Nicos Makris | Southern Methodist University (original) (raw)
Papers by Nicos Makris
Géotechnique, 1993
Analytical solutions are developed for harmonic wave propagation in an axially or laterally oscil... more Analytical solutions are developed for harmonic wave propagation in an axially or laterally oscillating pile embedded in homogeneous soil and excited at the top. Pile-soil interaction is realistically represented through a dynamic Winkler model, the springs and dashpots of which are given values based on results of finite element analyses with the soil treated as a linear hysteretic continuum. Closed form expressions are derived for the phase velocities of the generated waves; these are compared with characteristic phase velocities in rods and beams subjected to compression-extension (axial) and flexural (lateral) vibrations. The role of radiation and material damping is elucidated; it is shown that the presence of such damping radically changes the nature of wave propagation, especially in lateral oscillations where an upward propagating (reflected) wave is generated even in a semi-infinite head-loaded pile. Solutions are then developed for the phase differences between pile displa...
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AIP Conference Proceedings, 2008
ABSTRACT
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The Earthquake Engineering Online Archive - (Nisee e-library). Engineering seismology. Inzhenerna... more The Earthquake Engineering Online Archive - (Nisee e-library). Engineering seismology. Inzhenernaya seismologiya. Medvedev, SV. Jerusalem, Israel Program for Scientific Translations; [available from US Dept. of Commerce ...
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This paper derives the causal time-response functions of three-parameter mechanical networks that... more This paper derives the causal time-response functions of three-parameter mechanical networks that have been reported in the literature and involve the inerter-a two-node element in which the force-output is proportional to the relative acceleration of its end-nodes. This two-terminal device is the mechanical analogue of the capacitor in a force-current/velocity-voltage analogy. The paper shows that all frequency-response functions that exhibit singularities along the real frequency axis need to be enhanced with the addition of a Dirac delta function or with its derivative depending on the strength of the singularity. In this way the real and imaginary parts of the enhanced frequency response functions are Hilbert pairs; therefore, yielding a causal time-response function in the time domain. The integral representation of the output signals offers an attractive computational alternative given that the constitutive equations of the three-parameter networks examined herein involve the ...
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Motivated from studies on anomalous diffusion, we show that the memory function M(t) of complex m... more Motivated from studies on anomalous diffusion, we show that the memory function M(t) of complex materials, that their creep compliance follows a power law, J(t)∼ t^q with q∈R^+, is the fractional derivative of the Dirac delta function, d^qδ(t-0)/dt^q with q∈R^+. This leads to the finding that the inverse Laplace transform of s^q for any q∈R^+ is the fractional derivative of the Dirac delta function, d^qδ(t-0)/dt^q. This result, in association with the convolution theorem, makes possible the calculation of the inverse Laplace transform of s^q/s^α∓λ where α<q∈R^+ which is the fractional derivative of order q of the Rabotnov function ε_α-1(±λ, t)=t^α-1E_α, α(±λ t^α). The fractional derivative of order q∈R^+ of the Rabotnov function, ε_α-1(±λ, t) produces singularities which are extracted with a finite number of fractional derivatives of the Dirac delta function depending on the strength of q in association with the recurrence formula of the two-parameter Mittag-Leffler function.
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Motivated from the classical expressions of the mean squared displacement and the velocity autoco... more Motivated from the classical expressions of the mean squared displacement and the velocity autocorrelation function of Brownian particles suspended either in a Newtonian viscous fluid or trapped in a harmonic potential, we show that for all time-scales the mean squared displacement of Brownian microspheres with mass m and radius R suspended in any linear, isotropic viscoelastic material is identical to the creep compliance of a linear mechanical network that is a parallel connection of the linear viscoelastic material with an inerter with distributed inertance, m_R=m/6π R. The synthesis of this mechanical network leads to the statement of a viscous-viscoelastic correspondence principle for Brownian motion which simplifies appreciably the calculations of the mean squared displacement and the velocity autocorrelation function of Brownian particles suspended in viscoelastic materials where inertia effects are non-negligible at longer time-scales. The viscous-viscoelastic correspondence...
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This paper revisits the physical meaning of linear, time-domain constitutive models with complex ... more This paper revisits the physical meaning of linear, time-domain constitutive models with complex parameters that have been presented in the literature and concludes that such models are not physically realizable. While complex-parameter phenomenological models (including those with complex-order time derivatives) may be efficient in capturing in the frequency domain the frequency-dependent behavior of viscoelastic materials over a finite frequency band, they do not possess physically acceptable time-response functions. The paper first reviews the intimate relation between the causality of a physically realizable constitutive model and the analyticity of its frequency-response function and explains that in theory it is sufficient to conduct a nonlinear regression analysis for estimating the model parameters either on only the real part or on only the imaginary part of its frequency-response function, given that they are related with the Hilbert transform. Consequently, the resulting ...
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Roc Rocking Roc king Response Response and and Ov Over Ov er ertur er tur turning
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Geotechnical Engineering for the Preservation of Monuments and Historic Sites
In the archaeological site of Ancient Nemea, Greece, southeast of the Temple of Zeus, there is an... more In the archaeological site of Ancient Nemea, Greece, southeast of the Temple of Zeus, there is an ancient tunnel that was buried with earth until it was discovered in 1978. At present, some limestone blocks of the tunnel show appreciable damage mainly due to the humidity fluctuation within the tunnel. In this paper we present a comprehensive structural analysis of the underground tunnel based on the thrust line limit-analysis of the masonry arch and its surrounding soil. The study concludes that the tunnel with its over-burden-surrounding soil is structurally stable and has ample bearing capacity. At the same time the study shows that the stones which suffer the most noticeable exfoliation due to the humidity fluctuation are those that their visible surface from the inside of the tunnel is in compression. In conclusion, selective stones of the structure need to be retrofitted in order to avoid further local failures, while the humidity fluctuation inside the tunnel needs to be minimized
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Journal of Engineering Mechanics-asce, 2021
AbstractThis paper presents the development, testing, and characterization of an innovative low-c... more AbstractThis paper presents the development, testing, and characterization of an innovative low-cost fail-safe sustainable energy-dissipation device in which the material surrounding the moving pis...
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In this paper, the problem of computing nonlinear dynamic response of a structure resting on pile... more In this paper, the problem of computing nonlinear dynamic response of a structure resting on piles is investigated. The superstructure is modeled by a simple two degree-of-freedom system. The Bouc-Wen model is used to model nonlinear behavior of the superstructure. A time-domain formulation is presented in which the restoring force from the foundation is given by means of a convolution integral that uses the velocity history of the foundation relative motion and the dynamic relaxation stiffness of the foundation. This relaxation stiffness is calculated by numerically transforming available dynamic impedances into the time domain. The method is first validated at the linear limit by comparing time with frequency domain analyses. Subsequently, it is used to compute the nonlinear behavior of a superstructure resting on pile groups that behave elastically. The applicability and advantages of using the proposed technique are summarized.
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This paper examines and compares the minimum horizontal acceleration that is needed to initiate u... more This paper examines and compares the minimum horizontal acceleration that is needed to initiate uplift of the single-nave barrel vault and of the rocking frame which are the two most common masonry structural systems used to bridge a span. The paper concludes that regardless of the direction of the rupture of the buttresses, the single-nave barrel vault uplifts with a seismic coefficient, e, that is always smaller than the slenderness of the buttresses, s=b/h. In contrast, the rocking frame always uplifts with a seismic coefficient, e=b/h, regardless of the mass of its prismatic epistyle; therefore, the rocking frame has a superior seismic performance than the single-nave barrel vault.
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Soil Dynamics and Earthquake Engineering
Abstract This paper investigates the seismic response of one- and two-degree-of-freedom yielding ... more Abstract This paper investigates the seismic response of one- and two-degree-of-freedom yielding structures equipped with inerters at the first story. Inerters are mechanical devices that their resisting force is proportional to the relative acceleration at their end-nodes. This class of response modification devices complements the traditional supplemental damping devices that their resisting force is proportional to the relative velocity at their end-nodes, also examined in this study for comparison. The paper develops a stable nonlinear response analysis methodology that implements a state-space formulation. Given that the engagement with an inerter lengthens the apparent preyielding period of the inelastic structure, the paper shows that when a yielding structure is equipped with supplemental rotational inertia, the equal-displacement rule is valid starting from lower values of the preyielding period. The effectiveness of a single inerter versus the use of a pair of clutching inerters that can only resist the motion of the yielding structure is examined, and the paper concludes that a single inerter suppresses effectively the displacement response of inelastic structures by outperforming the response modification with supplemental damping in particular when the supporting frame of the response modification devices is compliant.
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Rheologica Acta
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Earthquake Engineering & Structural Dynamics
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Physical Review E
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Meccanica
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Journal of Structural Engineering
AbstractThis study investigates the seismic response of a two-degrees-of-freedom structure with s... more AbstractThis study investigates the seismic response of a two-degrees-of-freedom structure with supplemental rotational inertia at its first story. The proposed response-modification strategy uses ...
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Journal of Structural Engineering
AbstractThis paper investigates the inelastic response of a yielding single-degree-of-freedom osc... more AbstractThis paper investigates the inelastic response of a yielding single-degree-of-freedom oscillator coupled with a rocking wall. Configurations of both a stepping rocking wall and a pinned roc...
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Géotechnique, 1993
Analytical solutions are developed for harmonic wave propagation in an axially or laterally oscil... more Analytical solutions are developed for harmonic wave propagation in an axially or laterally oscillating pile embedded in homogeneous soil and excited at the top. Pile-soil interaction is realistically represented through a dynamic Winkler model, the springs and dashpots of which are given values based on results of finite element analyses with the soil treated as a linear hysteretic continuum. Closed form expressions are derived for the phase velocities of the generated waves; these are compared with characteristic phase velocities in rods and beams subjected to compression-extension (axial) and flexural (lateral) vibrations. The role of radiation and material damping is elucidated; it is shown that the presence of such damping radically changes the nature of wave propagation, especially in lateral oscillations where an upward propagating (reflected) wave is generated even in a semi-infinite head-loaded pile. Solutions are then developed for the phase differences between pile displa...
Bookmarks Related papers MentionsView impact
AIP Conference Proceedings, 2008
ABSTRACT
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The Earthquake Engineering Online Archive - (Nisee e-library). Engineering seismology. Inzhenerna... more The Earthquake Engineering Online Archive - (Nisee e-library). Engineering seismology. Inzhenernaya seismologiya. Medvedev, SV. Jerusalem, Israel Program for Scientific Translations; [available from US Dept. of Commerce ...
Bookmarks Related papers MentionsView impact
Bookmarks Related papers MentionsView impact
This paper derives the causal time-response functions of three-parameter mechanical networks that... more This paper derives the causal time-response functions of three-parameter mechanical networks that have been reported in the literature and involve the inerter-a two-node element in which the force-output is proportional to the relative acceleration of its end-nodes. This two-terminal device is the mechanical analogue of the capacitor in a force-current/velocity-voltage analogy. The paper shows that all frequency-response functions that exhibit singularities along the real frequency axis need to be enhanced with the addition of a Dirac delta function or with its derivative depending on the strength of the singularity. In this way the real and imaginary parts of the enhanced frequency response functions are Hilbert pairs; therefore, yielding a causal time-response function in the time domain. The integral representation of the output signals offers an attractive computational alternative given that the constitutive equations of the three-parameter networks examined herein involve the ...
Bookmarks Related papers MentionsView impact
Motivated from studies on anomalous diffusion, we show that the memory function M(t) of complex m... more Motivated from studies on anomalous diffusion, we show that the memory function M(t) of complex materials, that their creep compliance follows a power law, J(t)∼ t^q with q∈R^+, is the fractional derivative of the Dirac delta function, d^qδ(t-0)/dt^q with q∈R^+. This leads to the finding that the inverse Laplace transform of s^q for any q∈R^+ is the fractional derivative of the Dirac delta function, d^qδ(t-0)/dt^q. This result, in association with the convolution theorem, makes possible the calculation of the inverse Laplace transform of s^q/s^α∓λ where α<q∈R^+ which is the fractional derivative of order q of the Rabotnov function ε_α-1(±λ, t)=t^α-1E_α, α(±λ t^α). The fractional derivative of order q∈R^+ of the Rabotnov function, ε_α-1(±λ, t) produces singularities which are extracted with a finite number of fractional derivatives of the Dirac delta function depending on the strength of q in association with the recurrence formula of the two-parameter Mittag-Leffler function.
Bookmarks Related papers MentionsView impact
Motivated from the classical expressions of the mean squared displacement and the velocity autoco... more Motivated from the classical expressions of the mean squared displacement and the velocity autocorrelation function of Brownian particles suspended either in a Newtonian viscous fluid or trapped in a harmonic potential, we show that for all time-scales the mean squared displacement of Brownian microspheres with mass m and radius R suspended in any linear, isotropic viscoelastic material is identical to the creep compliance of a linear mechanical network that is a parallel connection of the linear viscoelastic material with an inerter with distributed inertance, m_R=m/6π R. The synthesis of this mechanical network leads to the statement of a viscous-viscoelastic correspondence principle for Brownian motion which simplifies appreciably the calculations of the mean squared displacement and the velocity autocorrelation function of Brownian particles suspended in viscoelastic materials where inertia effects are non-negligible at longer time-scales. The viscous-viscoelastic correspondence...
Bookmarks Related papers MentionsView impact
This paper revisits the physical meaning of linear, time-domain constitutive models with complex ... more This paper revisits the physical meaning of linear, time-domain constitutive models with complex parameters that have been presented in the literature and concludes that such models are not physically realizable. While complex-parameter phenomenological models (including those with complex-order time derivatives) may be efficient in capturing in the frequency domain the frequency-dependent behavior of viscoelastic materials over a finite frequency band, they do not possess physically acceptable time-response functions. The paper first reviews the intimate relation between the causality of a physically realizable constitutive model and the analyticity of its frequency-response function and explains that in theory it is sufficient to conduct a nonlinear regression analysis for estimating the model parameters either on only the real part or on only the imaginary part of its frequency-response function, given that they are related with the Hilbert transform. Consequently, the resulting ...
Bookmarks Related papers MentionsView impact
Roc Rocking Roc king Response Response and and Ov Over Ov er ertur er tur turning
Bookmarks Related papers MentionsView impact
Geotechnical Engineering for the Preservation of Monuments and Historic Sites
In the archaeological site of Ancient Nemea, Greece, southeast of the Temple of Zeus, there is an... more In the archaeological site of Ancient Nemea, Greece, southeast of the Temple of Zeus, there is an ancient tunnel that was buried with earth until it was discovered in 1978. At present, some limestone blocks of the tunnel show appreciable damage mainly due to the humidity fluctuation within the tunnel. In this paper we present a comprehensive structural analysis of the underground tunnel based on the thrust line limit-analysis of the masonry arch and its surrounding soil. The study concludes that the tunnel with its over-burden-surrounding soil is structurally stable and has ample bearing capacity. At the same time the study shows that the stones which suffer the most noticeable exfoliation due to the humidity fluctuation are those that their visible surface from the inside of the tunnel is in compression. In conclusion, selective stones of the structure need to be retrofitted in order to avoid further local failures, while the humidity fluctuation inside the tunnel needs to be minimized
Bookmarks Related papers MentionsView impact
Journal of Engineering Mechanics-asce, 2021
AbstractThis paper presents the development, testing, and characterization of an innovative low-c... more AbstractThis paper presents the development, testing, and characterization of an innovative low-cost fail-safe sustainable energy-dissipation device in which the material surrounding the moving pis...
Bookmarks Related papers MentionsView impact
In this paper, the problem of computing nonlinear dynamic response of a structure resting on pile... more In this paper, the problem of computing nonlinear dynamic response of a structure resting on piles is investigated. The superstructure is modeled by a simple two degree-of-freedom system. The Bouc-Wen model is used to model nonlinear behavior of the superstructure. A time-domain formulation is presented in which the restoring force from the foundation is given by means of a convolution integral that uses the velocity history of the foundation relative motion and the dynamic relaxation stiffness of the foundation. This relaxation stiffness is calculated by numerically transforming available dynamic impedances into the time domain. The method is first validated at the linear limit by comparing time with frequency domain analyses. Subsequently, it is used to compute the nonlinear behavior of a superstructure resting on pile groups that behave elastically. The applicability and advantages of using the proposed technique are summarized.
Bookmarks Related papers MentionsView impact
This paper examines and compares the minimum horizontal acceleration that is needed to initiate u... more This paper examines and compares the minimum horizontal acceleration that is needed to initiate uplift of the single-nave barrel vault and of the rocking frame which are the two most common masonry structural systems used to bridge a span. The paper concludes that regardless of the direction of the rupture of the buttresses, the single-nave barrel vault uplifts with a seismic coefficient, e, that is always smaller than the slenderness of the buttresses, s=b/h. In contrast, the rocking frame always uplifts with a seismic coefficient, e=b/h, regardless of the mass of its prismatic epistyle; therefore, the rocking frame has a superior seismic performance than the single-nave barrel vault.
Bookmarks Related papers MentionsView impact
Soil Dynamics and Earthquake Engineering
Abstract This paper investigates the seismic response of one- and two-degree-of-freedom yielding ... more Abstract This paper investigates the seismic response of one- and two-degree-of-freedom yielding structures equipped with inerters at the first story. Inerters are mechanical devices that their resisting force is proportional to the relative acceleration at their end-nodes. This class of response modification devices complements the traditional supplemental damping devices that their resisting force is proportional to the relative velocity at their end-nodes, also examined in this study for comparison. The paper develops a stable nonlinear response analysis methodology that implements a state-space formulation. Given that the engagement with an inerter lengthens the apparent preyielding period of the inelastic structure, the paper shows that when a yielding structure is equipped with supplemental rotational inertia, the equal-displacement rule is valid starting from lower values of the preyielding period. The effectiveness of a single inerter versus the use of a pair of clutching inerters that can only resist the motion of the yielding structure is examined, and the paper concludes that a single inerter suppresses effectively the displacement response of inelastic structures by outperforming the response modification with supplemental damping in particular when the supporting frame of the response modification devices is compliant.
Bookmarks Related papers MentionsView impact
Rheologica Acta
Bookmarks Related papers MentionsView impact
Earthquake Engineering & Structural Dynamics
Bookmarks Related papers MentionsView impact
Physical Review E
Bookmarks Related papers MentionsView impact
Meccanica
Bookmarks Related papers MentionsView impact
Journal of Structural Engineering
AbstractThis study investigates the seismic response of a two-degrees-of-freedom structure with s... more AbstractThis study investigates the seismic response of a two-degrees-of-freedom structure with supplemental rotational inertia at its first story. The proposed response-modification strategy uses ...
Bookmarks Related papers MentionsView impact
Journal of Structural Engineering
AbstractThis paper investigates the inelastic response of a yielding single-degree-of-freedom osc... more AbstractThis paper investigates the inelastic response of a yielding single-degree-of-freedom oscillator coupled with a rocking wall. Configurations of both a stepping rocking wall and a pinned roc...
Bookmarks Related papers MentionsView impact