Browsing by Author "Spanos, Pol D."
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Item A harmonic balance solution of the coupled, nonlinear equations of motion of a flexible structure subject to vortex shedding(1991) Swerdon, Sylvia Hull; Spanos, Pol D.This investigation presents an approximate method of determining the response of a viscously damped single-degree-of-freedom system exhibiting both in-line (drag) and transverse (lift) flow-induced oscillations. A modified Morison theory is utilized involving the relative system-fluid velocity and accounting for coupling effects between in-line and transverse forcing terms. The method of harmonic balance is adopted to construct a solution of the coupled equations of motion containing periodic terms. Results pertaining to the coupled system are compared with uncoupled results to determine the effect of coupling. Results of the approximate solution are further compared to a numerical time integration of the nonlinear coupled system equations to determine the relative accuracy of the approximate method. Finally, applications to multi-degree-of-freedom methods such as marine riser analysis are discussed.Item A Lanczos component mode synthesis algorithm for locally nonlinear systems with applications to seismic structural pounding(1991) Lavelle, Francis M., III; Spanos, Pol D.A Component Mode Synthesis (CMS) algorithm employing load dependent Lanczos vectors is presented. The proposed algorithm yields a sparse set of reduced system equations and is an efficient method for computing the forced vibration response of multi-component and/or locally nonlinear dynamic systems. The beneficial aspects of traditional CMS methods employing fixed interface component normal modes and the computational advantages of load dependent Ritz/Lanczos vectors are combined in the new algorithm. By exploiting the tridiagonal property of Lanczos vectors, the system equations are nearly as sparse as traditional CMS equations. The Lanczos CMS transformation projects the solution onto the same subspace spanned by a previously proposed Ritz CMS transformation. For loads which have fixed spatial distributions, the complete static response of each component is completely represented by its first retained Lanczos vector. Several numerical integration techniques which take advantage of the special structure of the synthesized equations of motion are studied. Operations counts demonstrate that the integration costs for the proposed algorithm are substantially lower than the costs associated with fully coupled Ritz CMS equations and nearly identical to traditional CMS integration costs. In general, the accuracy of the proposed algorithm is comparable to traditional CMS algorithms. For specific applications, the rates of convergence of the two methods depend on the applied loading conditions and the degree of interaction between the structural components. The analysis of several multi-component earthquake engineering problems has lead to an investigation of seismic structural pounding. Structural pounding occurs when the separation between adjacent buildings is not sufficient to prevent collisions during seismic excitations. An inelastic linking mechanism which reduces pounding hazards for a particularly vulnerable class of structures is presented. Inelastic links are a viable retrofitting strategy for many existing buildings which have inadequate separation and dissimilar dynamic characteristics. The analytical model for the linked structures is a two-component locally nonlinear system. The proposed Lanczos CMS reduction algorithm is a efficient method for predicting the seismic response of inelastically linked buildings.Item A Monte Carlo study of vibration isolation systems using linear and nonlinear multiple tuned mass damper oscillators(2005) Gkaras, Vasileios; Spanos, Pol D.The vibration isolation effect of linear and nonlinear single degree of freedom oscillators attached to a structure is studied. This system of oscillators, directly attached to the main structure, induces a decrease to the amplitude of the structural response, over a wide excitation frequency band. This is achieved by distributing the natural frequencies of the attachments over an a priori specified frequency interval, which is related to the excitation power spectrum density. The use of nonlinear Duffing type oscillators increases the vibration isolation effect of the attachments. The study of the vibration isolation system behavior is conducted using the Monte Carlo technique. An implicit Newmark integration scheme is used for the linear attachment case. In the case of nonlinear attached oscillators, the system of equations of motion is integrated by an iterative decoupled Newmark integration technique. This scheme improves significantly the efficiency of the Monte Carlo method.Item A non-linear finite element model for the determination of elastic and thermal properties of nanocomposites(2009) Elsbernd, Paul; Spanos, Pol D.This thesis presents a non-linear model for the thermal and elastic properties of single-walled carbon nanotube reinforced polymer composites. Finite Element Analysis (1-EA), in conjunction with the Embedded Fiber Method (EFM), is used to calculate the effective stress-strain curve and thermal conductivity of the composite material. First, the geometry of a user-defined volume fraction of nanotubes is randomly generated and their properties are incorporated into the polymer matrix using the EFM. Non-linear FEA is next performed to account for the non-linear properties of the polymer matrix and the carbon nanotubes. Finally, Monte Carlo Analysis of five hundred random microstructures is performed to capture the stochastic nature of the random fiber generation and to derive statistically sound results. The model is validated by comparison with several different experiments reported in the open literature.Item A Numerical Resistor Network Model for the Determination of Electrical Properties of Nanocomposites(2011) Ward, Bradley; Spanos, Pol D.This thesis introduces a comprehensive numerical model for the determination of the electrical properties of carbon nanotube reinforced polymer composites. Procedures of this model are based on a new spanning network identification algorithm and the resistor network method. First, realistic nanotube geometry is generated from input parameters defined by the user. The spanning network algorithm then determines the connectivity between nanotubes in the representative volume element. Next, interconnected nanotube networks are converted to equivalent resistor circuits. Finally, Kirchhoff's Current Law is used in conjunction with finite element analysis to solve for the voltages and currents in the system and calculate the effective electrical conductivity of the nanocomposite. The Monte Carlo method is used to eliminate statistical variation by simulating five hundred random geometries. The model accounts for electrical transport mechanisms such as electron hopping and simultaneously calculates percolation probability, identifies the backbone, and determines effective conductivity. The accuracy of the model is validated by comparison to both models and experiments reported in the literature.Item A physically motivated reduced-order modal energy technique for ARMA spectrum estimation(1995) Eberle, Robert Raymond; Spanos, Pol D.A reduced-order modal energy (ROME) technique for spectrum estimation is introduced. In this technique the transfer function of a higher-order autoregressive (AR) model of a power spectrum is decomposed into partial fractions. These individual fractions are examined from the perspective of relative significance to the total energy of the system. First, the technique is formulated for a scalar random process (the univariate case). In the derivation, two solution procedures are discussed. In one procedure, a system of equations is solved to determine the unknown numerator coefficients of the partial fraction expansion. In the second procedure, a unique approach is used which yields each numerator coefficient directly, avoids solving a system of equations, and greatly reduces the requisite computation time. Next, the reduced-order modal energy technique is formulated for a vector random process (the multivariate case); it provides a parsimonious estimate of the power spectral density by capturing frequencies associated with significant spectral values. Numerical examples involving short data sequences, Space Shuttle acceleration data, and sunspot and temperature measurements are presented which demonstrate the usefulness of the technique.Item A probabilisitc approach to the frequency domain analysis of drill-string lateral vibrations(1998) Chevallier, Arnaud Michel; Spanos, Pol D.Drill-string failure is recognized by the drilling community as one of its most costly and frequently encountered problems. In order to diminish the frequency of such failures, the drilling community has been focusing on the modeling of the static and dynamic behaviors of drill-strings, towards increasing efficiency. Drill-string dynamics involves complex phenomena with excitations in axial, lateral and torsional directions, and coupling of these three and other factors such as mass imbalance, whirling, or stick-slip motion of the bit. The present study focuses on one aspect which has not been studied in detail by the drilling community, namely the consideration of random loads on the BHA studied by a frequency domain approach. A comprehensive literature survey is attempted and elucidating numerical results are provided.Item A probabilistic approach to the Critical Element Model for fatigue in composite materials(1989) Gonnaud, Jean-Louis; Spanos, Pol D.The suitability of traditional fatigue design methods to deal with complex damage modes in composite materials is critically assessed. After a survey of the recent fatigue models, a new methodology is developed, based on both the Markovian discrete time discrete state stochastic processes and the Critical Element Model for damage in composite materials. In a practical application of the methodology, the fatigue behavior of cross ply Carbon Epoxy laminates is derived from a Monte-Carlo simulation.Item A probabilistic model for fatigue damage accumulation in composite laminates(1993) Rowatt, John David; Spanos, Pol D.A stochastic model for the accumulation of fatigue damage in composite laminates is proposed. The model considers the accumulation of fatigue damage as an evolutionary stochastic process and attempts to predict the distribution of damage in terms of the stiffness loss in the laminate as a function of the number of load cycles. The cumulative damage process is modeled as an embedded discrete time, finite state, non-stationary Markov process utilizing a stationary discrete time, finite state, stationary model in conjunction with a time transformation-condensation method. Furthermore, the mechanisms of the complex damage development process in composite laminates are incorporated into the model. This feature affords a more complete and accurate representation of the fatigue damage accumulation process in which the states of the model can be directly related to the stiffness loss in the laminate.Item A residual flexibility approach for decoupled analysis of nonlinear, nonclassically damped systems of combined components(1995) Majed, Arya; Spanos, Pol D.A residual flexibility approach for the analysis of systems comprised of multiple components subjected to dynamic loading is presented. In it, the reactive forces at the junctions of the components are computed directly without the synthesis of component modes or the determination of system modes. This is accomplished by expressing the displacements at the junction coordinates of the components in terms of the retained component free-junction normal modes and a first-order account of the residual flexibility of the unretained modes. Once the components are represented in this manner, the requirement of displacement compatibility and force equilibrium at the junction coordinates is enforced. This leads to a set of junction-sized, simultaneous algebraic equations, similar in form to that of the flexibility formulation in statics, in terms of the unknown junction forces. The computed forces at a given time-step then serve to base-drive each component's equations of motion separately, hence the term decoupled analysis. Due to the formulation of the method, the nonlinear, nonclassically damped problem becomes a natural progression. The new method compares well to the traditional method of Component-Mode Synthesis for solutions to a nonclassically damped fixed-fixed beam comprised of two classically damped cantilevered beam components.Item A stochastic approach for estimating fatigue life of equipment located at topside of FPSO offshore systems(2002) Wang, Juan; Spanos, Pol D.Floating Production, Storage and Offloading (FPSO) Systems are subjected to stochastic wave loads. In this context, an approach for stochastic fatigue analysis of FPSO topside equipment is developed. Proper FPSO transfer functions, and the Ochi-Hubble sea wave elevation spectrum are combined to provide the design spectrum at the topside of the FPSO. The equipment response is simulated by a time series model; it is approximated as the output of digital filters to a band-limited white noise input. The rainflow cycle counting method is applied to the equipment response time history to identify significant cycles that produce fatigue damage. By using a S-N fatigue life curve, and Miner's linear damage accumulation rule, the fatigue life is estimated for a generic piece of equipment. The results of the rainflow cycle counting method are supplemented by results from a power spectrum based, exclusively, approach.Item A stochastic approach to motorcycle dynamics(2009) Robledo Ricardo, Luis Alejandro; Spanos, Pol D.A study on the applicability of the Monte Carlo method in the analysis of the dynamical behavior of motorcycles subject to road excitation is presented. To this end, a time-domain numerical simulation of the response of a motorcycle modeled as a linear four-degree-of-freedom (4-DOF) system, and traveling at constant speed is carried out. To validate the accuracy of the solutions obtained, the linear 4-DOF model is also analyzed using the frequency domain approach. Although the Monte Carlo simulation can be computationally costly, it provides an excellent scheme of analyzing, as well, non-linear systems, in which case the frequency domain approach cannot be applied. In this context the applicability of auto-regressive (AR) and autoregressive-moving-average (ARMA) filters for efficient implementation of the Monte Carlo simulation is pointed out. Furthermore, a practical engineering approach is presented for improved road roughness power spectral density (PSD) representation, and statistical parameters of the excitation signals synthesized.Item A wavelet-based numerical scheme for stochastic mechanics(2000) Rao, Vallabhajosyula Ravi Shankar; Spanos, Pol D.Uncertainty is an inherent part of many physical systems. This is often ignored to simplify mathematical models thereby leading to a deterministic treatment of the system. Incorporation of the uncertainty into the model, particularly in the presence of strong correlation across scales is a difficult task for the conventional modeling techniques. This work studies a biorthogonal wavelet framework for the representation of random fields. It is shown that such a representation scheme leads to significantly decorrelated wavelet coefficients. The amount of decorrelation obtained is an improvement over that achieved with orthonormal wavelet basis functions. It is shown that a biorthogonal dual wavelets with sufficient number of vanishing moments and corresponding to a low primal order perform better than Daubechies wavelets at this task. These observations are used in pursuing the development of Wavelet based Galerkin and Petrov-Galerkin schemes for one-dimensional and two-dimensional stochastic mechanics problems.Item An analysis of nonlinear damping and stiffness effects in force-limited random vibration testing(1998) Davis, Gregory Laurence; Spanos, Pol D.The effects of both stiffness and damping nonlinearities on force-limited, random vibration test specifications are investigated. The response of the source-load vibratory system to a random, Gaussian excitation is analyzed using the modal- and residual-mass two degree-of-freedom system. The technique of statistical linearization is used in conjunction with the frequency shift method to derive force-limiting specifications for a nonlinear load mass modeled as a Duffing, Rayleigh damped, and linear plus quadratically damped oscillator, respectively. The normalized force-limiting specification for each nonlinear system is determined for a range of nonlinear stiffness and damping coefficients and compared with its linear counterpart over the same range of effective mass parameters. In general, deviations in the force-limiting spectrum arising from nonlinear stiffness effects will be apparent only at low frequencies on systems that are lightly damped, have large nonlinear stiffness parameters, and that experience moderately high input excitations. Deviations in the force-limiting spectrum arising from nonlinear damping effects will be apparent at lower frequencies on systems that are lightly damped, but having smaller nonlinear damping parameters and input excitations than their nonlinear stiffness counterparts. Case studies are presented to illustrate the methodology for deriving both linear and nonlinear force-limiting specifications for use in the test laboratory.Item An approach for efficient analysis of drill-string random vibrations(2002) Politis, Nikolaos P.; Spanos, Pol D.Lateral vibrations are widely recognized as the leading cause of drill-string failures in oil well operations. The finite elements method formulation is used for the mathematical modelling. Due to the erratic nature of the forces at the drill-bit, a stochastic dynamics approach is followed. Both the method of statistical linearization, and the Monte Carlo method are used to analyze the system dynamics. Numerical results pertaining to data obtained by measurement while drilling tools are presented. The significance of the present study, over studies available in the literature, hinges upon the computational efficiency of the adopted piecewise linear model of the drill-string---well formation interaction and the derivation of information on the probability density function, and the power spectrum of the erratic drill-string motion. It is expected that this study will enhance the interest in using stochastic dynamics techniques in drilling system analysis and design.Item An engineering approach for estimating seismic power spectra(1992) Tein, When-Yen; Spanos, Pol D.The aseismic design of large structures may need to account for the nonstationary and the multivariate aspects of strong ground motions. These aspects influence both the time and the spatial variation of the dynamic response of the structure. Current techniques for treating this problem have considerable limitations. An approach is developed in the thesis for addressing this issue based on energy considerations. Estimates of evolutionary seismic auto- and cross-spectra are obtained. It is assumed that the available accelerograms are realizations of broad-band stochastic processes. By analyzing the output of lightly damped linear systems excited by these processes, estimates are obtained for the associated auto and cross spectral density functions. The proposed estimation techniques have two main advantages. Firstly, the evolutionary auto- and cross-spectra can be estimated without having to assume a specific form for the evolutionary spectrum. Secondly, with the evolutionary auto- and cross-spectra determined, the moments of structural responses to these stochastic seismic models, which are functions of time, can be approximated from the spectra without having to resort to simulation. The proposed method is further extended to provide for situations where not enough data are available to accurately assess the stochastic character of the ground motion. Based on a stochastic interpretation of ground accelerations, a weighted least squares method is used to estimate the coefficients of a commensurate model from the responses of a lightly damped linear system excited by these accelerograms.Item Analysis of stochastic systems with discrete elements(1989) Ghanem, Roger George; Spanos, Pol D.Two new methods for the solution of problems involving material variability are proposed. Medium properties are modeled as second order stochastic processes defined by their mean and convariance functions. Both methods make use of the Karhunen-Loeve expansion which is a mean-square convergent orthogonal expansion of a continuous process in terms of a countable set of uncorrelated random variables. The first of the proposed methods relies on implementing the Karhunen-Loeve expansion for the medium property in conjunction with a Neumann expansion of the inverse operator. This results in an explicit expression for the response process as a multivariate polynomial functional of a set of uncorrelated random variables. The second method treats the solution process as an element in the Hilbert space of random functions, in which a sequence of projection operators is identified as the Polynomial Chaoses of consecutive order. The solution process is then determined by its projection onto the spaces spanned by these polynomials. These concepts can be construed as extensions of the deterministic finite element methods to the space of random functions. Both of the proposed methods are exemplified by three problems from the field of engineering mechanics. The corresponding results are found in agreement with those obtained by a Monte-Carlo simulation solution of the problems. In addition to the two methods mentioned above, a new formulation is presented for a class of problems involving deterministic media subjected to random external excitations. The formulation involves a combination of the boundary element method with the Karhunen-Loeve expansion for the exciting process. Namely, the boundary element method is used as a discretization tool to restate the problem as a set of discrete equations. Further, the Karhunen-Loeve expansion is utilized to represent the random processes in a manner conducing their optimal discretization.Item Application of Markov chains to the critical element model for determining the fatigue life of composites(1995) Rowatt, John David; Spanos, Pol D.A stochastic model for predicting the lifetime of composite laminates subjected to multiaxial fatigue loading is proposed. The model is based on the application of Markov chains to the well known "critical element" model for the fatigue of composite laminates. The model considers the accumulation of fatigue damage as an evolutionary random process characterized by changes in the global compliance of a laminate. These changes are modeled as nonstationary, discrete time, discrete state Markov processes (Markov chains) utilizing stationary Markov chains and polynomial transformations of their indexing parameters. The stationary Markov chains are developed on the assumption of "equivalent damage". Their parameters are determined from experimental data. The Markov chain models yield full cycle dependent probability distributions for the changes in laminate compliance. These changes and their respective distributions are used as input into a mechanical analysis to determine the stresses on the life controlling critical elements of a laminate. The stresses on the critical elements and their derived probability distributions are used in turn to predict the lifetime of a laminate based on Markov chain models of the fatigue behavior of the critical elements. The predictive capability of the proposed model is demonstrated by comparison with experimental results.Item Ascent performance feasibility for next-generation spacecraft(1998) Mancuso, Salvatore Massimo; Miele, Angelo; Spanos, Pol D.This thesis deals with the optimization of the ascent trajectories for single-stage suborbital (SSSO), single-stage-to-orbit (SSTO), and two-stage-to-orbit (TSTO) rocket-powered spacecraft. The maximum payload weight problem has been solved using the sequential gradient-restoration algorithm. For the TSTO case, some modifications to the original version of the algorithm have been necessary in order to deal with discontinuities due to staging and the fact that the functional being minimized depends on interface conditions. The optimization problem is studied for different values of the initial thrust-to-weight ratio in the range 1.3 to 1.6, engine specific impulse in the range 400 to 500 sec, and spacecraft structural factor in the range 0.08 to 0.12. For the TSTO configuration, two subproblems are studied: uniform structural factor between stages and nonuniform structural factor between stages. Due to the regular behavior of the results obtained, engineering approximations have been developed which connect the maximum payload weight to the engine specific impulse and spacecraft structural factor; in turn, this leads to useful design considerations. Also, performance sensitivity to the scale of the aerodynamic drag is studied, and it is shown that its effect on payload weight is relatively small, even for drag changes approaching $\pm 50\%.$ The main conclusions are that: the design of a SSSO configuration appears to be feasible; the design of a SSTO configuration might be comfortably feasible, marginally feasible, or unfeasible, depending on the parameter values assumed; the design of a TSTO configuration is not only feasible, but its payload appears to be considerably larger than that of a SSTO configuration. Improvements in engine specific impulse and spacecraft structural factor are desirable and crucial for SSTO feasibility; indeed, it appears that aerodynamic improvements do not yield significant improvements in payload weight.Item Assessment of critical factors in the Tropical Storm Allison impact on the Brays Bayou watershed(2002) Safiolea, Eleftheria; Bedient, Philip B.; Spanos, Pol D.Floods are calamities with potential for many fatalities and enormous economic losses. However, the degree of vulnerability to a disaster is a function of human action and behavior. The rapid development of modern metropolitan areas has changed the response of floodplains to rainfall and increased the risk of flooding. The current study is concerned with the flooding along Brays Bayou, a 31-mile waterway located on the southwest part of the city of Houston. The first objective of this study is to simulate the runoff from Tropical Storm Allison and evaluate the use of NEXRAD (next generation radar) for Allison over Brays. T.S. Allison's severity was not identical for all Brays Bayou. Thus, the second objective of this research is to develop scenarios that investigate the significance of the dissimilarity of Allison's rainfall patterns along the watershed to the magnitude of consequences on the middle and lower part of Brays Bayou.