The structural health monitoring by piezoelectric wafer active sensor (PWAS) using electromechanical impedance method used for monitoring of structure. In present work impedance method of elasto-plastic beam structure is studied. In order to model the effect of a plastic in beam, the moment-curvature relationship for elasto-plastic region for loading and unloading is used. The finite difference method is used to discretize beam with piezoelectric. The piezoelectric actuator is modeled by equivalent moment. Then output current of piezoelectric sensor is calculated. Firstly, elastic modeling of beam is considered that this is leads to linear system equation. In linear system, time domain system equations are calculated and Fourier transform of current output obtained, and then impedance of PWAS in frequency domain is calculated. Secondly, the elasto-plastic of beam is modeled. This phenomenon leads to the nonlinear system equations. These nonlinear equations are solved using finite difference method for any harmonic voltage applied to actuator. Then impedance of PWAS is calculated. Two methods are used to detect elasto-plastic modeling on PWAS impedance. At the first, frequency response of elastic beam as intact model is compared with elasto-plastic results in a desired frequency range. Second, only frequency response of one harmonic is computed with its super-harmonics. Finally, the detection method of linear is compared with nonlinear model.

This work explores the effects of geometrical nonlinearities in the vibration analysis of rotating structures and helicopter blades. Structures are modelled via higher-order beam theories with variable kinematics. These theories fall in the domain of the Carrera Unified Formulation (CUF), according to which the nonlinear equations of motion of rotating blades can be written in terms of fundamental nuclei, whose formalism is an invariant of the theory approximation. The inherent three-dimensional nature of CUF enables one to include all Green-Lagrange strain components as well as all coupling effects due to the geometrical features and the three-dimensional constitutive law. Numerical solutions are considered and opportunely discussed. Also, linearized and full nonlinear solutions for vibrating rotating blades are compared both in case of small amplitudes and in the large deflections/rotations regime.

Multiphase flows are encountered in many engineering problems. Particularly in the oil and gas industry, many applications involve the transportation of a mixture of oil and natural gas in long pipelines from offshore platforms to the continent. Numerical simulations of steady and unsteady flows in pipelines are usually based on one-dimensional models, such as the two-fluid model, the drift-flux model and the homogeneous equilibrium model. The 1991’s version of the well-known and widely-used commercial software OLGA describes a system of non-linear equations of the two-fluid-model type, with an extra equation for the presence of liquid droplets. It is well known that one-dimensional formulations may be physically inconsistent due to the loss of hyperbolicity. In these cases, the associated eigenvalues become complex numbers and the model loses physical meaning locally. This paper presents a numerical study of the 1991’s version of the software OLGA, for an isothermal flow of stratified pattern, in a horizontal pipeline. For each point of interest in the stratified-pattern flow map, the eigenvalues are numerically calculated in order to verify if the eigenvalues are real and also to assess their signs. The results indicate that the model is conditionally hyperbolic and loses hyperbolicity in a vast area of the stratified region under certain flow conditions. Even though the model is not unconditionally hyperbolic, some simulations here performed for typical offshore pipeline flows are shown to be in the hyperbolic region.

In this work, an impact experiment on a composite plate with unknown material properties (its group velocity profile is unknown) is implemented to localize the impact points. A pencil lead break is used to generate acoustic emission (AE) signals which are acquired by six piezoelectric wafer active sensors (PWAS). These sensors are distributed with a particular configuration in two clusters on the plate. The time of flight (TOF) of acquired signals is estimated at the starting points of these signals. The continuous wavelet transform (CWT) of received signals are calculated with AGU Vallen wavelet program to get the accurate values of the TOF of these signals. Two methods are used for determining the coordinates of impact points (localization the impact point). The first method is the new technique (method 1) by Kundu. This technique has two linear equations with two unknowns (the coordinate of AE source point). The second method is the nonlinear algorithm (method 2). This algorithm has a set of six nonlinear equations with five unknowns. Two MATLAB codes are implemented separately to solve the linear and nonlinear equations. The results show good indications for the location of impact points in both methods. The location errors of calculated impact points are divided by constant distance to get independent percentage errors with the site of the coordinate.

During drilling operations, drill string interacts continuously with rock formation, which result in severe shock and vibrations. Lateral, torsion and axial vibration modes often cause failures of Bottom Hole Assembly (BHA), drill pipe abrasive wear, drill bit and wall borehole damages. It also leads to reduction in Rate of Penetration (ROP) and consequently incur unnecessarily high costs. The Lagrangian approach has been used in this study to attain drill pipe lateral and torsional vibration coupling equations of motion. The mathematical model is expressed in terms of four independent degrees of freedom. The effects of bending and torsion vibrations, and whirling motion of the drill string are incorporated in the developed model. A set of nonlinear equations are solved numerically to obtain the response of the system. In this work, we also present a brief description of an in-house constructed experimental setup. The setup has the capability to imitate the downhole axial, lateral and torsional vibration modes and mechanisms. Experimental investigations for the drill pipe fatigue failure due to lateral and torsional cyclic stresses induced in the drill string are also presented. Such investigations are essential for oil/gas industry as they provide solutions for very common problems such as drill string fatigue failure. The performance of the setup was validated. Numbers of tests were performed to investigate the effects of rotational speeds on the vibration amplitudes of different drill string sizes.

One of the main objectives of the structural health monitoring by piezoelectric wafer active sensor (PWAS) using electromechanical impedance method is continuously damage detection applications. In present work impedance method of beam structure is considered and the effect of early crack using breathing crack modeling is studied. In order to model the effect of a crack in beam, the beam is connected with a rotational spring in crack location. The Rayleigh–Ritz method is used to generate ordinary differential equation of cracked beam. Firstly, only open crack is considered that this is leads to linear system equation. In linear system, time domain system equations are converted to frequency domain, and then impedance of PWAS in frequency domain is calculated. Secondly, the breathing crack is modeled to be fully open or fully closed. This phenomenon leads to the nonlinear system equations. These nonlinear equations are solved using pseudo-arc length continuation scheme and collocation method for any harmonic voltage applied to actuator. Then impedance of PWAS is calculated. Two methods are used to detect early crack using breathing crack modeling on PWAS impedance. At the first, frequency response of breathing crack in the frequency range with its sub-harmonics is calculated. Second, only frequency response of one harmonic is computed with its super-harmonics. Finally, the detection method of linear is compared with nonlinear model.

Micro-Electro-Mechanical devices have shown enormous popularity in engineering devices as sensors and actuators. In this paper, the instability, i.e. the dynamic pull-in behavior, of an electrically actuated circular micro-membrane is studied. In order to investigate the periodic solutions, detect bifurcations and follow branches of the solution, the non-linear equation of motion is derived using an energy approach, and, is solved by using a pseudo arc-length continuation and collocation technique. It has been shown that, both hardening and/or softening nonlinear responses could emerge depending on the applied DC voltage. The results indicate that the critical load parameters, namely DC and AC voltages and the excitation frequency, have a major influence on the pull-in characteristics of the micro-membrane. The results reveal different dynamic pull-in mechanisms. In addition, they accurately show the decrease of the pull-in voltage due to dynamic loading. The proposed approximate solution is very fast and robust for detecting the pull-in instability. It allows observation of both global and local softening behavior even close to dynamic pullin, where the resonance frequency is almost equal to zero.

The nonlinear vibrations of a water-filled circular cylindrical shell subjected to radial harmonic excitation in the spectral neighborhood of the lowest resonances are investigated numerically and experimentally by using a seamless aluminum sample. The experimental boundary conditions are close to a simply supported circular cylindrical shell. Modal analysis reveals the presence of predominantly radial driven and companion modes in the low frequency range, implying the existence of a traveling wave phenomenon in the nonlinear field. Experimental studies previously carried out on cylindrical shells did not permit the complete identification of the characteristic traveling wave response and of its non-stationary nature. The added mass of the internal quiescent, incompressible and inviscid fluid results in an increase of the weakly softening behavior of the shell, as expected. The minimization of the added mass due to the excitation system and the negligible entity of the geometric imperfections of the shell allow the appearance of an exact one-to-one internal resonance between driven and companion modes. This internal resonance gives rise to a travelling wave response around the shell circumference and non-stationary, quasi-periodic vibrations, which are experimentally verified by means of stepped-sine testing with feedback control of the excitation amplitude. The same phenomenon is observed in the nonlinear response obtained numerically. The traveling wave is measured by means of state-of-the-art laser Doppler vibrometry applied to multiple points on the structure simultaneously. Previous studies present in literature did not show if this vibration can be chaotic for relatively small vibration amplitudes. Chaos is here observed in the frequency region where the travelling wave response is present for vibrations amplitudes smaller than the thickness of the shell. The relevant nonlinear reduced order model of the shell is based on the Novozhilov nonlinear shell theory retaining in-plane inertia and on an expansion of the displacements in terms of a properly chosen base of linear modes. An energy approach is used to obtain the nonlinear equations of motion, which are numerically studied (i) by using a code based on arc-length continuation and collocation method that allows bifurcation analysis in case of stationary vibrations, (ii) by a continuation code based on direct integration and Poincaré maps, which also evaluates the maximum Lyapunov exponent in case of non-stationary vibrations. The comparison of experimental and numerical results is particularly satisfactory throughout the various excitation amplitude levels considered. The two methods concur in describing the progressive development of the companion mode into a fully developed traveling wave and the subsequent appearance of quasi-periodic and eventually chaotic vibrations.

Structural elements with thin-walled open cross-sections are common in metal and composite structures. These thin-walled beams have generally a good flexural strength with respect to the axis of greatest inertia, but a low flexural stiffness in relation to the second principal axis and a low torsional stiffness. These elements generally have an instability, which leads to a flexural-flexural-torsional coupling. The same applies to the vibration modes. Many of these structures work in a nonlinear regime, and a nonlinear formulation that takes into account large displacements and the flexural-flexural-torsional coupling is required. In this work a nonlinear beam theory that takes into account large displacements, warping and shortening effects, as well as flexural-flexural-torsional coupling is adopted. The governing nonlinear equations of motion are discretized in space using the Galerkin method and the discretized equations of motion are solved by the Runge-Kutta method. Special attention is given to the nonlinear oscillations of beams with low torsional stiffness and its influence on the bifurcations and instabilities of the structure, a problem not tackled in the previous literature on this subject. Time responses, phase portraits and bifurcation diagrams are used to unveil the complex dynamic.

The design criteria of converter cooling system for a 2.5 MW permanent magnet direct-drive wind turbine generator were investigated. Two (2) distribution networks with pipe sizes of DN40 and DN50 were used as basis for fluid flow analysis. The theoretical system pressure drop and system volume flow rate of converter cooling system were calculated using the governing equations of mass conservation, pump performance curve and distribution network characteristics. The system of nonlinear equations was solved using multivariable Newton-Raphson method with the solution vector determined using LU decomposition method. Numerical results suggest that the DN50 pipe provides a pressure drop limit of less than 300 Pa/m in the converter cooling system better than the pressure drop obtained from a DN40 pipe. The system volume flow rate of DN50 pipe was found to be above the operating limit of heat exchanger requirement of 135.30 L/min which needs to dissipate heat with a minimum of 50 kW.

This paper demonstrates the importance of the intelligent controllers over the conventional methods. A speed control of the DC motor is developed using both Neural Networks and Fuzzy logic controller in MATLAB environment as intelligent controllers. In addition a conventional PID controller is developed for comparison purposes. Both intelligent controllers are designed based on the simulation results of the nonlinear equations in addition to the expert pre knowledge of the system. The output response of the system is obtained using the two types of the intelligent controllers, in addition to the conventional PID controller. The performance of the designed Neural Networks, Fuzzy logic controller and the PID controller is compared and investigated. Finally, the results show that the neural network has minimum overshoot, and minimum steady state parameters. This shows more efficiency of the intelligent controllers over the conventional PID controller. Also it shows that Neural Networks is better than Fuzzy logic controller in terms of over shoot and rising time. At the end of this paper an implementation of Graphical User Interface (GUI) method is developed. The main purpose of the GUI is to give the users a chance to use the program in a simple way without the need to understand the program languages.

Large offshore renewable energy investments require the use of maintenance boats to keep them in operable conditions. Unfortunately, due to rough seas in some of the project locations, the transferring of crew members from vessel to turbine or platform is no easy task. Thus, the research presented is focused at further looking into add on stability systems for marine vessels to further ease the process of offshore platform maintenance and crew member safety. The rolling and pitching of ships and boats induced by the ocean waves results in undesirable motion. In an effort to increase the stability of the deck/platform and human comfort and safety, various add-on stability systems have been developed. Of interest in the research presented are internal active systems, specifically the active gyroscopic stabilizer. Previous research and industrial use of active gyroscopic roll stabilizers has shown and proven the effectiveness of the system to reduce rolling motion. The research presented here is focused on developing a more detailed mathematical analysis of a marine vessel installed with active gyroscopic roll stabilizer(s). Through the use of the moving frame method developed by the second author, a novel approach has been developed to derive a mathematical model for two different cases: 1) a marine vessel with a single gyroscopic roll stabilizer and 2) a marine vessel with two gyroscopic roll stabilizers. The moving frame method allows for a systematic derivation despite the increase in complexity of the system as the number of stabilizers is increased. Lastly, the nonlinear equations of motion of a ship with a gyroscopic roll stabilizer are derived.

Global attempts to increase generation of clean and reproducible natural energy have greatly contributed to the progress of solar, wind, biomass, and geothermal energy generation. To meet the goal set by the Renewable Portfolio Standards (RPS) in the United States, it is advisable for several of the coastal states to tap into the least explored resource: ocean-wave energy. There are many advantages to ocean-wave energy generation. First, the energy per unit area is 20 to 30 times larger compared with solar and five to ten times larger when compared to wind energy. Second, waves are more easily predicted than wind. Currently, there are several challenges with capturing ocean energy: With respect to the environment, noise pollution and effects on marine life need to be taken into consideration; with respect to design, ocean-wave power generators need to withstand large waves due to hurricanes and be designed to lessen visual pollution. There are various methods and devices used to capture ocean wave energy. Point absorbers, such as PowerBuoy , can harness vertical or heaving motion into electricity while attenuators like Pelamis use the induced movement of its joints from the incoming waves. Unfortunately, many have few parameters that can be varied to optimize power generation and or suffer from the various challenges mentioned above. The gyroscopic ocean wave energy converter harnesses the rocking or pitching motion induced by the ocean waves and converts it into rotary motion that is then fed to a generator. Furthermore, it is a fully enclosed floating device that has several parameters that can be varied to optimize power output. Previous work has demonstrated the viability of such a device, but the theoretical modeling of these converters is still in its infancy compared to that of other ocean wave energy converters. The objective of the research presented is to fully understand the mechanisms of power generation in the gyroscopic ocean wave energy converter. Using the moving frame method, a mathematical model of the device is developed. The nonlinear equations of motion are derived through the use of this novel method and then solved numerically. The results are then used to optimize the system and identify key parameters and their effect on the output power generated. Additionally, the resulting equations serve as a tool for identifying an appropriate control strategy for the system. Finally, a scale model of a gyroscopic ocean wave energy converter is developed to validate the equations of motion that have been derived.

Due to the problems associated with increase of greenhouse gases, and the limited supply of fossil fuels, switching to clean and renewable sources of energy seems necessary. Wind energy is a very suitable form of renewable energy which can be a good choice for those areas around the world with sufficient amount of wind annually. However, in order for the commercial wind turbines to be cost-effective, they need to operate at very high elevations, and therefore, blades with the length as high as 60–70 m are common. Because of the high manufacturing and transportation costs of the wind turbine components, it is necessary to evaluate and predict the performance of the turbine prior to shipping it to the installation site. Computational Fluid Dynamics (CFD) has proven to be a simple, cheap and yet relatively accurate tool for prediction of wind turbine performance, where suitability of different designs can be evaluated at a low cost. Total lift and drag forces can be calculated, from which one can estimate the torque, and ultimately the output power. Reynolds Stress Model (RSM) is a well-known Reynolds Averaged Navier-Stokes (RANS) turbulence model, which is typically more accurate than eddy viscosity models, but it comes with higher computational cost. In the present work, turbulent flow of air around a horizontal axis wind turbine blade is modeled computationally by using a modified version of RSM, known as Algebraic Stress Model (ASM) for the near-blade region. Because of the periodicity nature of the flow domain, only one of three blades is modeled by applying the periodic conditions on the sides of a 120 degree sector of the domain. While the flow is solved in the bulk fluid using the k-epsilon model, in order to better capture the near-wall effects and to make the computations cost effective, it is proposed to apply ASM only in the locations very close to the blade surface. A number of reasonable assumptions are made in ASM in order to convert the transport differential equations of the Reynolds stresses into an algebraic form. The highly coupled system of non-linear equations is then solved concurrently for six Reynolds stress components. Turbulent kinetic energy, turbulent dissipation rate, and mean velocity gradients are calculated from the k-epsilon model and used as initial values and iterated through the ASM computations. To the best of our knowledge, this is the first time that ASM is used for analysis of Reynolds stress for flow around rotating wind turbines blades. Reynolds stresses are obtained at several locations (heights) along the blade, and at different radial distances from the blade. Different variations of implicit and explicit ASM are examined and compared in terms of accuracy. Results indicate that the implicit ASM method using the full form of pressure-strain term tends to show predictions that are closer to the predictions of the fully-resolved RSM simulation, as compared to the other ASM models examined. Therefore, there seems to be a good potential for reducing computational costs for determination of near wall Reynolds stresses and ultimately calculating torque and power generated from wind turbines without sacrificing the accuracy.

This research presents an analytical model to describe the indeterminate contact status and analyze the loaded condition, then acquire the key design parameters so as to improve the carrying capacity of spherical roller bearings. The model based on the non-Hertzian contact theory is applied to reflect the indeterminate contact status due to the self-aligning feature. The loaded condition, which is including the load distribution, the size of the contact region and the maximum contact pressure, is calculated according to the force analysis of spherical roller bearings. The non-linear equations are solved by using secant method and the proposed model is validated by comparing with the published reference. The importance of the indeterminate contact status is illustrated by comparing with the computing results of the Hertzian contact model. The fitted method based on the least square method is used to obtain the equivalent stiffness and the load-deformation exponent, whereby the computing procedure is simplified. In view of the operating condition and the lubricated effect, properly increasing the osculation number or the number of the rollers will obviously improve the carrying ability of spherical roller bearings.

Nonlinear free vibration of a microstructure has been analyzed in this study. A fluid-conveying microtube is mathematically modeled using non-classical beam theory. Partial differential equation of the model is considered in non-dimensional form. Simply-supported boundaries are taken into account and assuming three vibrating modes, an analytical method is employed to obtain the nonlinear equations of motion. Variational iteration method has been utilized as an analytical solution technique. In order to obtain the nonlinear natural frequencies of the system, analytical expressions are found based on this method. A parametric study is also carried out to investigate the effect of different parameters on the vibration characteristics of the microstructure.

The Virtual Fields Method (VFM) is a technique for computing material properties from full-field data. Recently, a variant of this technique, called Eigenfunction Virtual Fields Method (EVFM) has been proposed and applied to homogeneous linear elastic property evaluation. In this work, we extend this technique to heterogeneous materials by applying it to linear elastic material with exponentially varying elastic modulus. For such materials, there are three constitutive parameters to be evaluated: an elastic modulus, the Poisson’s ratio and a material length scale parameter β that controls spatial variation of the elastic modulus. We consider a plate made of such a material, with a circular hole, subjected to uni-axial tension in this study. The elasticity solution to this problem is synthesized using FEM, and strain fields in the vicinity of the hole are obtained on a rectangular grid. These strain component fields are assembled into an augmented strain matrix, whose eigenfunctions are obtained through Principal Components Analysis (PCA). EVFM is then performed using these eigenfunctions as virtual fields and solution of the resulting system of nonlinear equations yields values for the material parameters that are in excellent agreement with the true values.

Simulations are playing an important role to predict derailment, switching, wheel climbing and curving in the study of dynamics of railroad vehicles. For a successful simulation, a robust and efficient approach for computation of all common normal between wheel and rail surface is needed. In a previous work, the authors had devised an approach based on sign distant function to compute all common normal between a pair of wheel and surface. As part of this approach, two major computational tasks were formulated. They were computation of cauchy index around a cell (a closed curve) and computation of the zero’s of the gradient of the signed distance function. In this study, a bookkeeping technique is devised to compute the cauchy index more efficiently. Also the performance of trust region method as a solver for a set of nonlinear equation is compared to Newton’s method.

Computation of contact points between the wheel and rail is a fundamental problem in dynamic simulation of trains. To compute these contact points, one needs to locate common normals first. The objective of this study is to develop an efficient method to compute common normals between wheel and rail surface. This is done by devising a method to compute an estimate of location of common normals and then using them as the initial guess to compute them. To generate an estimate of the location of common normal, a local approximation of the rail is constructed. To achieve this, the intersection of the vertical mid-plane of the wheelset with a track curve of a rail is computed and the tangent line at this point is generated. The rail profile is place on the tangent line and is swept along it. The resulting rail is called linearized rail in this study. It is shown that the four nonlinear equations governing the location of the common normal can be reduced to one equation in one unknown. This equation is referred to as reduced equation. A bracketing algorithm is added to identify the intervals within which this reduced equation changes sign. These intervals contain the zero of the reduced function. The zeros of the reduced equation are used to compute an estimate of the common normals. These estimates are used as an initial guess for a Newton iterate to accurately locate all common normals. It is observed that the CPU time to compute all common normals is of the order of mili-second.

A Lotka-Volterra differential equation is discretized using a method proposed recently by the same authors for nonlinear autonomous systems and the stability of equilibrium points of the resulting discrete-time model is investigated. It is shown that when Jacobian matrix of the nonlinear equation is invertible, the equilibrium points of the model are identical to those of the original continuous-time system, and their asymptotic stability and instability are retained for any sampling period. While the method can be applied to any Lotka-Volterra types, simulation results are presented for a competitive-type example, where the continuous-time system and their discrete-time models obtained by the forward-difference, Mickens’, Kahan’s, and the proposed methods are compared. They illustrate that, in general, the proposed model performs better than other discrete-time models.