0000000000359057
AUTHOR
Athanasios A. Pantelous
showing 9 related works from this author
Higher order matrix differential equations with singular coefficient matrices
2015
In this article, the class of higher order linear matrix differential equations with constant coefficient matrices and stochastic process terms is studied. The coefficient of the highest order is considered to be singular; thus, rendering the response determination of such systems in a straightforward manner a difficult task. In this regard, the notion of the generalized inverse of a singular matrix is used for determining response statistics. Further, an application relevant to engineering dynamics problems is included.
Implicit analytic solutions for a nonlinear fractional partial differential beam equation
2020
Abstract Analytic solutions in implicit form are derived for a nonlinear partial differential equation (PDE) with fractional derivative elements, which can model the dynamics of a deterministically excited Euler-Bernoulli beam resting on a viscoelastic foundation. Specifically, the initial-boundary value problem for the corresponding PDE is reduced to an initial value problem for a nonlinear ordinary differential equation in a Hilbert space. Next, by employing the cosine and sine families of operators, a variation of parameters representation of the solution map is introduced. Due to the presence of a nonlinear term, a local fixed point theorem is employed to prove the local existence and u…
A dynamic analysis of SP 500, FTSE 100 and EURO STOXX 50 indices under different exchange rates.
2018
In this study, we assess the dynamic evolution of short-term correlation, long-term cointe-gration and Error Correction Model (hereafter referred to as ECM)-based long-term Granger causality between each pair of US, UK, and Eurozone stock markets from 1980 to 2015 using the rolling-window technique. A comparative analysis of pairwise dynamic integration and causality of stock markets, measured in common and domestic currency terms, is conducted to evaluate comprehensively how exchange rate fluctuations affect the time-varying integration among the S&P 500, FTSE 100 and EURO STOXX 50 indices. The results obtained show that the dynamic correlation, cointegration and ECM-based long-run Gra…
Response determination of linear dynamical systems with singular matrices: A polynomial matrix theory approach
2017
Abstract An approach is developed based on polynomial matrix theory for formulating the equations of motion and for determining the response of multi-degree-of-freedom (MDOF) linear dynamical systems with singular matrices and subject to linear constraints. This system modeling may appear for reasons such as utilizing redundant DOFs, and can be advantageous from a computational cost perspective, especially for complex (multi-body) systems. The herein developed approach can be construed as an alternative to the recently proposed methodology by Udwadia and coworkers, and has the significant advantage that it circumvents the use of pseudoinverses in determining the system response. In fact, ba…
A Dynamic Analysis of S&P 500, FTSE 100 and EURO STOXX 50 Indices Under Different Exchange Rates
2017
The persistence analysis of short- and long-term interaction and causality in the international financial markets is a key issue for policy makers and portfolio investors. This paper assesses the dynamic evolution of short-term correlation, long-term cointegration and Error Correction Model (hereafter referred to as ECM)-based long-term Granger causality between each pair of US, UK, and Eurozone stock markets over the period of 1980--2015 using the rolling-window technique. A comparative analysis of pairwise dynamic integration and causality of stock markets, measured in common and domestic currency terms, is conducted to evaluate comprehensively how exchange rate fluctuations affect the ti…
Stochastic response determination of structural systems modeled via dependent coordinates: a frequency domain treatment based on generalized modal an…
2019
Generalized independent coordinates are typically utilized within an analytical dynamics framework to model the motion of structural and mechanical engineering systems. Nevertheless, for complex systems, such as multi-body structures, an explicit formulation of the equations of motion by utilizing generalized, independent, coordinates can be a daunting task. In this regard, employing a set of redundant coordinates can facilitate the formulation of the governing dynamics equations. In this setting, however, standard response analysis techniques cannot be applied in a straightforward manner. For instance, defining and determining a transfer function within a frequency domain response analysis…
Modal Analysis of Multi-Degrees-of-Freedom Systems with Singular Matrices: Analytical Dynamics Approach
2017
Complex mechanical (e.g., multibody) systems with different types of constraints are generally performed through analytical dynamics methods. In some cases, however, it is possible that the (augmented) mass and/or stiffness matrices may derive to be singular; consequently, modal analysis, which is used extensively in the classical dynamics literature, fails. In this paper, if the uniqueness condition is satisfied by the constraints, a properly modified modal analysis is elucidated into analytical dynamics leading to the evaluation of the natural frequencies in a simple and straightforward way. Under that framework, advances of both classical and analytical dynamics are taken into considerat…
Random vibration of linear and nonlinear structural systems with singular matrices: A frequency domain approach
2017
Abstract A frequency domain methodology is developed for stochastic response determination of multi-degree-of-freedom (MDOF) linear and nonlinear structural systems with singular matrices. This system modeling can arise when a greater than the minimum number of coordinates/DOFs is utilized, and can be advantageous, for instance, in cases of complex multibody systems where the explicit formulation of the equations of motion can be a nontrivial task. In such cases, the introduction of additional/redundant DOFs can facilitate the formulation of the equations of motion in a less labor intensive manner. Specifically, relying on the generalized matrix inverse theory, a Moore-Penrose (M-P) based f…
Deterministic and Random Vibration of Linear Systems with Singular Parameter Matrices and Fractional Derivative Terms
2021
Both time- and frequency-domain solution techniques are developed for determining the response of linear multi-degree-of-freedom systems exhibiting singular parameter matrices and endowed with derivative terms of noninteger orders modeled as rational numbers. This is done based on the Moore-Penrose matrix inverse theory, in conjunction with a state variable formulation and with a complex modal analysis treatment. It is worth noting that, for the class of systems considered herein, this treatment also yields decoupled governing equations, thus facilitating further their numerical solution. Next, a generalization of the standard frequency-domain input-output (excitation-response) relationship…