High-order Average Component Acceleration method with longitudinal distribution of the average component term for fast flood flow simulations under various downstream conditions

The present study examines the temporal structure of the fast flow in the plasma sheet using both observations and simulations. The data analysis part adopts the strictest criterion ever for the satellite location so that selected flows are mostly convective. From Geotail measurements at X > −31 RE, 818 earthward‐flow and 290 tailward‐flow events are selected. Superposed epoch analyses are conducted with two different reference times: the start of the fast flow and the time of a sharp change in the Bz component. The results are summarized as follows: (1) The magnetic field becomes dipolar in the course of the fast earthward flow; (2) Sharp dipolarization tends to be preceded by a transient decrease in BZ, which starts along with the fast flow and is accompanied by an increase in the plasma density; (3) The corresponding signatures, albeit less clear, can also be found for the tailward flow; (4) Whereas the plasma density decreases in association with the fast flow irrespective of the flow direction (though, more gradually for the tailward flow), the ion temperature increases for the earthward flow and decreases for the tailward flow; (5) The plasma and total pressures decrease in the course of the fast flow, suggesting the reduction of the lobe field strength; (6) In general, magnetic field and plasma parameters change more gradually in time for the tailward flow than for the earthward flow. Those characteristics of the fast flow can be found irrespective of the X distance, even though the ambient magnetic field and plasma vary significantly between X = −5 and −31 RE. The near‐Earth reconnection is inferred to be the responsible mechanism for most, if not all, flow events, and the difference between the earthward and tailward flows presumably reflects difference in downstream conditions. On the earthward side of the reconnection site, the flow needs to proceed against the rigid terrestrial magnetic field, whereas on the tailward side the flow does not have any obstruction once reconnection reaches the lobe magnetic field. This idea is consistent with the change of the magnetic inclination, which suggests that the plasma sheet becomes thicker and thinner in the course of the earthward and tailward flows, respectively. These observational results are compared with fast plasma flows modeled by two‐fluid simulations of magnetic reconnection. A focus is placed on the reduction of BZ prior to dipolarization for the earthward flow (the precursory BZ increase for the tailward flow) since this is the new finding owing to our strict condition for the convective flow. It is found that the fragmentation of the current sheet and the formation of multiple neutral lines create signatures similar to the satellite observations. After multiple X lines form, one of them dominates and establishes the overall flow pattern associated with reconnection. Magnetic islands formed between the X lines are swept downstream by the reconnection process. The signature of this earthward convection of a magnetic island past a satellite at rest in the magnetotail is a strongly bipolar signature in Bz with a sudden enhancement in the density: Bz spikes negative and then positive in rapid succession, with a maximum in the density between these two spikes. It is therefore suggested that the temporal structure of the observed fast plasma flows contains information directly linked to their genesis.

This thesis investigated the application of seismic analysis methods and the response of idealized shear frames subjected to seismic loading. To complete this research, a Design Basis Earthquake (DBE) for a project site in San Luis Obispo, CA, and five past earthquake records were considered. The DBE was produced per the American Society of Civil Engineers’ Minimum Design Loads for Buildings and Other Structures (ASCE 7-10) and used for application of the Equivalent Lateral Force Procedure (ELFP) and Response Spectrum Analysis (RSA). When applying RSA, the modal peak responses were combined using the Absolute Sum (ABS), Square-Root-of-the-Sum-of-Squares (SRSS), and Complete Quadratic Combination (CQC) method. MATLAB scripts were developed to produce several displacement, velocity, and acceleration spectrums for each earthquake. Moreover, MATLAB scripts were written to yield both analytical and numerical solutions for each system through application of Linear Time History Analysis (THA). To obtain analytical solutions, two implicit forms of the Newmark-beta Method were employed: the Average Acceleration Method and the Linear Acceleration Method. To generate a comparison, the ELFP, RSA, and THA methods were applied to shear frames up to ten stories in height. The system parameters that impacted the accuracy of each method and the response of the systems were analyzed, including the effects of classical damping and nonclassical damping models. In addition to varying levels of Rayleigh damping, non-linear hysteric friction spring dampers (FSDs) were implemented into the systems. The design of the FSDs was based on target stiffness values, which were defined as portions of the system’s lateral stiffness. To perform the required Nonlinear Time History Analysis (NTHA), a SAP2000 model was developed. The efficiencies of the FSDs at each target stiffness, with and without the addition of low levels of viscous modal damping are analyzed. It was concluded that the ELFP should be supplemented by RSA when performing seismic response analysis. Regardless of system parameters, the ELFP yielded system responses 30% to 50% higher than RSA when combing responses with the SRSS or CQC method. When applying RSA, the ABS method produced inconsistent and inaccurate results, whereas the SRSS and CQC results were similar for regular, symmetric systems. Generally, the SRSS and CQC results were within 5% of the analytical solution yielded through THA. On the contrary, for irregular structures, the SRSS method significantly underestimated the response, and the CQC method was four to five times more accurate. Additionally, both the Average Acceleration Method and

The use of fractional derivatives in the constitutive equations of systems with damping materials provides a powerful tool for modeling these systems because the model does not exhibit many of the short comings of those based on integer-order derivatives. The resulting equations of motion possess closed-form solutions only for single-degree-of-freedom systems and only for a small number of loadings. For practical applications, therefore, the equations of motion must be solved using numerical methods. This paper presents two numerical schemes to solve single-degree- and multi-degree-of-freedom systems with fractional damp ing subjected to a number of commonly used loading conditions. The techniques employed are based on the central difference method and the average acceleration method. Whenever possible, the numerical results are compared with the analytical solutions. The results of the two numerical methods are essentially identical, with the exact solutions for zero initial conditions, but differ for nonzero conditions and large damping. For small damping, the average method has the advantage of its simpler formulation, especially with regard to the starting values. For arbitrary damping, however, the central difference method, in view of its robustness, is the preferred method.

Numerical properties of the time integration method proposed by the first author of this paper in 2007 are the same as those of the constant average acceleration method (AAM) for linear elastic systems, except that the capability to capture dynamic loading was not explored. It was found that there were different quadrature equations to predict the next step displacement increment. A modified quadrature equation of this method was derived so that the equation to determine the next step displacement was numerically equivalent to the equation used in the constant AAM. It was verified that the original form of this method, in general, had a better capability to capture dynamic loadings than the constant AAM. This excellent property, in addition to computational efficiency, will help to make this method competitive with general secondorder accurate integration methods.

Stability, convergence and growth and decay of energy of the average acceleration method in nonlinear structural dynamics

A fault-tolerant control method which can achieve high reliability is proposed in this paper. In the traditional fault-tolerant control methods, average velocity method and acceleration method are not accurate enough to compensate and estimate hall sensor signals. Therefore, the fault diagnosis theory proposed in this paper is based on hall state and transition edge time, which can realize fast fault detection. For purpose of improving the precision of position estimation after fault tolerance, this paper proposes a position estimation method based on sliding-modeobserver (SMO) and an improved switch function. According to the switching algorithm, the PMSM can smoothly switch to sensorless operation after failure. Finally, the efficacy of the proposed method is verified by the simulations.KeywordsPermanent magnet synchronous motor (PMSM)Hall effect sensorFault diagnosis (FD)Sliding-modeobserver (SMO)

Written for senior-year undergraduates and first-year graduate students with solid backgrounds in differential and integral calculus, this paper is oriented toward engineers and applied mathematicians. Consequently, this paper should be useful to senior-year undergraduates the finite element method [1]. The scaled direct approach is adopted for this purpose and each step in the finite element solution process is given in full detail. For this reason, all students must be exposed to (and indeed should master). This paper provides the general framework for the development of nearly all (nonstructural) finite element models. The finite element method of analysis is a very powerful, modern computational tool. Applications range from deformation and stress analysis of automotive, aircraft, building, and bridge structures to field analysis of beat flux, fluid flow, magnetic flux, seepage, and other flow problems. This paper presents study and comparison of numerical methods which are used for evaluation of dynamic response. A Single Degree of Freedom (SDF)-linear problem is solved by means of Newmark’s Average acceleration method [2], Linear acceleration method [2], Central Difference method [6,7] with the help of MATLAB. The advantages, disadvantages, relative precision and applicability of these numerical methods are discussed throughout the analysis.

The energy approach is used to theoretically verify that the average acceleration method (AAM), which is unconditionally stable for linear dynamic systems, is also unconditionally stable for structures with typical nonlinear damping, including the special case of velocity power type damping with a bilinear restoring force model. Based on the energy approach, the stability of the AAM is proven for SDOF structures using the mathematical features of the velocity power function and for MDOF structures by applying the virtual displacement theorem. Finally, numerical examples are given to demonstrate the accuracy of the theoretical analysis.

In this article, various non‐polynomial higher‐order shear deformation theories are applied for the first time to analyze the free vibration and transient responses of plates with functionally graded material (FGM) supported on an elastic foundation. The shear deformation theories account for the non‐linear variation of the transverse shear strains with various warping functions, namely trigonometric, inverse hyperbolic, and inverse trigonometric ones. These models also inherently satisfy the traction‐free boundary conditions of transverse shear stresses at the top and bottom surfaces of the plates and do not require any shear correction factor. A two‐parameter model, namely Winkler‐Pasternak's elastic foundation model, is utilized to develop the interaction between the FGM plates and the elastic medium. The governing equations of motion are obtained using Hamilton's principle and solved analytically using Navier's solution scheme. Furthermore, the transient responses of the plates are obtained using Newmark's average acceleration method. The applicability of the present theories is established by solving several numerical problems and validating the results with the solutions available in the literature. The effects of various parameters like span‐thickness ratios, aspect ratios, gradation coefficients, mechanical loads, and foundation stiffness on the fundamental frequencies and the transient responses of the plates are thoroughly investigated. The comparison of the results reveals the efficiency of the non‐polynomial functions, and the capability of efficient prediction of the structural responses of the FGM plates at a similar computational cost compared to established models in the literature. Furthermore, the results show that the stiffness of the elastic foundation can tweak the stiffness characteristics of the FGM plate resulting in significant changes in the natural frequencies and more controlled displacement‐time responses.

Seismic behaviors of the Meru structure as one of the sacred buildings in Balinese Temples have not been investigated extensively. Most research investigated the Meru building in terms of its philosophy and history. The Meru buildings were observed to survive many earthquake events that occurred in Bali Islands. This paper presents the analysis results of the Meru structure in responding to earthquake excitations. As many as five types of the Meru structure traditionally built were modeled and analyzed using finite element-based software. Each type of Meru has three variations in the roof masses that were obtained from increasing the roof thickness from 500 mm, 600 mm, and 700 mm. Time history analysis follows Newmark’s average acceleration method with an input earthquake record of the scaled El-Centro N-S 1940 to meet seismic conditions in the Bali area. The results show that the dynamic responses of the Meru structure increase as the number of roof levels and mass increase. All of the Meru types have met the limitation of the code’s lateral allowable limits. The dimensions of the structural elements determined according to Balinese scripts can provide capacity greater than twice the capacity demand. Keeping the roof mass in a certain proportion with the mass of the lowest roof twice of the above one will keep the Meru stable during an earthquake.

A unified formulation for thermoviscoelasticity of hollow sphere based on the second sound theories

By use of the generalized least‐squares procedure, in conjunction with a finite element approximation in time, a simple three‐time‐level family of time integration schemes is derived. This results in fourth‐order accurate unconditionally stable algorithms and stable eighth‐order accurate non‐dissipative algorithms. Numerical examples show the accuracy of the proposed schemes in comparison with the Fox‐Goodwin formula and Newmark's average acceleration method.

A simplified approach for modeling an open crack in a rotor based on the change of the flexibility is proposed in this paper. The crack model is incorporated in a two-node Timoshenko beam with 4 DOF at each node, which in turn represents one element of the finite element model of the rotor bearing system. The objectives of this work are twofold. The primary objective is to study the effect of the presence of crack on movement equation of rotor bearing system. Theoretically, it was shown that the crack generates external inertial, damping and elastic excitation forces which depend on the second harmonic of the rotational speed. The second objective is to calculate the dynamic response of the rotor bearing system with NEWMARK numerical integration method (average acceleration method) of non-linear equation. Results show that transverse crack produces peaks in the second harmonic of rotating speed modulated with natural frequency and the third harmonic of the rotation speed. The presence of a crack in a symmetric rotor causes asymmetry in the stiffness and consequently causes critical frequencies in backward whirl.KeywordsOpen crackrotor modelingdynamic response

The conventional function of an offshore platform is oil and gas exploration and production. Yet, these platforms also serve as an excellent alternative for space rocket launches, offering advantages in the form of easy environmental impact clearance. This paper conducts dynamic analyses on an offshore triceratops integrated with a missile/rocket launcher, under irregular waves. Numerical analysis is carried out for two different conditions, namely, with and without rocket launch. Average acceleration method is used to solve the governing equation in time-domain. Subsequently, power spectral densities in the active degrees of freedom are obtained from the time response analysis. It confirms the compliant nature of the structure whereby it is stiff in heave and pitch degrees of freedom while flexible in surge degree of freedom. The results provide evidence for the distinctive and innovative responsive behaviors exhibited in harsh deep ocean environments.

Numerical Evaluation of Dynamic Response of a Steel Structure Model Under Various Seismic Excitations