About

Pol D. Spanos is the Lewis B. Ryon Professor in Mechanical & Civil Engineering and a Professor of Materials Science and NanoEngineering at Rice University. His research focuses on the dynamics and vibrations of structural and mechanical systems under various loads, with particular attention to systems exhibiting nonlinear behavior and those exposed to hazard or risk-inducing conditions. His group is also interested in the mechanical properties and fatigue/fracture issues of modern materials such as nanocomposites, as well as signal processing algorithms for dynamic effects in biomedical applications. Professor Spanos develops analytic and numerical methods involving deterministic and stochastic differential equations, finite element models, Monte Carlo simulations, and advanced signal processing techniques, applying these to diverse themes including vehicle and robot dynamics, seismic spectrum estimation, flow-induced vibrations, space payload certification, offshore rig stability, wind load simulation, and biomedical signal analysis. He has received numerous awards and honors, including the NSF Presidential Young Investigator Award, the ASME T.K. Caughey Medal, the ASCE Theodore Von Karman Medal, and the ASME Gold Medal, among others. He has published over 400 technical papers, authored or edited more than 20 books, and serves as Editor-in-Chief of the International Journal of Non-Linear Mechanics and as editor of the Journal of Probabilistic Engineering Mechanics. With extensive experience supervising students and hosting visiting scholars, his work has been funded by agencies such as NSF, NASA, and DOE, and he has served as a technical advisor, expert witness, and federal court master. He is a Fellow and Honorary Member of several professional societies, a member of the National Academy of Engineering, and has held leadership roles including President of the ASCE Engineering Mechanics Institute.

Research topics

• Computer Science
• Applied mathematics
• Mathematics
• Mathematical analysis
• Statistics
• Physics
• Mathematical optimization
• Engineering
• Acoustics
• Pure mathematics

Selected publications

• Stochastic Analysis of Fractional Structural Systems Subjected to Fractional Ground Motions

  Journal of Engineering Mechanics · 2026-05-20

  articleSenior author

  In this paper, the nonstationary stochastic response of fractional structural systems subjected to fractional excitations is examined. Fractional operators provide an effective mathematical construct to model energy dissipation and stiffness–damping coupling mechanisms that cannot be modeled by integer operators. In particular, the memory property of fractional operators makes them suitable for treating the non-Markovian features exhibited by systems with path-dependent responses, such as the damping and stiffness mechanisms in structural systems and soils under dynamic loading. In this paper, particular attention is devoted to fractional structural systems excited by a proposed stochastic ground motion model consisting of a nonstationary filtered fractional Kanai–Tajimi process, thus accounting for path-dependent energy dissipation in both the structure and the seismic waves’ propagating medium. The work attempts to elucidate the sensitivity and effects on probabilistic structural response predictions due to non-Markovian features in the excitation when both the system and the excitation are modeled using fractional operators. To analyze the fractional operators describing the structure and soil, the operators are discretized and approximated as the superposition of the solutions of a system of linear first-order ordinary differential equations, which, together with the system dynamics equations, are transformed into an equivalent first-order linear state-space model. The stochastic response evaluation for the system is conducted in closed form by solving the associated Lyapunov covariance equation. The analytical results from stochastic analyses are juxtaposed with pertinent Monte Carlo simulations to demonstrate the accuracy of the proposed method. Validation results using measured data from the 2023 Turkey–Syria earthquake demonstrated that the recorded ground motions exhibit fractional features with an energy rate of decay in the spectral density that is captured more accurately by the proposed fractional model than the traditional integer Kanai–Tajimi model.

  PublisherDOI

• A discretized paths-based sequential integration method involving the self-similarity of the fractional Brownian motion

  Probabilistic Engineering Mechanics · 2025-04-01 · 1 citations

  articleOpen accessSenior author

  The discretized paths-based sequential integration method (SIM) is a quite versatile approach for solving various problems, including barrier problems, first passage problems, reflecting barrier problems and so on. This method builds upon the Chapman–Kolmogorov equation and is not applicable to non-Markovian problems, as in the case of fractional Brownian motion (FBM). In this paper, it is shown that the loss of the Markovian property can be overcome by utilizing the self-similarity of the FBM. In order to apply the discretized paths-based SIM, we have to solve a specific stochastic boundary value problem, also called stochastic “bridge” problem, which involves selecting only the trajectories of the FBM that ends at an assigned value, say x ̄ at t k , at the beginning of the time interval t k − t k + 1 . It is shown that, due to self-similarity, the stochastic “bridge” problem may be solved only once, regardless of the value x ̄ at t k . It is also shown that the trajectories of the stochastic ”bridge” problem exhibit self-similarity, which circumvents the loss of Markovian property in FBM, thus allowing the discretized paths-based SIM to be employed without invoking the classical Chapman–Kolmogorov equation. Further, an application involving the classical first passage problem is presented.

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• Efficient stochastic response analysis of high-dimensional nonlinear systems subject to multiplicative noise via the DR-PDEE

  Journal of Computational Physics · 2025-03-17 · 11 citations

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• Phase-Shifting Filtering Method for Simulating Three-Dimensional Directional Ocean Waves

  Journal of Engineering Mechanics · 2025-10-07

  article

  Ocean wave action is a key environmental load on marine structures, and its numerical simulation is a critical issue in the field of ocean engineering. In stochastic dynamic response analysis and time-variant reliability analysis, say, by the dimension-reduced probability density evolution equation (DR-PDEE), accurate representation of wave excitation through filtering methods is essential. To advance the probability density level analysis in ocean engineering, it is necessary to develop filtering methods for wave fields that align with fundamental physical principles. In this paper, a phase-shifting method for calculating the phase difference between wave elevations at different points on the sea surface based on the Fourier transform and its inverse is first introduced. The method enables the generation of wave elevations in long-crested waves from a single-point signal. To simulate short-crested wave fields, the wave direction is discretized into multiple intervals, and a filtering simulation method based on the linear superposition principle along with the Mitsuyasu-type directional spreading function is proposed using a designed digital filter system. The validity of the proposed method is verified by illustrating three numerical examples: the long-crested wave case, the short-crested wave case, and the case of wave force calculation on two columns in a wave field. The necessity of adopting wave fields for calculating wave loads on large offshore structures is demonstrated. The proposed method can be applied in the dynamic response analysis of various ocean engineering structures.

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• Stochastic response spectrum determination of nonlinear systems endowed with fractional derivative elements

  Nonlinear Dynamics · 2025-03-10 · 4 citations

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• A phase-control-based method for the simulation of homogeneous random fields of fluctuating wind speed

  Structural Safety · 2025-03-20 · 2 citations

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• Non-stationary response determination of linear systems/structures with fractional derivative elements

  Reliability Engineering & System Safety · 2025-04-06 · 13 citations

  articleSenior authorCorresponding
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• Response statistics of nonlinear systems with fractional derivative elements subject to nonstationary excitations

  Nonlinear Dynamics · 2025-08-23 · 1 citations

  articleSenior authorCorresponding
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• Linear Systems Under Gaussian White Noise Excitation: Exact Closed-Form Solutions

  2024-01-01

  book-chapterSenior author
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• Nonlinear Systems with Singular Diffusion Matrices: A Broad Perspective Including Hysteresis Modeling

  2024-01-01

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Recent grants

• Wavelets Based Response of Structural / Mechanical Systems to Evolutionary Earthquake & Wind

  NSF · $242k · 2003–2008

• Versatile Modeling of Smart Materials Performance in Infrastructure Applications via Distributed Hysterons

  NSF · $283k · 2008–2012

Frequent coauthors

• Ioannis A. Kougioumtzoglou

  Columbia University

  43 shared

• Roger Ghanem

  25 shared

• Giovanni Malara

  25 shared

• Michael Beer

  22 shared

• Agathoklis Giaralis

  Khalifa University of Science and Technology

  19 shared

• B. A. Zeldin

  Vignet (United States)

  18 shared

• Marc P. Mignolet

  Arizona State University

  17 shared

• Y.Z. Pappas

  16 shared

Awards & honors

• NSF Presidential Young Investigator Award
• Richards Investigator Award from NSF
• American Society of Mechanical Engineers (ASME) Pi Tau Sigma…
• American Society of Mechanical Engineers (ASME) Larson Medal
• American Society of Mechanical Engineers (ASME) Richards Med…