Assumed Boundary Conditions Research Articles

Active Vibration Suppression of a 3-DOF Flexible Parallel Manipulator Using Efficient Modal Control

This paper addresses the dynamic modeling and efficient modal control of a planar parallel manipulator (PPM) with three flexible linkages actuated by linear ultrasonic motors (LUSM). To achieve active vibration control, multiple lead zirconate titanate (PZT) transducers are mounted on the flexible links as vibration sensors and actuators. Based on Lagrange’s equations, the dynamic model of the flexible links is derived with the dynamics of PZT actuators incorporated. Using the assumed mode method (AMM), the elastic motion of the flexible links are discretized under the assumptions of pinned-free boundary conditions, and the assumed mode shapes are validated through experimental modal test. Efficient modal control (EMC), in which the feedback forces in different modes are determined according to the vibration amplitude or energy of their own, is employed to control the PZT actuators to realize active vibration suppression. Modal filters are developed to extract the modal displacements and velocities from the vibration sensors. Numerical simulation and vibration control experiments are conducted to verify the proposed dynamic model and controller. The results show that the EMC method has the capability of suppressing multimode vibration simultaneously, and both the structural and residual vibrations of the flexible links are effectively suppressed using EMC approach.

Effect of mechanical stress on phase stability and polarization states in ferroelectric barium titanate and lead titanate

The effect of normal and shear stress on phase transitions in BaTiO3 and PbTiO3 has been investigated using a modified Landau–Ginzburg–Devonshire phenomenological model based on assumption of constant stress boundary conditions. Stress–temperature phase diagrams have been developed, and the influence of stress on polarization stability has been analyzed. The results show monoclinic phases with various polarization states absent in stress-free BaTiO3 may exist under uniaxial, biaxial, anisotropic three-dimensional, and shear stress conditions. For PbTiO3, our calculations show that, under normal stress new phases cannot be generated and the only stable ferroelectric phase has tetragonal symmetry, but under shear stress orthorhombic, rhombohedral, and monoclinic phases can be stabilized.

Numerical Simulating Nonlinear Effects of Ultrasonic Propagation on High-speed Ultrasonic Gas Flow Measurement

The effects of nonlinear ultrasonic propagation on high-speed ultrasonic gas flow measurement are analyzed based on the sound line equation derived from Snell's geometric acoustic law. A math ematical model for the ultrasonic propagation path in ultrasonic flowmeter pipe is built, and the relationship between x and r is calcula ted by MATLAB programming and ode45 simulating. The ultrasonic propagation path at the flow rate of 3 � 30m/s is simulated in the assumed boundary conditions of the pipeline, transducer installation and fluid state. It shows that the nonlinear propagation characte ristics cause the large deviations of the position of received ultrasonic waves in conditions of different flow rates, which strongly aff ects the stability and accuracy of flow measurement. The simulated offset data of the receiving position are useful for the high-s peed gas ultrasonic flowmeter installation and dry calibration on clamp-on ultrasonic flowmeters.

Applicability of the crack faces thermoelectric boundary conditions for thermopiezoelectric materials

The applicability and effect of the crack surfaces thermoelectric boundary conditions in thermopiezoelectric fracture mechanics problem are discussed by using the finite thickness notch approach. The stress and electric displacement intensity factors at the notch tips, and thermal flux and electric displacement inside the notch are derived in closed-form. The numerical results are compared with the ideal crack solutions. It is found that the electrically impermeable crack boundary condition assumption is reasonable if the flaw in the material is a notch with finite width, and the thermal conductivity of air or vacuum inside the crack must be considered.

Wave propagation in a piezoelectric solid bar of circular cross-section immersed in fluid

Wave propagation in a piezoelectric solid bar of circular cross-section immersed in fluid is discussed using three-dimensional theory of piezoelectricity. The equations of motion of the cylinder are formulated using the constitutive equations of a piezoelectric material. The equations of motion of the fluid are formulated using the constitutive equations of an inviscid fluid. Three displacement potential functions are introduced to uncouple the equations of motion, electric conduction. The frequency equation of the coupled system consisting of cylinder and fluid is developed under the assumption of perfect-slip boundary conditions at the fluid–solid interfaces. The frequency equations are obtained for longitudinal and flexural modes of vibration and are studied numerically for PZT-4 material bar immersed in fluid. The computed non-dimensional wave numbers are presented in the form of dispersion curves. The secant method is used to obtain the roots of the frequency equation.

Extensions of the Justen–Ramlau blind deconvolution method

Blind deconvolution problems arise in many image restoration applications. Most available blind deconvolution methods are iterative. Recently, Justen and Ramlau proposed a novel non-iterative blind deconvolution method. The method was derived under the assumption of periodic boundary conditions. These boundary conditions may introduce oscillatory artifacts into the computed restoration. We describe extensions of the Justen---Ramlau method that allow the use of Neumann and antireflective boundary conditions.

Transient thermal elastic fracture of a piezoelectric cylinder specimen

A finite piezoelectric cylinder with an embedded penny-shaped crack is investigated for a thermal shock load on the outer surface of the cylinder. The theory of linear electro-elasticity is applied to solve the transient temperature field and the associated thermal stresses and electrical displacements without crack. These thermal stresses and electrical displacements are added to the surfaces of the crack to form an electromechanical coupling and mixed mode boundary-value problem. The electrically permeable crack face boundary condition assumption is used, and the thermal stress intensity factor and electrical displacement intensity factor at the crack border are evaluated. The thermal shock resistance of the piezoelectric cylinder is evaluated for the analysis of piezoelectric material failure in practical engineering applications.

Fracture and effective properties of finite magnetoelectroelastic media

Magnetoelectroelastic materials are inherently brittle and prone to cracking. It is important to understand how cracks influence the magnetoelectrical coupling properties of the magnetoelectroelastic materials. This article establishes an analytical model for a finite crack in a finite magnetoelectroelastic medium. The stress, electric displacement, and magnetic induction and their intensity factors are obtained by the integral equation technique. The temperature effect is also studied. The effect of cracking on the effective thermomagnetoelectromechanical properties is discussed. In addition, crack is modeled as a notch of finite height to study the effect of the crack-face electric and magnetic boundary condition assumptions on the predicted properties of the magnetoelectroelastic medium.

Classical geometry to quantum behavior correspondence in a virtual extra dimension

In the Lorentz invariant formalism of compact space–time dimensions the assumption of periodic boundary conditions represents a consistent semi-classical quantization condition for relativistic fields. In Dolce (2011) [18] we have shown, for instance, that the ordinary Feynman path integral is obtained from the interference between the classical paths with different winding numbers associated with the cyclic dynamics of the field solutions. By means of the boundary conditions, the kinematical information of interactions can be encoded on the relativistic geometrodynamics of the boundary, see Dolce (2012) [8]. Furthermore, such a purely four-dimensional theory is manifestly dual to an extra-dimensional field theory. The resulting correspondence between extra-dimensional geometrodynamics and ordinary quantum behavior can be interpreted in terms of AdS/CFT correspondence. By applying this approach to a simple Quark–Gluon–Plasma freeze-out model we obtain fundamental analogies with basic aspects of AdS/QCD phenomenology.

Evaluating Kinematic Controls on Planar Translational Slope Failure Mechanisms Using Three-Dimensional Distinct Element Modelling

This paper investigates the importance of kinematic release mechanisms on planar translational slope failure using three-dimensional distinct element codes. The importance of the dip and dip direction of the rear, basal and lateral release surfaces and their influence on failure mechanism, dilation, and the development of step-path failures is illustrated. The three-dimensional block shape and volume of the unstable rock masses simulated with the different discontinuity set geometries are characterized. Two assumed three-dimensional slope models are investigated in order to assess the importance of varying kinematic confinement/release mechanisms. These two assumed boundary conditions are shown to be critical in the development of asymmetrical rock mass deformation patterns. Scale effects due to the block size and discontinuity persistence are shown to control the calculated displacement and failure mechanisms. The numerical modelling results are also demonstrated to be sensitive to the assumed normal and shear stiffness of the discontinuities. The influence of the factors investigated on the failure of a single rock block versus a rock mass are compared and discussed.

Dynamic Radiation Environment Assimilation Model: DREAM

The Dynamic Radiation Environment Assimilation Model (DREAM) was developed to provide accurate, global specification of the Earth's radiation belts and to better understand the physical processes that control radiation belt structure and dynamics. DREAM is designed using a modular software approach in order to provide a computational framework that makes it easy to change components such as the global magnetic field model, radiation belt dynamics model, boundary conditions, etc. This paper provides a broad overview of the DREAM model and a summary of some of the principal results to date. We describe the structure of the DREAM model, describe the five major components, and illustrate the various options that are available for each component. We discuss how the data assimilation is performed and the data preprocessing and postprocessing that are required for producing the final DREAM outputs. We describe how we apply global magnetic field models for conversion between flux and phase space density and, in particular, the benefits of using a self‐consistent, coupled ring current–magnetic field model. We discuss some of the results from DREAM including testing of boundary condition assumptions and effects of adding a source term to radial diffusion models. We also describe some of the testing and validation of DREAM and prospects for future development.

An On-Line Fatigue Life Monitoring System for Boiler Drums Based on the Inverse Problem of Heat Conduction Method

A method based on solution of the inverse heat conduction problem was presented for online stress monitoring and fatigue life analysis of boiler drums. The mathematical model of the drum temperature distribution is based on the assumptions that the difference of temperature along the longitudinal axis of the boiler drum is negligible with changes only in the radial direction and the circumferential direction, and that the outer surface of drum is thermally insulated. Combining this model with the control-volume method provides temperatures at different points on a cross-section of the drum. With the temperature data, the stresses of the boiler drum are derived according to the FEM and the life expectancy of it is calculated based on the rain flow method. Applying this method to the cold start-up process of a 300 MW boiler demonstrated the absence of errors caused by the boundary condition assumptions on the inner surface of the drum and an applicable technique for the online stress monitoring and fatigue life analysis of boiler drums.

Reanalysis of radiation belt electron phase space density using various boundary conditions and loss models

Data assimilation is becoming an increasingly important tool for understanding the near Earth hazardous radiation environments. Reanalysis of the radiation belts can be used to identify the electron acceleration mechanism and distinguish local acceleration from radial diffusion. However, for any practical applications we need to determine how reliable is reanalysis, and how significant is the dependence of the results on the assumptions of the code and choice of boundary conditions. We present the sensitivity of reanalysis of the radiation belt electron phase space density (PSD) to the assumed location of the outer boundary, using the VERB code and a Kalman filter. We analyze the sensitivity of reanalysis to changes in the electron-loss throughout the domain, and the sensitivity to the assumed boundary condition and its effect on the innovation vector. All the simulations presented in this study for all assumed loss models and boundary conditions, show that peaks in the phase space density of relativistic electrons build up between 4.5 and 6 R E during relativistic electron flux enhancements in the outer radiation belt. This clearly shows that peaks build up in the heart of the electron radiation belt independent of the assumptions in the model, and that local acceleration is operating there. The work here is also an important step toward performing reanalysis using observations from current and future missions.

Millennial-scale diffusive migration of solutes in thick clay-rich aquitards: evidence from multiple environmental tracers

High-resolution one-dimensional profiles of naturally occurring environmental tracers (3H, δD, δ18O, 14C-DIC, 14C-DOC, 36Cl, 4He, and major ions) and hydraulic data were used to study residence times, transport mechanisms, and sources of pore water and solutes in an aquitard system in Saskatchewan, Canada. The aquitard system consisted of 80 m of plastic clay-rich Battleford till discomformably overlying 77 m of Late Cretaceous plastic marine clay. Individual tracers independently revealed molecular diffusion as the dominant transport mechanism in the unoxidized nonfractured till and clay. Transport modeling indicated that late Pleistocene-age pore water at 35–55 m below ground was emplaced 15–30 thousand years Before Present (ka BP) during till deposition and ice retreat. The late Holocene climatic transition was estimated to have occurred 7–12 ka BP. Differences in the timing of events determined with different tracers were attributed to inaccuracies in transport parameters and boundary condition assumptions. This study showed that solute transport in clay-rich aquitards can be accurately predicted for time scales beyond 20 ka, and proved such aquitards are suitable for long-term isolation of most wastes.

Surface morphology of Kr+-polished amorphous Si layers

The surface morphology of low-energy Kr+-polished amorphous Si layers is studied by topographical methods as a function of initial substrate roughness. An analysis in terms of power spectral densities reveals that for spatial frequencies 2×10−2–2×10−3 nm−1, the layers that are deposited and subsequently ion polished reduce the initial substrate roughness to a rms value of 0.1 nm at the surface. In this system, the observed dominant term in linear surface relaxation, proportional to the spatial frequency, is likely to be caused by the combined processes of (a) ion-induced viscous flow and (b) annihilation of (subsurface) free volume during the ion-polishing treatment. Correspondingly, a modification of the generally assumed boundary conditions, which imply strict surface confinement of the ion-induced viscous flow mechanism, is proposed. Data on surface morphology are in agreement with the optical response in extreme ultraviolet from a full Mo/Si multilayered system deposited onto the modified substrates.

Strain tensors in layer systems by precision ion channeling measurements

A powerful method for analyzing general strain states in layer systems is the measurement of changes in the ion channeling directions. We present a systematic derivation and compilation of the required relations between the strain induced angle changes and the components of the strain tensor for general crystalline layer systems of reduced symmetry compared to the basic (cubic) crystal. It is shown that, for the evaluation of channeling measurements, virtually all layers of interest may be described as being “pseudo-orthorhombic.” The commonly assumed boundary conditions and the effects of surface misorientations on them are discussed. Asymmetric strain relaxation in layers of reduced symmetry is attributed to a restriction in the slip system of the dislocations inducing it. The results are applied to {110}SiGe/Si layer systems.

Simulating the effects of geologic heterogeneity and transient boundary conditions on streambed temperatures — Implications for temperature-based water flux calculations

Analytical solutions to the one-dimensional heat transport equation for steady-state conditions can provide simple means to quantify groundwater surface water exchange. The errors in exchange flux calculations that are introduced when the underlying assumptions of homogeneous sediments and constant temperature boundary conditions are violated were systematically evaluated in a simulation study. Temperatures in heterogeneous sediments were simulated using a numerical model. Heterogeneity in the sediments was represented by discrete, binary geologic units. High contrasts between the hydraulic conductivities ( K) of the geologic units were found to lead to large errors, while the influence of the structural arrangement of the units was smaller. The effects of transient temperature boundary conditions were investigated using an analytical equation. Errors introduced by transient boundary conditions were small for Darcy-velocities > 0.1 m d − 1 in the period near maximum and minimum annual surface water temperatures. For smaller fluxes, however, errors can be large. Assuming steady-state conditions and vertical flow in homogeneous sediments is acceptable at certain times of the year and for medium to high exchange fluxes, but pronounced geologic heterogeneity can lead to large errors.

An effective 3-D inverse procedure to retrieve cooling conditions in an aluminium alloy continuous casting problem

The paper discusses a three-dimensional numerical solution of the inverse boundary problem for a continuous casting process of an aluminium alloy. Because verified information of heat flux distribution is crucial for a good mould design, effective cooling system and the whole caster in general, the main goal of the analysis presented within the paper is identifying of the heat fluxes along the external surface of the ingot. To model the solidification process, an enthalpy-porosity technique implemented in a commercial package was used. In this method, the phase change interface was determined based on the liquid fraction approach. In the inverse procedure, a sensitivity analysis was used to estimate the boundary condition retrieval. While the measured temperatures required to solve the problem are always burdened by measurement errors, a comparison of the measured and retrieved values showed a computational high accuracy. The average percentage error of the sensors was considerably lower than the maximum percentage error of the numerically simulated measurements. In addition, the computationally effective method was independent of the mesh size, the starting value of the assumed boundary condition and the maximum error of measurements used for calculations.

Effect of substrate thickness and material on heat transfer in microchannel heat sinks

Heat and fluid flow in microchannels of size (200μm × 200 μm, 5 cm long) of different substrate thicknesses ( t = 100 μm–1000 μm) and different MEMS (Microelectromechanical Systems) materials (Polyimide, Silica Glass, Quartz, Steel, Silicon, Copper) was studied to observe the effects of thermal conductivity and substrate thickness on convective heat transfer in laminar internal flows. The results of the model were first validated by the theoretical results recommended by standard forced convection problem with H1 (Constant heat flux boundary condition) condition before the results from the actual microchannel configurations were obtained. Thereafter, general Nusselt number results were obtained from the models of many microchannel configurations based on the commercial package COMSOL MULTIPHYSICS ® 3.4 and were discussed on both local and average basis. A general Nusselt number correlation for fully developed laminar flow was developed as a function of two dimensionless parameters, namely Bi, Biot number and relative conductivity k ∗, to take the conduction effects of the solid substrate on heat transfer into account. It was also demonstrated when the commonly used assumption of constant heat flux boundary (H1) condition is applicable in heat and fluid flow analysis in microfluidic systems. For this, a new dimensionless parameter was employed. A value of 1.651 for this suggested dimensionless parameter ( Bi 0.04 k ∗−0.24) corresponds to 95% of the Nusselt number associated with the constant heat flux boundary condition so that it could be set as a boundary for the applicability of constant heat flux boundary (H1) condition in microfluidic systems involving heat transfer.

Modeling of the Weld Shape Development During the Autogenous Welding Process by Coupling Welding Arc with Weld Pool

A numerical model of the welding arc is coupled to a model for the heat transfer and fluid flow in the weld pool of a SUS304 stainless steel during a moving GTA welding process. The described model avoids the use of the assumption of the empirical Gaussian boundary conditions, and at the same time, provides reliable boundary conditions to analyze the weld pool. Based on the two-dimensional axisymmetric numerical modeling of the argon arc, the heat flux to workpiece, the input current density, and the plasma drag stress are obtained. The arc temperature contours, the distributions of heat flux, and current density at the anode are in fair agreement with the reported experimental results. Numerical simulation and experimental studies to the weld pool development are carried out for a moving GTA welding on SUS304 stainless steel with different oxygen content from 30 to 220 ppm. The calculated result show that the oxygen can change the Marangoni convection from outward to inward direction on the liquid pool surface and make the wide shallow weld shape become narrow deep one. The calculated result for the weld shape and weld D/W ratio agrees well with the experimental one.