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Radio Frequency (RF) Wireless Power Transfer (WPT) is a technology that allows devices to be powered wirelessly. This project aims to develop a functional Radio Frequency (RF) energy harvesting demonstration kit, and to assess the feasibility of building a RF energy harvesting kit. The objective of the kit is to harvest and convert RF energy from a transmitter into DC energy to power up a sensor device, or end device. The main focus is on configuring and evaluating the power management circuit and the end device in the kit. The performance of the kit was evaluated. Testing results showed that the demonstration kit was able to power up the end device when RF energy is transmitted to the receiving antenna in the demonstration kit. When the transmitter is placed 94.0 cm away from the receiving antenna, the demonstration kit can be powered up with a minimum power of 21.90 dBm delivered to the transmitter, and the end device can be powered on continuously with a minimum power of 23.30 dBm delivered to the transmitter.

The conventional pseudo-static approach often neglects the effect of the vertical seismic acceleration on the stability of a slope, but some analyses under plane-strain (2D) conditions show a significant effect on the slope stability. The purpose of this study is to investigate the effect of the vertical acceleration on the safety of three-dimensional (3D) slopes. In the strict framework of limit analysis, a 3D kinematically admissible rotational failure mechanism is adopted here for 3D homogeneous slopes in frictional/cohesive soils. A set of stability charts is presented in a wide range of parameters for 3D slopes under combined horizontal and vertical seismic loading conditions. Accounting for the effects of the vertical seismic acceleration, the difference in safety factors for 3D slopes can exceed 10%, which will significantly overestimate the safety of the 3D slopes.

A method of simulating spatially varying ground motions in V-shaped symmetric canyon is presented. The topographic amplification effect is taken into account by considering a 2-dimension wave propagation model. Two approaches are developed to simulate spatially varying ground motions. First, the spatially varying ground motions are simulated by using the power spectral density and an empirical coherency loss function. Second, the spatially varying ground motions are simulated by using given ground motions and an empirical coherency loss function. These two proposed methods are validated by comparing statistical characteristics of the synthetic motions with target theoretical models.

Simulation of sample realizations of stochastic processes is the bedrock of the Monte Carlo method, and the accurate modeling of stochastic processes is crucial to determine realistic struc...

A simple and efficient simulation method is proposed to generate multidimensional non-Gaussian vector fields based on the spectral representation method, according to the target cross spect...

In dynamic analyses of important structures, seismic input may be defined in the form of time series. It is required that the response spectrum of this input time series be compatible with a specified target response spectrum. Time domain spectral matching, which is used to generate spectrum compatible acceleration time series, is investigated in some detail. First, a new, improved wavelet is presented, and the new adjustment wavelet can prevent drifts in the resulting velocity and displacement time series without applying a baseline correction. Next, the analytical solution of the matrix accounting for the cross correlation of each wavelet is given in order to ensure the speed of the matching procedure. Finally, some aspects, such as the reduction factors and the matching order, are discussed to ensure the stability and efficiency of the matching procedure. Accordingly, the characteristics of the matching procedure are illustrated by numerical examples.

Pullout resistance is one of the most important factors governing seismic stability of reinforced soil walls. The previous studies on the seismic stability of reinforced soil walls have focused on the axial resistance of the reinforcement against the pullout. However, the kinematics of failure causes the reinforcement to be subjected to the oblique pullout force and bending deformation. Considering the kinematics of failure and bending deformation of the reinforcement, this paper presents a pseudo-static seismic analysis for evaluating the pullout resistance of reinforcements in soil wall subjected to oblique pullout forces. A modified horizontal slice method (HSM) and Pasternak model are used to calculate the required force to maintain the stability of the reinforced soil wall and shear resistance mobilized in the reinforcements, respectively. In addition, this paper studies the effect of various parameters on the pullout resistance of the reinforcements in soil wall subjected to seismic loads. Results of this study are compared with the published data and their differences are analyzed in detail.

This paper presents a variational limit equilibrium closed-form solution for the stability of slurry-supported trenches in cohesive soil, frictional cohesive soil, and cohesionless soil. Study results indicate that the critical slip-surface geometry is either planar or log spiral. The normal stress distribution, which indicates the likely depth of a tension crack at the crest over the slip surface, was also obtained as part of the complete solution and as a function of groundwater-table level. The closed-form solution was used to produce stability charts for a practical range of parameters. The charts can be used to conveniently assess the stability of a given slurry trench for preliminary design. The paper gives two different examples for trenches to illustrate the influence of the slurry level on the trench stability. To introduce the analytical solution, this study is limited to a simple slurry trench problem; however, extension of the present framework to deal with complex problems would be st...

The spectral representation method (SRM) is widely used when simulating spatially variable ground motions. It has mainly two formulas, i.e., the random amplitudes and the random phases formulas. There exist three methods for decomposing the cross spectral density matrix: Cholesky decomposition, eigen decomposition, and root decomposition. Therefore, there are six forms with respect to the different combinations of the simulation formulas and the decomposition methods. To provide researchers and engineers with the guidance on choosing simulation method, the six forms are systematically investigated from five aspects: the power intensity, response spectra, and stochastic error of auto/cross spectral density, Fourier spectra, and difference indexes for Fourier amplitudes and phases. Finally, we give the following advice: the characteristics of the ground motions simulated by the random amplitudes formula are independent of the decomposition method, while the characteristics of the ground motions simulated by...

A three-dimensional (3D) kinematically admissible rotational failure mechanism is extended from toe failure to include face failure and base failure for homogeneous slopes in both purely cohesive and frictional/cohesive soils. In the strict framework of limit analysis, an analytical approach is derived to obtain the upper bounds on slope stability and the corresponding type of the critical failure mechanism. Compared with the available results from the finite-element limit-analysis method, the 3D rotational failure mechanisms give the best estimate on the upper bound. A set of stability charts is presented in a wide range of parameters for 3D homogeneous slopes under both static and pseudostatic seismic loading conditions. This set is useful in assessing the safety of the 3D homogeneous slopes in practical applications.

Multivariate random processes are usually simulated by the spectral representation method (SRM). According to the matrix for decomposition, the SRM has two main types, that is, the SRM based on the decomposition of the power spectral density (PSD) matrix denoting the PSD matrix-based SRM, and the SRM based on the decomposition of the coherency matrix denoting the coherency matrix based-SRM. The stochastic errors of the PSD for the PSD matrix-based SRM have been given. This paper presents the stochastic errors of the PSD for the coherency matrix-based SRM, and makes a comparison of these errors for the PSD matrix-based SRM. For the random amplitudes formulas and random phase formula and Cholesky decomposition method, the stochastic errors of the PSDs for the PSD matrix-based SRM are the same as or the coherency matrix-based SRM, whereas for the random phases formula and eigendecomposition method and random phases formula and root decomposition method, they are different. However, the differences ar...

The spectral representation method (SRM) is most widely used in simulating the stochastic field. The proper orthogonal decomposition (POD) based SRM is an important form. This paper investigates the approximate approaches to the POD-based SRM in simulating two typical problems, i.e., the seismic ground motion and wind velocity fields simulations. Then, the accuracy resulting from the power spectral density matrix-based POD method (PSRM) is compared to that of the coherency matrix-based POD method (CPSRM). It is concluded that the CPSRM maintains a much higher accuracy than the PSRM. In the CPSRM, the linear interpolation of eigenvectors and third-order polynomial interpolation of eigenvalues can be accepted to attain high accuracy; the linearly distributed interpolation nodes are effective in the ground motions simulation; however, the exponentially distributed interpolation nodes are effective in the wind velocity simulation.

This paper reports a series solution of wave functions for two-dimensional scattering and diffraction of plane SH waves induced by a symmetrical V-shaped canyon with different shape ratios. A half-space with a symmetrical V-shaped canyon is divided into two sub-regions by using a circular-arc auxiliary boundary. The two sub-regions are represented by global and local cylindrical coordinate systems, respectively. In each coordinate system, the wave field satisfying the Helmholtz equation is represented by the separation of variables method, in terms of the series of both Bessel functions and Hankel functions with unknown complex coefficients. Then, the two wave fields are described in the local coordinate system using the Graf addition theorem. Finally, the unknown coefficients are sought by satisfying the continuity conditions of the auxiliary boundary. To consider the phase characteristics of the wave scattering, a parametric analysis is carried out in the time domain by assuming an incident signal of the Ricker type. Surface and subsurface transient responses demonstrate the characteristics and mechanisms of wave propagating and scattering.

SUMMARY Topographies have significant effects on seismic waves. The wavefunction expansion method has been frequently employed to study the topographic effect because this method can reveal the physics of the wave scattering and can testify the accuracy of numerical methods. The 2-D scattering and diffraction of plane SH waves induced by a non-symmetrical V-shaped canyon is examined here by using the wavefunction expansion method. Through a new domain decomposition strategy, the half-space containing a V-shaped canyon is divided into three subregions. Then the wavefield for every subregion is constructed in terms of an infinite series of wavefunctions with unknown coefficients in three coordinate systems, respectively. After that, three wavefields are all represented in the same coordinate system using the Graf addition theorem. The unknown coefficients are obtained by satisfying the continuity conditions of the auxiliary boundary. The proposed series solution of wavefunctions for a non-symmetrical V-shaped canyon can be reduced to a symmetrical case. Results in this study for the symmetrical case agree very well with those in the published literature. To show the effects of the non-symmetrical-geometry topography on the surface ground motion, a parametric study is carried out in the frequency domain. Surface and subsurface transient responses in the time domain demonstrate the phenomenon of wave propagating and scattering. Finally, the proposed model is successfully applied to two idealized cross sections of Pacoima canyon and Feitsui canyon.

The series solution of wave functions for 2D scattering and diffraction of plane SH (shear horizontal) waves induced by a U‐shaped canyon is proposed herein to account for the topographic effect of such a canyon. The wave function expansion method has been frequently employed to study the topographic effect because it can reveal the physics of the wave scattering and can test the accuracy of other methods. Through a new domain decomposition strategy, the half‐space having a U‐shaped canyon is divided into three subregions. Hence, we defined three cylindrical coordinate systems. In each coordinate system, the wave field satisfying the Helmholtz equation was represented by means of the separation of variables method, in terms of the series of both Bessel functions and Hankel functions with unknown complex coefficients. Then three wave fields are all represented in the same coordinate system using the Graf addition theorem. The unknown coefficients are solved by satisfying the continuity conditions of the auxiliary boundary and the traction‐free boundary conditions on the bottom of the canyon. To show the effects of symmetrical and nonsymmetrical U‐shaped canyons on the surface ground motion, a parametric analysis is carried out in the frequency domain. Surface and subsurface transient responses in the time domain demonstrate the phenomenon of wave propagating and scattering. It is found that a zone of amplification can obviously take place at the bottom of a U‐shaped canyon with nearly vertical walls.

The spectral representation method (SRM), based on the Cholesky decomposition of either cross spectral density matrix or lagged coherency matrix, is widely used in the simulation of spatially varying ground motions. In this study, the SRM, based on the decomposition of lagged coherency matrix, is modified to apply to the common case which the auto spectral densities of simulation points are not the same. When using interpolation approximation approach to improve the efficiency, the SRM based on the decomposition of lagged coherency matrix exhibits much higher accuracy than the SRM based on the decomposition of cross spectral density matrix, because the elements of lower triangular matrix obtained by the Cholesky decomposition of lagged coherency matrix vary slowly with the frequency. Therefore, the SRM, based on the decomposition of lagged coherency matrix, is generally suitable for the combination with the interpolation approximation approach.

Random fields, such as the wind velocity field and the seismic ground motion field, are usually simulated by the spectral representation method (SRM). The SRM mainly relies on two methods: the random amplitudes method and the random phases method. However, the temporal statistics estimated from one SRM-simulated sample process differs from the target characteristics. Such differences can usually be assessed by the statistical errors, i. e., bias errors and stochastic errors. The closed-form solutions of statistical errors produced by random phases method have been given. This paper gives the closed-form solutions of statistical errors produced by the random phases methods and compares the statistical errors produced by both methods. The comparison of the stochastic errors of power spectral density functions produced by different methods demonstrates that (1) the random amplitudes method exhibits higher but more uniformly distributed stochastic errors than the random phases method; and (2) the stoc...

In this thesis we have developed different structure preserving reduction methods for finite and infinite dimensional port Hamiltonian systems by using a balanced model reduction approach. In the first part we have defined a descriptor representation of port Hamiltonian systems with constraints. The balanced realization of the descriptor system has been used for reducing the port Hamiltonian descriptor system and conserving explicitly the constraint equations. In the second part, conditions have been derived on the weighting matrices of the LQG control problem such that the dynamical LQG controller is passive and has a port Hamiltonian realization. Two passive LQG control design methods have been suggested and one of them allows us to define a LQG balanced realization. Based on this realization, the effort constraint method has been used to reduce the LQG balanced port Hamiltonian system and obtain a reduced order passive LQG controller. In this way the closed-loop system is derived from the interconnection of 2 port Hamiltonian systems, hence the Hamiltonian structure has been preserved. In the third part, the proceeding results have been extended to a class of infinite dimensional port Hamiltonian system with bounded input operator. A passive LQG control design method for infinite dimensional port Hamiltonian system has been derived as by Control by Interconnection (CbI). Based on the balanced realization associated with this passive LQG control design, a finite dimensional approximation has been achieved and a reduced order passive LQG controller has been derived. As a consequence, the system in closed-loop with this reduced order LQG controller again admits a port Hamiltonian structure and satisfies the passivity; Dans ce mémoire nous avons développé des méthodes de réduction des systèmes hamiltoniens à port en dimension finie et infinie qui préservent leur structure. Dans la première partie, nous avons défini une représentation des systèmes hamiltoniens à port avec contraintes sous la forme d'équations différentielles algébriques (DEA) de type de système descripteur. De cette forme nous avons déduit une réalisation équilibrée du système hamiltonien à port exprimée sous forme de système descripteur contenant les mêmes systèmes d'équations de contrainte. Dans la deuxième partie, nous avons défini une classe de problèmes de commande LQG tels que le contrôleur dynamique LQG est passif et admet une réalisation hamiltonien à port. Deux méthodes de synthèse de commande passive LQG sont proposées et une de ces méthodes LQG nous a permis de définir une réalisation équilibrée LQG. Puis nous avons appliqué la méthode de contrainte de l'effort pour réduire le système hamiltonien à port et obtenir une commande LQG passive d'ordre réduit. Ce contrôleur LQG admettant une réalisation hamiltonienne, la structure hamiltonienne est préservée pour le système en boucle fermée par interconnexion de systèmes hamiltoniens à port. Dans la troisième partie, nous avons généralisé les résultats précédents aux systèmes hamiltoniens à ports linéaires de dimension infinie. Pour cela nous avons considéré une classe de systèmes hamiltoniens à ports de dimension infinie dont l'opérateur d'entrée est borné et un problème de commande LQG passif. Sous des conditions de nucléarité de l'opérateur de Hankel lié au problème LQG, nous définissons une réalisation équilibrée LQG passive du système et une approximation en dimension finie. Le contrôleur LQG passif d'ordre réduit obtenu par cette approximation admet une réalisation hamiltonienne à port et par conséquent la structure hamiltonienne et la passivité sont préservées en boucle fermée

A simplified method for the simulation of the ergodic spatially correlated seismic ground motion is proposed based on the commonly used original spectral representation method. To represent the correlation in the ground motion, the phase angles are given by explicit terms with a clear physical meaning. By these explicit terms, the computational efficiency can be improved by converting the decomposition of the complex cross-spectral matrix into the decomposition of the real incoherence coefficient matrix. Double-indexing frequencies are introduced to simulate the ergodic seismic ground motion, and the ergodic feature of the improved method is demonstrated theoretically. Subsequently, an explicit solution of the elements of the lower triangular matrix under the Cholesky decomposition is given. With this explicit solution, the improved method is simplified, and the computational efficiency can be improved greatly by avoiding the repetitive Cholesky decomposition of the cross-spectral matrix in each frequency step. Finally, a numerical example shows the good characteristic of the improved method.

A new model to simulate spatially correlated earthquake ground motions is developed. In the model, the main factors that characterize three distinct effects of spatial variability, namely, the incoherency effect, the wave-passage effect and the site-response effect, are taken into account, and corresponding terms/parameters are incorporated into the well known model of uniform ground motions. Some of these terms/parameters can be determined by the root operation, and others can be calculated directly. The proposed model is first verified theoretically, and examples of ground motion simulations are provided as a further illustration. It is proven that the ensemble expected value and the ensemble auto-/cross-spectral density functions of the simulated ground motions are identical to the target spectral density functions. The proposed model can also be used to simulate other correlated stochastic processes, such as wave and wind loads.

In this paper, the dynamic response of a simply supported viscously damped double-beam system under moving harmonic loads is investigated. The double-beam system consists of two elastic homogeneous isotropic beams, which are identical, parallel, and connected continuously by a layer of elastic springs provided with viscous damping. Two coupled governing equations describing the vibration of those two beams are decoupled by a simple change of variables, so that the analytical solutions for the dynamic deflections of both beams can be given. Numerical examples are employed to investigate the effects of moving speed and frequency of load, as well as the damping and the elasticity of the layer, on the dynamic responses of the beams. The deflections for the double-beam system are also compared to these of a single-beam system.

Random processes, such as the wind velocity field and spatially varying ground motions, are usually simulated as N-variate stochastic processes by the conditional-simulation method. However, the temporal power spectral density (PSD) function of a single, simulated sample process may be different from the target PSD. Such differences can usually be assessed by the statistical errors (i.e., the bias and stochastic errors). Therefore, this paper investigates the bias errors and the stochastic errors of the PSD functions produced by the conditional-simulation method. For the bias errors, it was found that the conditional-simulation method might produce the nonzero bias error of the PSD functions in some cases. However, this usually does not occur in the unconditional simulation, and it should be avoided. To avoid the nonzero bias error of the PSD functions, a modified conditional-simulation method was proposed. It was verified using both the theoretical derivation and the numerical example. For the st...

An analytical solution for diffraction of both plane and cylindrical SH waves induced by a horseshoe shaped cavity with an inverted arch is presented in this paper. The geometry of the cavity is assumed to be composed of two circular arcs. By introducing an auxiliary boundary, the whole physical region is divided into two computational regions. The scattered wavefield in the open region and the standing wavefield in the enclosed region are presented by means of the wave function expansion method. Both of the wavefields are given in terms of the wave function series with unknown coefficients. By applying the Graf’s addition formula, two systems of equations for seeking the unknowns are derived by taking advantage of the boundary conditions based on the region-matching strategy. The problem of wave scattering is finally solved after seeking the solutions of the two systems of equations through standard matrix techniques. Then the effects of the excitation frequency, the cavity embedment depth and cavity geometry are discussed. The differences in terms of ground motions under different excitations and the influence of source location under cylindrical waves are also examined.