Vibrational Behavior of Cylindrical Shells in Axial Magnetic Field
The investigation of the vibrational character of magnetic cylindrical shells placed in an axial magnetic field has important practical applications. In this work, we study the vibrational behaviour of such a cylindrical shell by making use of the so-called exact space treatment, which does not assume any hypothesis. We discuss the effects of several practically important boundary conditions on the vibrations of the described setup. We find that, for some cases of boundary conditions, e.g. clamped, simply supported or peripherally earthed, as well as for some values of the wave numbers, the vibrational frequencies of the shell are approximately zero. The theoretical and numerical exploration of this fact confirms that the vibrations are absent or attenuate very rapidly. For all the considered cases, the imaginary part of the frequencies is negative, which implies stability for the vibrational process.
Application of Method of Symmetries at a Calculation and Planning of Circular Plate with Variable Thickness
A problem is formulated for the natural oscillations of a circular plate of linearly variable thickness on the basis of the symmetry method. The equations of natural frequencies and forms for a plate are obtained, providing that it is rigidly fixed along the inner contour. The first three eigenfrequencies are calculated, and the eigenmodes of the oscillations of the acoustic element are constructed. An algorithm for applying the symmetry method and the factorization method for solving problems in the theory of oscillations for plates of variable thickness is shown. The effectiveness of the approach is demonstrated on the basis of comparison of known results and those obtained in the article. It is shown that the results are more accurate and reliable.
Introduction of the Fluid-Structure Coupling into the Force Analysis Technique
This paper presents a method to take into account
the fluid-structure coupling into an inverse method, the Force
Analysis Technique (FAT). The FAT method, also called RIFF method
(Filtered Windowed Inverse Resolution), allows to identify the force
distribution from local vibration field. In order to only identify the
external force applied on a structure, it is necessary to quantify the
fluid-structure coupling, especially in naval application, where the
fluid is heavy. This method can be decomposed in two parts, the first
one consists in identifying the fluid-structure coupling and the second
one to introduced it in the FAT method to reconstruct the external
force. Results of simulations on a plate coupled with a cavity filled
with water are presented.
Modal Dynamic Analysis of a Mechanism with Deformable Elements from an Oil Pump Unit Structure
On this research, experimental analyses have been performed in order to determine the oil pump mechanism dynamics and stability from an oil unit mechanical structure. The experimental tests were focused on the vibrations which occur inside of the rod element during functionality of the oil pump unit. The oil pump mechanism dynamic parameters were measured and also determined through numerical computations. Entire research is based on the oil pump unit mechanical system virtual prototyping. For a complete analysis of the mechanism, the frequency dynamic response was identified, mainly for the mechanism driven element, based on two methods: processing and virtual simulations with MSC Adams aid and experimental analysis. In fact, through this research, a complete methodology is presented where numerical simulations of a mechanism with deformed elements are developed on a dynamic mode and these can be correlated with experimental tests.
Second Sub-Harmonic Resonance in Vortex-Induced Vibrations of a Marine Pipeline Close to the Seabed
In this paper, using the method of multiple scales, the second sub-harmonic resonance in vortex-induced vibrations (VIV) of a marine pipeline close to the seabed is investigated based on a developed wake oscillator model. The amplitude-frequency equations are also derived. It is found that the oscillation will increase all the time when both discriminants of the amplitude-frequency equations are positive while the oscillation will decay when the discriminants are negative.
Parametrization of Piezoelectric Vibration Energy Harvesters for Low Power Embedded Systems
Matching an embedded electronic application with a
cantilever vibration energy harvester remains a difficult endeavour
due to the large number of factors influencing the output power.
In the presented work, complementary balanced energy harvester
parametrization is used as a methodology for simplification of
harvester integration in electronic applications. This is achieved
by a dual approach consisting of an adaptation of the general
parametrization methodology in conjunction with a straight forward
harvester benchmarking strategy. For this purpose, the design and
implementation of a suitable user friendly cantilever energy harvester
benchmarking platform is discussed. Its effectiveness is demonstrated
by applying the methodology to a commercially available Mide
V21BL vibration energy harvester, with excitation amplitude and
frequency as variables.
Vibration Analysis of a Solar Powered UAV
This paper presents the results of a Finite Element
based vibration analysis of a solar powered Unmanned Aerial
Vehicle (UAV). The purpose of this paper was to quantify the free
vibration, forced vibration response due to differing point inputs in
order to predict the relative response magnitudes and frequencies at
various wing locations of vibration induced power generators
(magnet in coil) excited by gust and/or control surface pulse-decays
used to help power the flight of the electric UAV. A Fluid Structure
Interaction (FSI) study was performed in order to ascertain pertinent
design stresses and deflections as well as aerodynamic parameters of
the UAV airfoil. The 10 ft span airfoil is modeled using Mylar as the
primary material. Results show that the free mode in bending is 4.8
Hz while the first forced bending mode is on range of 16.2 to 16.7 Hz
depending on the location of excitation. The free torsional bending
mode is 28.3 Hz, and the first forced torsional mode is range of 26.4
to 27.8 Hz, depending on the location of excitation. The FSI results
predict the coefficients of aerodynamic drag and lift of 0.0052 and
0.077, respectively, which matches hand-calculations used to validate
the Finite Element based results. FSI based maximum von Mises
stresses and deflections were found to be 0.282 MPa and 3.4 mm,
respectively. Dynamic pressures on the airfoil range from 1.04 to
1.23 kPa corresponding to velocity magnitudes in range of 22 to 66
The Analysis of Own Signals of PM Electrical Machines – Example of Eccentricity
This article presents a vibration diagnostic method
designed for Permanent Magnets (PM) electrical machines–traction
motors and generators. Those machines are commonly used in traction
drives of electrical vehicles and small wind or water systems. The
described method is very innovative and unique. Specific structural
properties of machines excited by permanent magnets are used in this
method - electromotive force (EMF) generated due to vibrations. There
was analyzed number of publications, which describe vibration
diagnostic methods, and tests of electrical machines and there was no
method found to determine the technical condition of such machine
basing on their own signals. This work presents field-circuit model,
results of static tests, results of calculations and simulations.
Permanent Magnet Machine Can Be a Vibration Sensor for Itself
This article presents a new vibration diagnostic
method designed to (PM) machines with permanent magnets. Those
devices are commonly used in small wind and water systems or
vehicles drives. The author’s method is very innovative and unique.
Specific structural properties of PM machines are used in this method
- electromotive force (EMF) generated due to vibrations. There was
analysed number of publications which describe vibration diagnostic
methods and tests of electrical PM machines and there was no
method found to determine the technical condition of such machine
basing on their own signals. In this article will be discussed: the
method genesis, the similarity of machines with permanent magnet to
vibration sensor and simulation and laboratory tests results. The
method of determination the technical condition of electrical machine
with permanent magnets basing on its own signals is the subject of
patent application and it is the main thesis of author’s doctoral
A Model for Analyzing the Startup Dynamics of a Belt Transmission Driven by a DC Motor
In this paper the vibration of a synchronous belt drive
during start-up is analyzed and discussed. Besides considering the
belt elasticity, the model here proposed also takes into consideration
the electromagnetic response of the DC motor. The solution of the
motion equations is obtained by means of the modal analysis in
state space, which allows to obtain the decoupling of all equations,
without introducing the hypothesis of proportional damping. The
mathematical model of the transmission and the solution algorithms
have been implemented within a computing software that allows the
user to simulate the dynamics of the system and to evaluate the effects
due to the elasticity of the belt branches and to the electromagnetic
behavior of the DC motor. In order to show the details of the
calculation procedure, the paper presents a case study developed with
the aid of the above-mentioned software.
PM Electrical Machines Diagnostic - Methods Selected
This paper presents a several diagnostic methods designed to electrical machinesespecially for permanent magnets (PM) machines. Those machines are commonly used in small wind and water systems and vehicles drives.Thosemethodsare preferred by the author in periodic diagnostic of electrical machines. The special attentionshould be paid to diagnostic method of turn-to-turn insulation and vibrations. Both of those methodswere createdinInstitute of Electrical Drives and MachinesKomel. The vibration diagnostic method is the main thesis of author’s doctoral dissertation. This is method of determination the technical condition of PM electrical machine basing on its own signals is the subject of patent application No P.405669. Specific structural properties of machines excited by permanent magnets are used in this method - electromotive force (EMF) generated due to vibrations. There was analysed number of publications which describe vibration diagnostic methods and tests of electrical machines with permanent magnets and there was no method found to determine the technical condition of such machine basing on their own signals.
Identification of Transformer Core Vibrations and the Effect of Third Harmonic in the Electricity Grid
In this work, an experimental technique is applied
for the measurements of the vibrations and deformation of a test
transformer core. Since the grid voltage contains some higher
harmonics, in addition to a purely sinusoidal magnetisation of the
core the presence of third harmonic is also studied. The vibrations of
the transformer core for points as well as the surface scan of the leg
show more deformation in the corners of the leg than the middle of
the leg. The influence of the higher harmonic of the magnetisation
on the core deformation is also more significant in the corners of the
leg. The core deformation shape under a sinusoidal magnetisation
with a higher harmonic is more wavy and fluctuating than that under
a purely sinusoidal magnetisation.
A Homogenisation Procedure for the Free Vibration Analysis of Functionally Graded Beams at Large Vibration Amplitudes
The purpose of the present paper is to show that the problem of geometrically nonlinear free vibrations of functionally graded beams (FGB) with immovable ends can be reduced to that of isotropic homogeneous beams with effective bending stiffness and axial stiffness parameters by using an homogenization procedure. The material properties of the functionally graded composites examined are assumed to be graded in the thickness direction and estimated through the rule of mixture. The theoretical model is based on the Euler-Bernouilli beam theory and the Von Kármán geometrical nonlinearity assumptions. Hamilton’s principle is applied and a multimode approach is derived to calculate the fundamental nonlinear frequency parameters, which are found to be in a good agreement with the published results. The non-dimensional curvatures associated to the nonlinear fundamental mode are also given for various vibration amplitudes in the case of clamped-clamped FGB.
Geometrically Non-Linear Axisymmetric Free Vibration Analysis of Functionally Graded Annular Plates
In this paper, the non-linear free axisymmetric vibration of a thin annular plate made of functionally graded material (FGM) has been studied by using the energy method and a multimode approach. FGM properties vary continuously as well as non-homogeneity through the thickness direction of the plate. The theoretical model is based on the classical plate theory and the Von Kármán geometrical non-linearity assumptions. An approximation has been adopted in the present work consisting of neglecting the in-plane deformation in the formulation. Hamilton’s principle is used to derive the governing equation of motion. The problem is solved by a numerical iterative procedure in order to obtain more accurate results for vibration amplitudes up to 1.5 times the plate thickness. The numerical results are given for the first axisymmetric non-linear mode shape for a wide range of vibration amplitudes and they are presented either in tabular form or in graphical form to show the effect that the vibration amplitude and the variation in material properties have significant effects on the frequencies and the bending stresses in large amplitude vibration of the functionally graded annular plate.
Large Vibration Amplitude of Circular Functionally Graded Plates Resting on Pasternak Foundations
In the present study, the problem of geometrically nonlinear free vibrations of functionally graded circular plates (FGCP) resting on Pasternak elastic foundation with immovable ends was studied. The material properties of the functionally graded composites examined were assumed to be graded in the thickness direction and estimated through the rule of mixture. The theoretical model is based on the classical Plate theory and the Von Kármán geometrical nonlinearity assumptions. Hamilton’s principle is applied and a multimode approach is derived to calculate the fundamental nonlinear frequency parameters, which are found to be in a good agreement with the published results dealing with the problem of functionally graded plates. On the other hand, the influence of the foundation parameters on the nonlinear frequency to the linear frequency ratio of the FGCP has been studied. The effect of the linear and shearing foundations is to decrease the frequency ratio, where it increases with the effect of the nonlinear foundation stiffness.
Geometrically Non-Linear Axisymmetric Free Vibrations of Thin Isotropic Annular Plates
The effects of large vibration amplitudes on the first axisymetric mode shape of thin isotropic annular plates having both edges clamped are examined in this paper. The theoretical model based on Hamilton’s principle and spectral analysis by using a basis of Bessel’s functions is adapted اhere to the case of annular plates. The model effectively reduces the large amplitude free vibration problem to the solution of a set of non-linear algebraic equations.
The governing non-linear eigenvalue problem has been linearised in the neighborhood of each resonance and a new one-step iterative technique has been proposed as a simple alternative method of solution to determine the basic function contributions to the non-linear mode shape considered.
Numerical results are given for the first non-linear mode shape for a wide range of vibration amplitudes. For each value of the vibration amplitude considered, the corresponding contributions of the basic functions defining the non-linear transverse displacement function and the associated non-linear frequency, the membrane and bending stress distributions are given. By comparison with the iterative method of solution, it was found that the present procedure is efficient for a wide range of vibration amplitudes, up to at least 1.8 times the plate thickness,
Experimental Investigation of Chatter Vibrations in Facing and Turning Processes
This paper investigates the occurrence of regenerative
chatter vibrations in facing and turning processes. Orthogonal turning
(facing) and normal turning experiments are carried out under stable
as well as in the presence of controlled chatter vibrations. The effects
of chatter vibrations on various sensor signals are captured and
analyzed using frequency domain methods, which successfully
detected the chatter vibrations close to the dominant mode of the
machine tool system.
Large Vibration Amplitudes of Circular Functionally Graded Thin Plates Resting on Winkler Elastic Foundations
This paper describes a study of geometrically
nonlinear free vibration of thin circular functionally graded (CFGP)
plates resting on Winkler elastic foundations. The material properties
of the functionally graded composites examined here are assumed to
be graded smoothly and continuously through the direction of the
plate thickness according to a power law and are estimated using the
rule of mixture. The theoretical model is based on the classical Plate
theory and the Von-Kármán geometrical nonlinearity assumptions.
An homogenization procedure (HP) is developed to reduce the
problem considered here to that of isotropic homogeneous circular
plates resting on Winkler foundation. Hamilton-s principle is applied
and a multimode approach is derived to calculate the fundamental
nonlinear frequency parameters which are found to be in a good
agreement with the published results. On the other hand, the
influence of the foundation parameters on the nonlinear fundamental
frequency has also been analysed.
Numerical Method Based On Initial Value-Finite Differences for Free Vibration of Stepped Thickness Plates
The main objective of the present paper is to derive an easy numerical technique for the analysis of the free vibration through the stepped regions of plates. Based on the utilities of the step by step integration initial values IV and Finite differences FD methods, the present improved Initial Value Finite Differences (IVFD) technique is achieved. The first initial conditions are formulated in convenient forms for the step by step integrations while the upper and lower edge conditions are expressed in finite difference modes. Also compatibility conditions are created due to the sudden variation of plate thickness. The present method (IVFD) is applied to solve the fourth order partial differential equation of motion for stepped plate across two different panels under the sudden step compatibility in addition to different types of end conditions. The obtained results are examined and the validity of the present method is proved showing excellent efficiency and rapid convergence.
Computational Initial Value Method for Vibration Analysis of Symmetrically Laminated Composite Plate
In the present paper, an improved initial value
numerical technique is presented to analyze the free vibration of
symmetrically laminated rectangular plate. A combination of the
initial value method (IV) and the finite differences (FD) devices is
utilized to develop the present (IVFD) technique. The achieved
technique is applied to the equation of motion of vibrating laminated
rectangular plate under various types of boundary conditions. Three
common types of laminated symmetrically cross-ply, orthotropic and
isotropic plates are analyzed here. The convergence and accuracy of
the presented Initial Value-Finite Differences (IVFD) technique have
been examined. Also, the merits and validity of improved technique
are satisfied via comparing the obtained results with those available
in literature indicating good agreements.
Influences of Thermal Relaxation Times on Generalized Thermoelastic Longitudinal Waves in Circular Cylinder
This paper is concerned with propagation of thermoelastic longitudinal vibrations of an infinite circular cylinder, in the context of the linear theory of generalized thermoelasticity with two relaxation time parameters (Green and Lindsay theory). Three displacement potential functions are introduced to uncouple the equations of motion. The frequency equation, by using the traction free boundary conditions, is given in the form of a determinant involving Bessel functions. The roots of the frequency equation give the value of the characteristic circular frequency as function of the wave number. These roots, which correspond to various modes, are numerically computed and presented graphically for different values of the thermal relaxation times. It is found that the influences of the thermal relaxation times on the amplitudes of the elastic and thermal waves are remarkable. Also, it is shown in this study that the propagation of thermoelastic longitudinal vibrations based on the generalized thermoelasticity can differ significantly compared with the results under the classical formulation. A comparison of the results for the case with no thermal effects shows well agreement with some of the corresponding earlier results.
Dynamic Modeling of Underplateform Damper used in Turbomachinery
The present work deals with the structural analysis of
turbine blades and modeling of turbine blades. A common failure
mode for turbine machines is high cycle of fatigue of compressor and
turbine blades due to high dynamic stresses caused by blade vibration
and resonance within the operation range of the machinery. In this
work, proper damping system will be analyzed to reduce the
vibrating blade. The main focus of the work is the modeling of under
platform damper to evaluate the dynamic analysis of turbine-blade
vibrations. The system is analyzed using Bond graph technique. Bond
graph is one of the most convenient ways to represent a system from
the physical aspect in foreground. It has advantage of putting together
multi-energy domains of a system in a single representation in a
unified manner. The bond graph model of dry friction damper is
simulated on SYMBOLS-shakti® software. In this work, the blades
are modeled as Timoshenko beam. Blade Vibrations under different
working conditions are being analyzed numerically.
Parametric Vibrations of Periodic Shells
Thin linear-elastic cylindrical circular shells having a
micro-periodic structure along two directions tangent to the shell
midsurface (biperiodic shells) are object of considerations. The aim
of this paper is twofold. First, we formulate an averaged nonasymptotic
model for the analysis of parametric vibrations or dynamical
stability of periodic shells under consideration, which has constant
coefficients and takes into account the effect of a cell size on the
overall shell behavior (a length-scale effect). This model is derived
employing the tolerance modeling procedure. Second we apply the
obtained model to derivation of frequency equation being a starting
point in the analysis of parametric vibrations. The effect of the microstructure
length oh this frequency equation is discussed.
Consideration of Criteria of Vibration Comfort of People in Diagnosis and Design of Buildings
The increasing influence of traffic on building
objects and people residing in them should be taken into account in
diagnosis and design. Users of buildings expect that vibrations
occurring in their environment, will not only lead to damage to the
building or its accelerated wear, but neither would affect the required
comfort in rooms designed to accommodate people. This article
describes the methods and principles useful in designing and building
diagnostics located near transportation routes, with particular
emphasis on the impact of traffic vibration on people in buildings. It
also describes the procedures used in obtaining information about the
parameters of vibrations in different cases of diagnostics and design.
A universal algorithm of procedure in diagnostics and design of
buildings taking into account assurance of human vibration comfort
of people residing in the these buildings was presented.
Pseudo-polynomial Motion Commands for Vibration Suppression of Belt-driven Rotary Platforms
The motion planning technique described in this paper has been developed to eliminate or reduce the residual vibrations of belt-driven rotary platforms, while maintaining unchanged the motion time and the total angular displacement of the platform. The proposed approach is based on a suitable choice of the motion command given to the servomotor that drives the mechanical device; this command is defined by some numerical coefficients which determine the shape of the displacement, velocity and acceleration profiles. Using a numerical optimization technique, these coefficients can be changed without altering the continuity conditions imposed on the displacement and its time derivatives at the initial and final time instants. The proposed technique can be easily and quickly implemented on an actual device, since it requires only a simple modification of the motion command profile mapped in the memory of the electronic motion controller.
Comparative Finite Element Simulation of Nonlinear Vibrations and Sensor Output Voltage of Smart Piezolaminated Structures
Two geometrically nonlinear plate theories, based either on first- or third-order transverse shear deformation theory are used for finite element modeling and simulation of the transient response of smart structures incorporating piezoelectric layers. In particular the time histories of nonlinear vibrations and sensor voltage output of a thin beam with a piezoelectric patch bonded to the surface due to an applied step force are studied.
Dynamic Optimization of Industrial Servomechanisms using Motion Laws Based On Bezier Curves
The motion planning procedure described in this paper has been developed in order to eliminate or reduce the residual vibrations of electromechanical positioning systems, without augmenting the motion time (usually imposed by production requirements), nor introducing overtime for vibration damping. The proposed technique is based on a suitable choice of the motion law assigned to the servomotor that drives the mechanism. The reference profile is defined by a Bezier curve, whose shape can be easily changed by modifying some numerical parameters. By means of an optimization technique these parameters can be modified without altering the continuity conditions imposed on the displacement and on its time derivatives at the initial and final time instants.
Bearing Fault Feature Extraction by Recurrence Quantification Analysis
In rotating machinery one of the critical components
that is prone to premature failure is the rolling bearing.
Consequently, early warning of an imminent bearing failure is much
critical to the safety and reliability of any high speed rotating
machines. This study is concerned with the application of Recurrence
Quantification Analysis (RQA) in fault detection of rolling element
bearings in rotating machinery. Based on the results from this study it
is reported that the RQA variable, percent determinism, is sensitive
to the type of fault investigated and therefore can provide useful
information on bearing damage in rolling element bearings.