International Science Index
Vibration Analysis of Magnetostrictive Nano-Plate by Using Modified Couple Stress and Nonlocal Elasticity Theories
In the present study, the free vibration of magnetostrictive nano-plate (MsNP) resting on the Pasternak foundation is investigated. Firstly, the modified couple stress (MCS) and nonlocal elasticity theories are compared together and taken into account to consider the small scale effects; in this paper not only two theories are analyzed but also it improves the MCS theory is more accurate than nonlocal elasticity theory in such problems. A feedback control system is utilized to investigate the effects of a magnetic field. First-order shear deformation theory (FSDT), Hamilton’s principle and energy method are utilized in order to drive the equations of motion and these equations are solved by differential quadrature method (DQM) for simply supported boundary conditions. The MsNP undergoes in-plane forces in x and y directions. In this regard, the dimensionless frequency is plotted to study the effects of small scale parameter, magnetic field, aspect ratio, thickness ratio and compression and tension loads. Results indicate that these parameters play a key role on the natural frequency. According to the above results, MsNP can be used in the communications equipment, smart control vibration of nanostructure especially in sensor and actuators such as wireless linear micro motor and smart nano valves in injectors.
Detection of Coupling Misalignment in a Rotor System Using Wavelet Transforms
Vibration analysis of a misaligned rotor coupling bearing system has been carried out while decelerating through its critical speed. The finite element method (FEM) is used to model the rotor system and simulate flexural vibrations. A flexible coupling with a frictionless joint is considered in the present work. The continuous wavelet transform is used to extract the misalignment features from the simulated time response. Subcritical speeds at one-half, one-third, and one-fourth the critical speed have appeared in the wavelet transformed vibration response of a misaligned rotor coupling bearing system. These features are also verified through a parametric study.
C Vibration Analysis of a Beam on Elastic Foundation with Elastically Restrained Ends Using Spectral Element Method
In this study, a spectral element method (SEM) is employed to predict the free vibration of a Euler-Bernoulli beam resting on a Winkler foundation with elastically restrained ends. The formulation of the dynamic stiffness matrix has been established by solving the differential equation of motion which was transformed to frequency domain. Non-dimensional natural frequencies and shape modes are obtained by solving the partial differential equations, numerically. Numerical comparisons and examples are performed to show the effectiveness of the SEM and to investigate the effects of various parameters, such as the springs at the boundaries and the elastic foundation parameter on the vibration frequencies. The obtained results demonstrate that the present method can also be applied to solve the more general problem of the dynamic analysis of structures with higher order precision.
Monitoring of Belt-Drive Defects Using the Vibration Signals and Simulation Models
The main aim of this paper is to dedicate the belt drive system faults like cogs missing, misalignment and belt worm using vibration analysis technique. Experimentally, the belt drive test-rig is equipped to measure vibrations signals under different operating conditions. Finite element 3D model of belt drive system is created and vibration response analyzed using commercial finite element software ABAQUS/CAE. Root mean square (RMS) and Crest Factor will serve as indicators of average amplitude of envelope analysis signals. The vibration signals pattern obtained from the simulation model and experimental data have the same characteristics. It can be concluded that each case of the RMS is more effective in detecting the defect for acceleration response. While Crest Factor parameter has a response with the displacement and velocity of vibration signals. Also it can be noticed that the model has difficulty in completing the solution when the misalignment angle is higher than 1 degree.
Damping and Stability Evaluation for the Dynamical Hunting Motion of the Bullet Train Wheel Axle Equipped with Cylindrical Wheel Treads
Classical matrix calculus and Routh-Hurwitz stability conditions, applied to the snake-like motion of the conical wheel axle, lead to the conclusion that the hunting mode is inherently unstable, and its natural frequency is a complex number. In order to analytically solve such a complicated vibration model, either the inertia terms were neglected, in the model designated as geometrical, or restrictions on the creep coefficients and yawing diameter were imposed, in the so-called dynamical model. Here, an alternative solution is proposed to solve the hunting mode, based on the observation that the bullet train wheel axle is equipped with cylindrical wheels. One argues that for such wheel treads, the geometrical hunting is irrelevant, since its natural frequency becomes nil, but the dynamical hunting is significant since its natural frequency reduces to a real number. Moreover, one illustrates that the geometrical simplification of the wheel causes the stabilization of the hunting mode, since the characteristic quartic equation, derived for conical wheels, reduces to a quadratic equation of positive coefficients, for cylindrical wheels. Quite simple analytical expressions for the damping ratio and natural frequency are obtained, without applying restrictions into the model of contact. Graphs of the time-depending hunting lateral perturbation, including the maximal and inflexion points, are presented both for the critically-damped and the over-damped wheel axles.
Free Vibration of Axially Functionally Graded Simply Supported Beams Using Differential Transformation Method
Free vibration analysis of homogenous and axially functionally graded simply supported beams within the context of Euler-Bernoulli beam theory is presented in this paper. The material properties of the beams are assumed to obey the linear law distribution. The effective elastic modulus of the composite was predicted by using the rule of mixture. Here, the complexities which appear in solving differential equation of transverse vibration of composite beams which limit the analytical solution to some special cases are overcome using a relatively new approach called the Differential Transformation Method. This technique is applied for solving differential equation of transverse vibration of axially functionally graded beams. Natural frequencies and corresponding normalized mode shapes are calculated for different Young’s modulus ratios. MATLAB code is designed to solve the transformed differential equation of the beam. Comparison of the present results with the exact solutions proves the effectiveness, the accuracy, the simplicity, and computational stability of the differential transformation method. The effect of the Young’s modulus ratio on the normalized natural frequencies and mode shapes is found to be very important.
Modeling and Simulation of Ship Structures Using Finite Element Method
The development in the construction of unconventional ships and the implementation of lightweight materials have shown a large impulse towards finite element (FE) method, making it a general tool for ship design. This paper briefly presents the modeling and analysis techniques of ship structures using FE method for complex boundary conditions which are difficult to analyze by existing Ship Classification Societies rules. During operation, all ships experience complex loading conditions. These loads are general categories into thermal loads, linear static, dynamic and non-linear loads. General strength of the ship structure is analyzed using static FE analysis. FE method is also suitable to consider the local loads generated by ballast tanks and cargo in addition to hydrostatic and hydrodynamic loads. Vibration analysis of a ship structure and its components can be performed using FE method which helps in obtaining the dynamic stability of the ship. FE method has developed better techniques for calculation of natural frequencies and different mode shapes of ship structure to avoid resonance both globally and locally. There is a lot of development towards the ideal design in ship industry over the past few years for solving complex engineering problems by employing the data stored in the FE model. This paper provides an overview of ship modeling methodology for FE analysis and its general application. Historical background, the basic concept of FE, advantages, and disadvantages of FE analysis are also reported along with examples related to hull strength and structural components.
Free Vibration Analysis of Functionally Graded Pretwisted Plate in Thermal Environment Using Finite Element Method
The free vibration behavior of thick pretwisted cantilevered functionally graded material (FGM) plate subjected to the thermal environment is investigated numerically in the present paper. A mathematical model is developed in the framework of higher order shear deformation theory (HOST) with C0 finite element formulation i.e. independent displacement and rotations. The material properties are assumed to be temperature dependent and vary continuously through the thickness based on the volume fraction exponent in simple power rule. The finite element model has been discretized into eight node quadratic serendipity elements with node wise seven degrees of freedom. The effect of plate geometry, temperature field, material composition, and the modal analysis on the vibrational characteristics is examined. Finally, the results are verified by comparing with those available in literature.
Forced Vibration of a Planar Curved Beam on Pasternak Foundation
The objective of this study is to investigate the forced vibration analysis of a planar curved beam lying on elastic foundation by using the mixed finite element method. The finite element formulation is based on the Timoshenko beam theory. In order to solve the problems in frequency domain, the element matrices of two nodded curvilinear elements are transformed into Laplace space. The results are transformed back to the time domain by the well-known numerical Modified Durbin’s transformation algorithm. First, the presented finite element formulation is verified through the forced vibration analysis of a planar curved Timoshenko beam resting on Winkler foundation and the finite element results are compared with the results available in the literature. Then, the forced vibration analysis of a planar curved beam resting on Winkler-Pasternak foundation is conducted.
Finite Element Modeling of Stockbridge Damper and Vibration Analysis: Equivalent Cable Stiffness
Aeolian vibrations are the major cause for the
failure of conductor cables. Using a Stockbridge damper reduces
these vibrations and increases the life span of the conductor
cable. Designing an efficient Stockbridge damper that suits the
conductor cable requires a robust mathematical model with minimum
assumptions. However it is not easy to analytically model the complex
geometry of the messenger. Therefore an equivalent stiffness must be
determined so that it can be used in the analytical model. This paper
examines the bending stiffness of the cable and discusses the effect
of this stiffness on the natural frequencies. The obtained equivalent
stiffness compensates for the assumption of modeling the messenger
as a rod. The results from the free vibration analysis of the analytical
model with the equivalent stiffness is validated using the full scale
finite element model of the Stockbridge damper.
High Sensitivity Crack Detection and Locating with Optimized Spatial Wavelet Analysis
In this study, a spatial wavelet-based crack localization technique for a thick beam is presented. Wavelet scale in spatial wavelet transformation is optimized to enhance crack detection sensitivity. A windowing function is also employed to erase the edge effect of the wavelet transformation, which enables the method to detect and localize cracks near the beam/measurement boundaries. Theoretical model and vibration analysis considering the crack effect are first proposed and performed in MATLAB based on the Timoshenko beam model. Gabor wavelet family is applied to the beam vibration mode shapes derived from the theoretical beam model to magnify the crack effect so as to locate the crack. Relative wavelet coefficient is obtained for sensitivity analysis by comparing the coefficient values at different positions of the beam with the lowest value in the intact area of the beam. Afterward, the optimal wavelet scale corresponding to the highest relative wavelet coefficient at the crack position is obtained for each vibration mode, through numerical simulations. The same procedure is performed for cracks with different sizes and positions in order to find the optimal scale range for the Gabor wavelet family. Finally, Hanning window is applied to different vibration mode shapes in order to overcome the edge effect problem of wavelet transformation and its effect on the localization of crack close to the measurement boundaries. Comparison of the wavelet coefficients distribution of windowed and initial mode shapes demonstrates that window function eases the identification of the cracks close to the boundaries.
Health Monitoring and Failure Detection of Electronic and Structural Components in Small Unmanned Aerial Vehicles
Fully autonomous small Unmanned Aerial Vehicles
(UAVs) are increasingly being used in many commercial applications.
Although a lot of research has been done to develop safe, reliable
and durable UAVs, accidents due to electronic and structural failures
are not uncommon and pose a huge safety risk to the UAV operators
and the public. Hence there is a strong need for an automated health
monitoring system for UAVs with a view to minimizing mission
failures thereby increasing safety. This paper describes our approach
to monitoring the electronic and structural components in a small
UAV without the need for additional sensors to do the monitoring.
Our system monitors data from four sources; sensors, navigation
algorithms, control inputs from the operator and flight controller
outputs. It then does statistical analysis on the data and applies
a rule based engine to detect failures. This information can then
be fed back into the UAV and a decision to continue or abort the
mission can be taken automatically by the UAV and independent of
the operator. Our system has been verified using data obtained from
real flights over the past year from UAVs of various sizes that have
been designed and deployed by us for various applications.
Experimental Set-Up for Investigation of Fault Diagnosis of a Centrifugal Pump
Centrifugal pumps are complex machines which can experience different types of fault. Condition monitoring can be used in centrifugal pump fault detection through vibration analysis for mechanical and hydraulic forces. Vibration analysis methods have the potential to be combined with artificial intelligence systems where an automatic diagnostic method can be approached. An automatic fault diagnosis approach could be a good option to minimize human error and to provide a precise machine fault classification. This work aims to introduce an approach to centrifugal pump fault diagnosis based on artificial intelligence and genetic algorithm systems. An overview of the future works, research methodology and proposed experimental setup is presented and discussed. The expected results and outcomes based on the experimental work are illustrated.
Free Vibration Analysis of Conical Helicoidal Rods Having Elliptical Cross Sections Positioned in Different Orientation
In this study, the free vibration analysis of conical helicoidal rods with two different elliptically oriented cross sections is investigated and the results are compared by the circular cross-section keeping the net area for all cases equal to each other. Problems are solved by using the mixed finite element formulation. Element matrices based on Timoshenko beam theory are employed. The finite element matrices are derived by directly inserting the analytical expressions (arc length, curvature, and torsion) defining helix geometry into the formulation. Helicoidal rod domain is discretized by a two-noded curvilinear element. Each node of the element has 12 DOFs, namely, three translations, three rotations, two shear forces, one axial force, two bending moments and one torque. A parametric study is performed to investigate the influence of elliptical cross sectional geometry and its orientation over the natural frequencies of the conical type helicoidal rod.
Vibration and Parametric Instability Analysis of Delaminated Composite Beams
This paper revisits the free vibration problem of delaminated composite beams. It is shown that during the vibration of composite beams the delaminated parts are subjected to the parametric excitation. This can lead to the dynamic buckling during the motion of the structure. The equation of motion includes time-dependent stiffness and so it leads to a system of Mathieu-Hill differential equations. The free vibration analysis of beams is carried out in the usual way by using beam finite elements. The dynamic buckling problem is investigated locally, and the critical buckling forces are determined by the modified harmonic balance method by using an imposed time function of the motion. The stability diagrams are created, and the numerical predictions are compared to experimental results. The most important findings are the critical amplitudes at which delamination buckling takes place, the stability diagrams representing the instability of the system, and the realistic mode shape prediction in contrast with the unrealistic results of models available in the literature.
Formulating the Stochastic Finite Elements for Free Vibration Analysis of Plates with Variable Elastic Modulus
In this study, the effect of uncertainty in elastic modulus of a plate on free vibration response is investigated. For this purpose, the elastic modulus of the plate is modeled as stochastic variable with normal distribution. Moreover, the distance autocorrelation function is used for stochastic field. Then, by applying the finite element method and Monte Carlo simulation, stochastic finite element relations are extracted. Finally, with a numerical test, the effect of uncertainty in the elastic modulus on free vibration response of a plate is studied. The results show that the effect of uncertainty in elastic modulus of the plate cannot play an important role on the free vibration response.
Elman Neural Network for Diagnosis of Unbalance in a Rotor-Bearing System
The operational life of rotating machines has to be extended using a predictive condition maintenance tool. Among various condition monitoring techniques, vibration analysis is most widely used technique in industry. Signals are extracted for evaluating the condition of machine; further diagnostics is carried out with detected signals to extend the life of machine. With help of detected signals, further interpretations are done to predict the occurrence of defects. To study the problem of defects, a test rig with various possibilities of defects is constructed and experiments are performed considering the unbalanced condition. Further, this paper presents an approach for fault diagnosis of unbalance condition using Elman neural network and frequency-domain vibration analysis. Amplitudes with variation in acceleration are fed to Elman neural network to classify fault or no-fault condition. The Elman network is trained, validated and tested with experimental readings. Results illustrate the effectiveness of Elman network in rotor-bearing system.
Modeling of a Vehicle Wheel System Having a Built-in Suspension Structure Consisted of Radially Deployed Colloidal Spokes between Hub and Rim
In this work, by replacing the traditional solid spokes with colloidal spokes, a vehicle wheel with a built-in suspension structure is proposed. Following the background and description of the wheel system, firstly, a vibration model of the wheel equipped with colloidal spokes is proposed, and based on such model the equivalent damping coefficients and spring constants are identified. Then, a modified model of a quarter-vehicle moving on a rough pavement is proposed in order to estimate the transmissibility of vibration from the road roughness to vehicle body. In the end, the optimal design of the colloidal spokes and the optimum number of colloidal spokes are decided in order to minimize the transmissibility of vibration, i.e., to maximize the ride comfort of the vehicle.
Bearing Condition Monitoring with Acoustic Emission Techniques
Monitoring the conditions of rotating machinery, such
as bearings, is important in order to improve the stability of work.
Acoustic Emission (AE) and vibration analysis are some of the most
accomplished techniques used for this purpose. Acoustic emission
has the ability to detect the initial phase of component degradation.
Moreover, it has been observed that vibration analysis is not as
successful at low rotational speeds (below 100 rpm). This because the
energy generated within this speed region is not detectable using
conventional vibration. From this perspective, this paper has
presented a brief review of using acoustic emission techniques for
monitoring bearing conditions.
A Fault Analysis Cracked-Rotor-to-Stator Rub and Unbalance by Vibration Analysis Technique
An analytical 4-DOF nonlinear model of a de Laval
rotor-stator system based on Energy Principles has been used
theoretically and experimentally to investigate fault symptoms in a
rotating system. The faults, namely rotor-stator-rub, crack and
unbalance are modeled as excitations on the rotor shaft. Mayes
steering function is used to simulate the breathing behaviour of the
crack. The fault analysis technique is based on waveform signal,
orbits and Fast Fourier Transform (FFT) derived from simulated and
real measured signals. Simulated and experimental results manifest
considerable mutual resemblance of elliptic-shaped orbits and FFT
for a same range of test data.
Dynamic Simulation of IC Engine Bearings for Fault Detection and Wear Prediction
Journal bearings used in IC engines are prone to premature
failures and are likely to fail earlier than the rated life due to
highly impulsive and unstable operating conditions and frequent
starts/stops. Vibration signature extraction and wear debris analysis
techniques are prevalent in industry for condition monitoring of
rotary machinery. However, both techniques involve a great deal of
technical expertise, time, and cost. Limited literature is available on
the application of these techniques for fault detection in reciprocating
machinery, due to the complex nature of impact forces that
confounds the extraction of fault signals for vibration-based analysis
and wear prediction. In present study, a simulation model was developed to investigate
the bearing wear behaviour, resulting because of different operating
conditions, to complement the vibration analysis. In current
simulation, the dynamics of the engine was established first, based on
which the hydrodynamic journal bearing forces were evaluated by
numerical solution of the Reynold’s equation. In addition, the
essential outputs of interest in this study, critical to determine wear
rates are the tangential velocity and oil film thickness between the
journals and bearing sleeve, which if not maintained appropriately,
have a detrimental effect on the bearing performance. Archard’s wear prediction model was used in the simulation to
calculate the wear rate of bearings with specific location information
as all determinative parameters were obtained with reference to crank
rotation. Oil film thickness obtained from the model was used as a
criterion to determine if the lubrication is sufficient to prevent contact
between the journal and bearing thus causing accelerated wear. A
limiting value of 1 μm was used as the minimum oil film thickness
needed to prevent contact. The increased wear rate with growing
severity of operating conditions is analogous and comparable to the
rise in amplitude of the squared envelope of the referenced vibration
signals. Thus on one hand, the developed model demonstrated its
capability to explain wear behaviour and on the other hand it also
helps to establish a co-relation between wear based and vibration
based analysis. Therefore, the model provides a cost effective and
quick approach to predict the impending wear in IC engine bearings
under various operating conditions.
Effect of Infills in Influencing the Dynamic Responses of Multistoried Structures
Investigating the dynamic responses of high rise
structures under the effect of siesmic ground motion is extremely
important for the proper analysis and design of multitoried structures.
Since the presence of infilled walls strongly influences the behaviour
of frame systems in multistoried buildings, there is an increased need
for developing guidelines for the analysis and design of infilled
frames under the effect of dynamic loads for safe and proper design
of buildings. In this manuscript, we evaluate the natural frequencies
and natural periods of single bay single storey frames considering the
effect of infill walls by using the Eigen value analysis and validating
with SAP 2000 (free vibration analysis). Various parameters obtained
from the diagonal strut model followed for the free vibration analysis
is then compared with the Finite Element model, where infill is
modeled as shell elements (four noded). We also evaluated the effect
of various parameters on the natural periods of vibration obtained by
free vibration analysis in SAP 2000 comparing them with those
obtained by the empirical expressions presented in I.S. 1893(Part I)-
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
Application of Artificial Neural Network in the Investigation of Bearing Defects
Maintenance and design engineers have great concern
for the functioning of rotating machineries due to the vibration
phenomenon. Improper functioning in rotating machinery originates
from the damage to rolling element bearings. The status of rolling
element bearings require advanced technologies to monitor their
health status efficiently and effectively. Avoiding vibration during
machine running conditions is a complicated process. Vibration
simulation should be carried out using suitable sensors/ transducers to
recognize the level of damage on bearing during machine operating
conditions. Various issues arising in rotating systems are interlinked
with bearing faults. This paper presents an approach for fault
diagnosis of bearings using neural networks and time/frequencydomain
The Free Vibration Analysis of Honeycomb Sandwich Beam Using 3D and Continuum Model
In this study free vibration analysis of aluminum
honeycomb sandwich structures were carried out experimentally and
numerically. The natural frequencies and mode shapes of sandwich
structures fabricated with different configurations for clamped-free
boundary condition were determined. The effects of lower and upper
face sheet thickness, the core material thickness, cell diameter, cell
angle and foil thickness on the vibration characteristics were
examined. The numerical studies were performed with ANSYS
package. While the sandwich structures were modeled in ANSYS the
continuum model was used. Later, the numerical results were
compared with the experimental findings.
Out-of-Plane Free Vibrations of Circular Rods
In this study, out-of-plane free vibrations of a circular
rods is investigated theoretically. The governing equations for
naturally twisted and curved spatial rods are obtained using
Timoshenko beam theory and rewritten for circular rods. Effects of
the axial and shear deformations are considered in the formulations.
Ordinary differential equations in scalar form are solved analytically
by using transfer matrix method. The circular rods of the mass matrix
are obtained by using straight rod of consistent mass matrix. Free
vibrations frequencies obtained by solving eigenvalue problem. A
computer program coded in MATHEMATICA language is prepared.
Circular beams are analyzed through various examples for free
vibrations analysis. Results are compared with ANSYS results based
on finite element method and available in the literature.
Probabilistic Wavelet Neural Network Based Vibration Analysis of Induction Motor Drive
In this paper proposed the effective fault detection of industrial drives by using Biorthogonal Posterior Vibration Signal-Data Probabilistic Wavelet Neural Network (BPPVS-WNN) system. This system was focused to reducing the current flow and to identify faults with lesser execution time with harmonic values obtained through fifth derivative. Initially, the construction of Biorthogonal vibration signal-data based wavelet transform in BPPVS-WNN system localizes the time and frequency domain. The Biorthogonal wavelet approximates the broken bearing using double scaling and factor, identifies the transient disturbance due to fault on induction motor through approximate coefficients and detailed coefficient. Posterior Probabilistic Neural Network detects the final level of faults using the detailed coefficient till fifth derivative and the results obtained through it at a faster rate at constant frequency signal on the industrial drive. Experiment through the Simulink tool detects the healthy and unhealthy motor on measuring parametric factors such as fault detection rate based on time, current flow rate, and execution time.
Numerical Study of a Butterfly Valve for Vibration Analysis and Reduction
This work presents a Computational Fluid Dynamics
(CFD) simulation of a butterfly valve used to control the flow of
combustible gas mixture in an industrial process setting.The work
uses CFD simulation to analyze the flow characteristics in the
vicinity of the valve, including the pressure distributions and
Frequency spectrum of the pressure pulsations downstream the valves
and the vortex shedding allow predicting the torque fluctuations
acting on the valve shaft and the possibility of generating mechanical
vibration and resonance.These fluctuations are due to aerodynamic
torque resulting from fluid turbulence and vortex shedding in the
The valve analyzed is located in a pipeline between two opposing
90o elbows, which exposes the valve and the surrounding structure to
the turbulence generated upstream and downstream the elbows at
either end of the pipe.CFD simulations show that the best location for
the valve from a vibration point of view is in the middle of the pipe
joining the elbows.
Vibration Analysis of Functionally Graded Engesser- Timoshenko Beams Subjected to Axial Load Located on a Continuous Elastic Foundation
This paper studies free vibration of functionally
graded beams Subjected to Axial Load that is simply supported at
both ends lies on a continuous elastic foundation. The displacement
field of beam is assumed based on Engesser-Timoshenko beam
theory. The Young's modulus of beam is assumed to be graded
continuously across the beam thickness. Applying the Hamilton's
principle, the governing equation is established. Resulting equation is
solved using the Euler's Equation. The effects of the constituent
volume fractions and foundation coefficient on the vibration
frequency are presented. To investigate the accuracy of the present
analysis, a compression study is carried out with a known data.
Nonlinear Impact Responses for a Damped Frame Supported by Nonlinear Springs with Hysteresis Using Fast FEA
This paper deals with nonlinear vibration analysis
using finite element method for frame structures consisting of elastic
and viscoelastic damping layers supported by multiple nonlinear
concentrated springs with hysteresis damping. The frame is supported
by four nonlinear concentrated springs near the four corners. The
restoring forces of the springs have cubic non-linearity and linear
component of the nonlinear springs has complex quantity to represent
linear hysteresis damping. The damping layer of the frame structures
has complex modulus of elasticity. Further, the discretized equations in
physical coordinate are transformed into the nonlinear ordinary
coupled differential equations using normal coordinate corresponding
to linear natural modes. Comparing shares of strain energy of the
elastic frame, the damping layer and the springs, we evaluate the
influences of the damping couplings on the linear and nonlinear impact
responses. We also investigate influences of damping changed by
stiffness of the elastic frame on the nonlinear coupling in the damped