◽  
Forced Responses

Vibration properties of high-speed rotating and revolving planet rings with discrete and partially distributed stiffnesses were studied. The governing equations were obtained by Hamilton’s principle based on a rotating frame on the ring. The governing equations were cast in matrix differential operators and discretized, using Galerkin’s method. The eigenvalue problem was dealt with state space matrix, and the natural frequencies and vibration modes were computed in a wide range of rotation speed. The properties of natural frequencies and vibration modes with rotation speed were studied for free planet rings and planet rings with discrete and partially distributed stiffnesses. The influences of several parameters on the vibration properties of planet rings were also investigated. Finally, the forced responses of planet rings resulted from the excitation of rotating and revolving movement were studied. The results show that the revolving movement not only affects the free vibration of planet rings but results in excitation to the rings. Partially distributed stiffness changes the vibration modes heavily compared to the free planet ring. Each vibration mode comprises several nodal diameter components instead of a single component for a free planet ring. The distribution area and the number of partially distributed stiffnesses mainly affect the high-order frequencies. The forced responses caused by revolving movement are nonlinear and vary with a quasi-period of rotating speed, and the responses in the regions supported by partially distributed stiffnesses are suppressed.

The Use of Modan 3D in Experimental Modal Analysis

2013 ◽  
Vol 486 ◽  
pp. 36-41 ◽  
Author(s):  
Róbert Huňady ◽  
František Trebuňa ◽  
Martin Hagara ◽  
Martin Schrötter
Keyword(s):  
Modal Analysis ◽  
Vibration Analysis ◽  
High Speed ◽  
Mechanical Vibration ◽  
Steel Sample ◽  
Experimental Modal Analysis ◽  
Image Correlation ◽  
Optical Methods ◽  
Mode Shapes ◽  
Vibration Modes

Experimental modal analysis is a relatively young part of dynamics, which deals with the vibration modes identification of machines or their parts. Its development has started since the beginning of the eighties, when the computers hardware equipment has improved and the fast Fourier transform (FFT) could be used for the results determination. Nowadays it provides an uncountable set of vibration analysis possibilities starting with conventional contact transducers of acceleration and ending with modern noncontact optical methods. In this contribution we mention the use of high-speed digital image correlation by experimental determination of mode shapes and modal frequencies. The aim of our work is to create a program application called Modan 3D enabling the performing of experimental modal analysis and operational modal analysis. In this paper the experimental modal analysis of a thin steel sample performed with Q-450 Dantec Dynamics is described. In Modan 3D the experiment data were processed and the vibration modes were determined. The reached results were verified by PULSE modulus specialized for mechanical vibration analysis.

scholarly journals Vibration Characteristics of Piezoelectric Microbeams Based on the Modified Couple Stress Theory

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
R. Ansari ◽  
M. A. Ashrafi ◽  
S. Hosseinzadeh
Keyword(s):  
Boundary Conditions ◽  
Couple Stress ◽  
Natural Frequencies ◽  
Couple Stress Theory ◽  
Equations Of Motion ◽  
Modified Couple Stress Theory ◽  
Beam Model ◽  
Governing Equations ◽  
Stress Theory ◽  
Modified Couple Stress

The vibration behavior of piezoelectric microbeams is studied on the basis of the modified couple stress theory. The governing equations of motion and boundary conditions for the Euler-Bernoulli and Timoshenko beam models are derived using Hamilton’s principle. By the exact solution of the governing equations, an expression for natural frequencies of microbeams with simply supported boundary conditions is obtained. Numerical results for both beam models are presented and the effects of piezoelectricity and length scale parameter are illustrated. It is found that the influences of piezoelectricity and size effects are more prominent when the length of microbeams decreases. A comparison between two beam models also reveals that the Euler-Bernoulli beam model tends to overestimate the natural frequencies of microbeams as compared to its Timoshenko counterpart.

scholarly journals The modal analysis of cylindrical steel tank with selfsupported roof filled with different level of liquid

2013 ◽  
Vol 12 (2) ◽  
pp. 205-212
Author(s):  
Daniel Burkacki ◽  
Michał Wójcik ◽  
Robert Jankowski
Keyword(s):  
Modal Analysis ◽  
Natural Frequencies ◽  
Environmental Disaster ◽  
Natural Modes ◽  
Liquid Products ◽  
Safety And Reliability ◽  
Steel Tank ◽  
Steel Tanks ◽  
Cylindrical Steel Tanks ◽  
Cylindrical Steel

In technical branches, such as chemical or petroleum industries, cylindrical steel tanks are essential structures used for storage of liquid products. Therefore, their safety and reliability is essential, because any failure might have dangerous consequences, in extreme cases may even lead to an environmental disaster. The aim of the presented paper is to show the results of the modal analysis concerning the cylindrical steel tank with self-supported roof which has been constructed in northern Poland. The investigation was carried out with the use of the FEM commercial computer program Abaqus. The values of natural frequencies, as well as the natural modes, for different levels of liquid filling (empty tank, partly filled and tank fully filled) were determined in the study. The results of the study clearly indicate that the increase in the liquid level leads to the substantial decrease in the natural frequencies of the structure.

Vibration Response of a Thin-Walled Cylindrical Pipe with Liquid

2012 ◽  
Vol 189 ◽  
pp. 345-349
Author(s):  
Yu Lan Wei ◽  
Bing Li ◽  
Li Gao ◽  
Ying Jun Dai
Keyword(s):  
Finite Element ◽  
Natural Frequencies ◽  
Element Model ◽  
Beam Model ◽  
Vibration Modes ◽  
Timoshenko Beam Model ◽  
Cylindrical Pipe ◽  
Bending Vibration ◽  
Beam Bending ◽  
Thin Walled

Vibration characteristics of the thin-walled cylindrical pipe are affected by the liquid within the pipe. The natural frequencies and vibration modes of the pipe without liquid are analyzed by the theory of beam bending vibration and finite element model, which is based on the Timoshenko beam model. The first three natural frequencies and vibration modes of the pipe with or without liquid are acquired by experiments. As shown in the experiment results, the natural frequencies of the containing liquid pipe are lower than the natural frequencies of the pipe without liquid.

Experimental Evaluation of Tensile Forces in Short Steel Rods

2015 ◽  
Vol 732 ◽  
pp. 333-336 ◽  
Author(s):  
Michal Polak ◽  
Tomáš Plachy
Keyword(s):  
Tensile Force ◽  
String Model ◽  
Beam Model ◽  
Building Structures ◽  
Structural Elements ◽  
Frequency Method ◽  
Natural Modes ◽  
Tensile Forces ◽  
Torsion Springs ◽  
Fixed Beam

There are a lot of structures in building and civil engineering where the significant structural elements are loaded by large tensile forces (e.g. tension bars of building structures). In many practical cases it is important to know the actual value of tensile forces in tensile structural elements for assessment of their reliability. The four experimental techniques are used for determination of tensile forces in practice most often. The vibration frequency method, which is one of them, is very suitable for experiments done only one time or sometimes, especially in cases when the examined structural elements are already activated and the application of an experimental method is necessary in this situation. The experiment described in this paper was focused on the tensile force determination in steel rods, which were very short and relatively stiff. The evaluated tensile forces of the investigated short steel rods were affected by a significant error when only the simplest models (the string model, the simply supported beam and the fixed beam) and measured natural frequencies were applied. In order to precise the determined tensile forces, the theoretical beam model supported by simple supports with torsion springs (“the elastically fixed beam”) and the measured natural modes of the rods had to be necessarily taken into account.

Solution of Free Vibration Equations of Euler-Bernoulli Cracked Beams by Using Differential Transform Method

2011 ◽  
Vol 110-116 ◽  
pp. 4532-4536 ◽  
Author(s):  
K. Torabi ◽  
J. Nafar Dastgerdi ◽  
S. Marzban
Keyword(s):  
Analytical Solution ◽  
Differential Equations ◽  
Free Vibration ◽  
Boundary Conditions ◽  
Differential Transform Method ◽  
Beam Model ◽  
Cracked Beam ◽  
Transform Method ◽  
Simple Method ◽  
Differential Transform

In this paper, free vibration differential equations of cracked beam are solved by using differential transform method (DTM) that is one of the numerical methods for ordinary and partial differential equations. The Euler–Bernoulli beam model is proposed to study the frequency factors for bending vibration of cracked beam with ant symmetric boundary conditions (as one end is clamped and the other is simply supported). The beam is modeled as two segments connected by a rotational spring located at the cracked section. This model promotes discontinuities in both vertical displacement and rotational due to bending. The differential equations for the free bending vibrations are established and then solved individually for each segment with the corresponding boundary conditions and the appropriated compatibility conditions at the cracked section by using DTM and analytical solution. The results show that DTM provides simple method for solving equations and the results obtained by DTM converge to the analytical solution with much more accurate for both shallow and deep cracks. This study demonstrates that the differential transform is a feasible tool for obtaining the analytical form solution of free vibration differential equation of cracked beam with simple expression.

Finite Element Analysis Based on ANSYS of Bolt of Roof Bolter

2014 ◽  
Vol 926-930 ◽  
pp. 3042-3045
Author(s):  
Si Cong Yuan ◽  
Xin Guo ◽  
Xiao Yu Wang ◽  
Xi Yong Pei
Keyword(s):  
Modal Analysis ◽  
Static Analysis ◽  
Three Dimensional ◽  
Structure Design ◽  
Element Analysis ◽  
Shaft Diameter ◽  
Natural Modes ◽  
Roof Bolter ◽  
Solid Models ◽  
Reasonable Choice

The three-dimensional solid models of five different length and shaft diameter anchor of bolt were constructed based on ANSYS software, and making static analysis and modal analysis on it to obtain the stress nephogram and natural frequency of bolt. Research on the stress condition of bolt in static analysis. In modal analysis, researching on the effect regular of the change of length and shaft diameter size on the bolt transverse vibration, the longitudinal and torsional vibration of three natural modes of different frequency, providing a reference for the structure design and reasonable choice of bolt type for corresponding condition.

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