miodrag zigic - Academia.edu (original) (raw)

Papers by miodrag zigic

Research paper thumbnail of Viscoelastic body colliding against a rigid wall with and without dry friction effects

Applied Mathematical Modelling, 2017

The impact of a body against a rigid wall is studied. The body consists of a rigid block and a vi... more The impact of a body against a rigid wall is studied. The body consists of a rigid block and a viscoelastic rod described by the distributed-order fractional model and in particular its solid-like and fluid-like special cases. Translatory motion of a body is studied in two cases: without and with the influence of dry friction. When present, dry friction is modeled by the Coulomb friction law. The problem is treated analytically by the use of the Laplace transform method and solutions are obtained in a convolution form.

Research paper thumbnail of Viscoelastic body colliding against a rigid wall with and without dry friction effects

Applied Mathematical Modelling, May 1, 2017

The impact of a body against a rigid wall is studied. The body consists of a rigid block and a vi... more The impact of a body against a rigid wall is studied. The body consists of a rigid block and a viscoelastic rod described by the distributed-order fractional model and in particular its solid-like and fluid-like special cases. Translatory motion of a body is studied in two cases: without and with the influence of dry friction. When present, dry friction is modeled by the Coulomb friction law. The problem is treated analytically by the use of the Laplace transform method and solutions are obtained in a convolution form.

Research paper thumbnail of Dinamika Konstrukcije Sa Pasivnim Prigušivačima

Zbornik radova Građevinskog fakulteta, 2016

Dynamics of a structure consisting of two rigid blocks positioned one on another with a viscoelas... more Dynamics of a structure consisting of two rigid blocks positioned one on another with a viscoelastic and a friction damper is analyzed. Due to a horizontal ground excitation the viscoelastic plate is exposed to a shear loading. The fractional Zener model is used to describe properties of the viscoelastic body while the friction damper is modelled by the Coulomb friction law in a set-valued form. The horizontal ground motion is described by a simplified earthquake model by means of Ricker's waves.

Research paper thumbnail of O Viskoelastičnim Svojstvima Asfaltnih Mešavina

Zbornik radova Građevinskog fakulteta, 2017

This paper comprises the fractional Kelvin-Zener model of viscoelastic body, the Laplace transfor... more This paper comprises the fractional Kelvin-Zener model of viscoelastic body, the Laplace transform and a least squares method, all applied in creep/recovery testing of asphalt mixtures for the purpose of parameter identification. The parameters describing viscoelastic properties of these mixtures are: the order of the fractional derivative, modulus of elasticity, as well as two relaxation constants that obey restrictions that follow from the second law of thermodynamics. Knowing these four parameters one may predict the behavior of an asphalt mixture for different loads. Besides, the pattern of change of these parameters may be related to alterations of the viscoelastic properties of an asphalt mixture due to either aging or different environmental conditions.

Research paper thumbnail of Dinamika Susednih Konstrukcija Tokom Horizontalnog Kretanja Tla

Zbornik radova Građevinskog fakulteta, 2018

We analyzed two adjacent structures connected by a friction element to each other. Both structure... more We analyzed two adjacent structures connected by a friction element to each other. Both structures consist of two blocks and a viscoelastic damper, which is modeled by the fractional Zener model. The friction force within the friction element is described by the Coulomb friction law in a set-valued form. Horizontal ground motion induces movement of both structures which can cause a destroying pounding effect. Energy brought to the system consisting of two structures connected by a friction damper dissipates by work done by viscoelastic and friction forces. Ground excitation is modeled by a simplified earthquake model by means of Ricker's waves.

Research paper thumbnail of Impact of a body against a rigid wall. Problem involving non-smooth and history dependent energy dissipation mechanism

arXiv: Classical Physics, 2013

We study the impact of a body against a rigid wall. The body consists of a rigid block and a visc... more We study the impact of a body against a rigid wall. The body consists of a rigid block and a viscoelastic rod described by the fractional Zener model. Translatory motion of a body is influenced by the dry friction, described by the set-valued Coulomb friction law. The problem is treated analytically by the use of the Laplace transform method and solutions are obtained in a convolution form. These solutions are compared with the ones obtained by using the numerical method.

Research paper thumbnail of Dynamics of Adjacent Structures During Horizontal Ground Motion

Miodrag Žigić 1 Nenad Grahovac 2 Boris Brkić3 UDK: 624.042.7 DOI: 10.14415/konferencijaGFS2018.01... more Miodrag Žigić 1 Nenad Grahovac 2 Boris Brkić3 UDK: 624.042.7 DOI: 10.14415/konferencijaGFS2018.014 Summary: We analyzed two adjacent structures connected by a friction element to each other. Both structures consist of two blocks and a viscoelastic damper, which is modeled by the fractional Zener model. The friction force within the friction element is described by the Coulomb friction law in a set-valued form. Horizontal ground motion induces movement of both structures which can cause a destroying pounding effect. Energy brought to the system consisting of two structures connected by a friction damper dissipates by work done by viscoelastic and friction forces. Ground excitation is modeled by a simplified earthquake model by means of Ricker's waves.

Research paper thumbnail of The influence of foundation nonlinearity on the post-buckling behavior of a shearable rod near double eigenvalues

International Journal of Solids and Structures, 2020

The post-buckling behavior of a compressed, simply supported, shearable elastic rod on a nonlinea... more The post-buckling behavior of a compressed, simply supported, shearable elastic rod on a nonlinear elastic foundation is studied. For the critical values of auxiliary parameter the eigenvalues are double so that the Liapunov-Schmidt method leads to two bifurcation equations. These equations describe the postbuckling behavior for the values of auxiliary parameter near the critical ones. The occurrence of secondary bifurcations, depending on the nonlinearity of foundation and shear rigidity, is investigated. It is shown that these effects have a significant influence on the post-buckling behavior of the rod. The type of bifurcations, stability, mode interactions and asymptotic expansions of primary and secondary branches are determined. It is shown that the secondary branches can be stable for the nonlinear hardening elastic foundation. The complex bifurcation analysis reveals that for every critical value of the auxiliary parameter, there are eleven different post-buckling behaviors, depending on the nonlinearity of foundation and shear rigidity.

Research paper thumbnail of The increasing doses of methotrexate pharmacokinetics after intravenous administration in rats - model selection

Vojnosanitetski pregled, 2019

Background/Aim. Methotrexate (MTX) plays a significant role in the treatment of various diseases,... more Background/Aim. Methotrexate (MTX) plays a significant role in the treatment of various diseases, but the toxicity remains the main issue of its use, especially when administered in high doses. Considering altered pharmacokinetics of MTX as a factor strongly implicated in the large interpatient variability and unexpected toxicity in certain patients, the accurate description of MTX pharmacokinetic behaviour of both low and high doses is of the utmost importance. Therefore, the objective of this study was to determine the pharmacokinetics of MTX after intravenous (iv) administration in ascending doses of 5, 40, 80 and 160 mg/kg in rats and to select the appropriate mathematical model describing MTX pharmacokinetics. Methods. Plasma concentrations of MTX were measured using the liquid chromatography - mass spectrometry (LC/MS) method. Pharmacokinetic parameters were calculated by non-compartmental and two-compartmental integer-order analyses. Results. MTX showed linear pharmacokinetic...

Research paper thumbnail of Dinamički Odziv Konstrukcije Na Zemljotresnu Pobudu

Zbornik radova Građevinskog fakulteta, 2017

Behavior of a column like structure during earthquake excitation is studied. The structure consis... more Behavior of a column like structure during earthquake excitation is studied. The structure consists of rigid blocks which move translatory during a horizontal ground motion. Fractional derivatives are used within a constitutive model of а viscoelastic damper. Dry friction damping during relative motion of the blocks is also considered. Governing equations of motion of the structure subjected to a single component horizontal ground acceleration are derived. The posed problem is solved by use of mathematical tools for dealing with non-smooth mechanical systems containing fractional derivatives.

Research paper thumbnail of Secondary bifurcation of a shearable rod with nonlinear spring supports

European Journal of Mechanics - A/Solids, 2017

The postbuckling behavior of a compressed elastic rod is studied. The rod is supported by two ide... more The postbuckling behavior of a compressed elastic rod is studied. The rod is supported by two identical hardening spring supports at clamped ends. The constitutive equations of the rod take into account the effect of shear. For local bifurcation analysis the Liapunov-Schmidt method is used. It is shown that for the critical value of auxiliary parameter the lowest eigenvalue becomes double. This fact and double Z 2 symmetry lead to the occurrence of secondary bifurcations for the values of auxiliary parameter near the critical one. For primary and secondary branches asymptotic expansions are constructed. Depending on the values of parameters of nonlinear spring supports and shear rigidity five different groups of bifurcation diagrams are found.

Research paper thumbnail of Earthquake response of adjacent structures with viscoelastic and friction dampers

Theoretical and Applied Mechanics, 2015

We study the seismic response of two adjacent structures connected with a dry friction damper. Ea... more We study the seismic response of two adjacent structures connected with a dry friction damper. Each of them consists of a viscoelastic rod and a rigid block, which can slide without friction along the moving base. A simplified earthquake model is used for modeling the horizontal ground motion. Energy dissipation is taken by the presence of the friction damper, which is modeled by the set-valued Coulomb friction law. Deformation of viscoelastic rods during the relative motion of the blocks represents another way of energy dissipation. The constitutive equation of a viscoelastic body is described by the fractional Zener model, which includes fractional derivatives of stress and strain. The problem merges fractional derivatives as non-local operators and theory of set-valued functions as the non-smooth ones. Dynamical behaviour of the problem is governed by a pair of coupled multi-valued differential equations. The posed Cauchy problem is solved by use of the Gr?nwald-Letnikov numerica...

Research paper thumbnail of Seismic response of a column like structure with both fractional and dry friction type of dissipation

Konstrukcija u obliku stuba koja se sastoji od donjeg bloka (osnova) i gornjeg bloka, b) Uvećan d... more Konstrukcija u obliku stuba koja se sastoji od donjeg bloka (osnova) i gornjeg bloka, b) Uvećan detalj B 1 , c) Dekomponovani sistem.. .. .. .. .. . 2.2 Dinamiµ cki modeli neglatkog sistema u zavisnosti od relativne brzine bloka. 2.3 Faze kretanja neglatkog sistema tokom vremena.

Research paper thumbnail of On Impact Scripts with Both Fractional and Dry Friction Type of Dissipation

International Journal of Bifurcation and Chaos, 2012

We study the dynamics of a mass, sliding on a dry surface and impacting against a rigid wall thro... more We study the dynamics of a mass, sliding on a dry surface and impacting against a rigid wall through a viscoelastic body, that we model as a straight rod of negligible mass. The problem comprises a constitutive model of the viscoelastic body with fractional derivatives of stress and strain, restrictions on the coefficients that follow from Clausius–Duhem inequality, and discontinuous inequality constraint conditions imposed by the Coulomb friction model. We show that the dynamics of the problem is governed by a single integro-differential inclusion. By use of the slack variable algorithm the problem was solved numerically. The predictions of the model concerning the duration of the impact, maximal values of the impacting force and deformation, as well as the restitution coefficient are determined for several values of system parameters. Depending on the dry friction coefficient three different impact scripts are identified: rebound after the impact, capture in the approaching phase,...

Research paper thumbnail of Numerical algorithm for rigid body position estimation using the quaternion approach

Acta Mechanica Sinica, 2017

This paper deals with rigid body attitude estimation on the basis of the data obtained from an in... more This paper deals with rigid body attitude estimation on the basis of the data obtained from an inertial measurement unit mounted on the body. The aim of this work is to present the numerical algorithm, which can be easily applied to the wide class of problems concerning rigid body positioning, arising in aerospace and marine engineering, or in increasingly popular robotic systems and unmanned aerial vehicles. Following the considerations of kinematics of rigid bodies, the relations between accelerations of different points of the body are given. A rotation matrix is formed using the quaternion approach to avoid singularities. We present numerical procedures for determination of the absolute accelerations of the center of mass and of an arbitrary point of the body expressed in the inertial reference frame, as well as its attitude. An application of the algorithm to the example of a heavy symmetrical gyroscope is presented, where input data for the numerical procedure are obtained from the solution of differential equations of motion, instead of using sensor measurements.

Research paper thumbnail of Application of Fractional Calculus to Frontal Crash Modeling

Mathematical Problems in Engineering, 2017

Fractional derivative viscoelastic model is used in the analysis of a frontal impact of a vehicle... more Fractional derivative viscoelastic model is used in the analysis of a frontal impact of a vehicle against a rigid obstacle. The frontal part of the vehicle is first modeled as a viscoelastic fractional rod and then it is modeled as two different viscoelastic fractional rods with a different length. In the second model also the friction is taken into account. A motion is analyzed during several phases because of both different lengths of the rods and the presence of a dry friction force in the later model. Governing systems of differential equations together with the corresponding initial conditions are derived. Parameter identification is done on the basis of the existing experimental results using the solution of a posed impact problem. What makes the problem more complex, regarding the second model, is the fact that it belongs to the class of nonsmooth fractional order systems, which require special treatment when dealing with deformation history during different motion phases.

Research paper thumbnail of Viscoelastic body colliding against a rigid wall with and without dry friction effects

Applied Mathematical Modelling, 2017

The impact of a body against a rigid wall is studied. The body consists of a rigid block and a vi... more The impact of a body against a rigid wall is studied. The body consists of a rigid block and a viscoelastic rod described by the distributed-order fractional model and in particular its solid-like and fluid-like special cases. Translatory motion of a body is studied in two cases: without and with the influence of dry friction. When present, dry friction is modeled by the Coulomb friction law. The problem is treated analytically by the use of the Laplace transform method and solutions are obtained in a convolution form.

Research paper thumbnail of Viscoelastic body colliding against a rigid wall with and without dry friction effects

Applied Mathematical Modelling, May 1, 2017

The impact of a body against a rigid wall is studied. The body consists of a rigid block and a vi... more The impact of a body against a rigid wall is studied. The body consists of a rigid block and a viscoelastic rod described by the distributed-order fractional model and in particular its solid-like and fluid-like special cases. Translatory motion of a body is studied in two cases: without and with the influence of dry friction. When present, dry friction is modeled by the Coulomb friction law. The problem is treated analytically by the use of the Laplace transform method and solutions are obtained in a convolution form.

Research paper thumbnail of Dinamika Konstrukcije Sa Pasivnim Prigušivačima

Zbornik radova Građevinskog fakulteta, 2016

Dynamics of a structure consisting of two rigid blocks positioned one on another with a viscoelas... more Dynamics of a structure consisting of two rigid blocks positioned one on another with a viscoelastic and a friction damper is analyzed. Due to a horizontal ground excitation the viscoelastic plate is exposed to a shear loading. The fractional Zener model is used to describe properties of the viscoelastic body while the friction damper is modelled by the Coulomb friction law in a set-valued form. The horizontal ground motion is described by a simplified earthquake model by means of Ricker's waves.

Research paper thumbnail of O Viskoelastičnim Svojstvima Asfaltnih Mešavina

Zbornik radova Građevinskog fakulteta, 2017

This paper comprises the fractional Kelvin-Zener model of viscoelastic body, the Laplace transfor... more This paper comprises the fractional Kelvin-Zener model of viscoelastic body, the Laplace transform and a least squares method, all applied in creep/recovery testing of asphalt mixtures for the purpose of parameter identification. The parameters describing viscoelastic properties of these mixtures are: the order of the fractional derivative, modulus of elasticity, as well as two relaxation constants that obey restrictions that follow from the second law of thermodynamics. Knowing these four parameters one may predict the behavior of an asphalt mixture for different loads. Besides, the pattern of change of these parameters may be related to alterations of the viscoelastic properties of an asphalt mixture due to either aging or different environmental conditions.

Research paper thumbnail of Dinamika Susednih Konstrukcija Tokom Horizontalnog Kretanja Tla

Zbornik radova Građevinskog fakulteta, 2018

We analyzed two adjacent structures connected by a friction element to each other. Both structure... more We analyzed two adjacent structures connected by a friction element to each other. Both structures consist of two blocks and a viscoelastic damper, which is modeled by the fractional Zener model. The friction force within the friction element is described by the Coulomb friction law in a set-valued form. Horizontal ground motion induces movement of both structures which can cause a destroying pounding effect. Energy brought to the system consisting of two structures connected by a friction damper dissipates by work done by viscoelastic and friction forces. Ground excitation is modeled by a simplified earthquake model by means of Ricker's waves.

Research paper thumbnail of Impact of a body against a rigid wall. Problem involving non-smooth and history dependent energy dissipation mechanism

arXiv: Classical Physics, 2013

We study the impact of a body against a rigid wall. The body consists of a rigid block and a visc... more We study the impact of a body against a rigid wall. The body consists of a rigid block and a viscoelastic rod described by the fractional Zener model. Translatory motion of a body is influenced by the dry friction, described by the set-valued Coulomb friction law. The problem is treated analytically by the use of the Laplace transform method and solutions are obtained in a convolution form. These solutions are compared with the ones obtained by using the numerical method.

Research paper thumbnail of Dynamics of Adjacent Structures During Horizontal Ground Motion

Miodrag Žigić 1 Nenad Grahovac 2 Boris Brkić3 UDK: 624.042.7 DOI: 10.14415/konferencijaGFS2018.01... more Miodrag Žigić 1 Nenad Grahovac 2 Boris Brkić3 UDK: 624.042.7 DOI: 10.14415/konferencijaGFS2018.014 Summary: We analyzed two adjacent structures connected by a friction element to each other. Both structures consist of two blocks and a viscoelastic damper, which is modeled by the fractional Zener model. The friction force within the friction element is described by the Coulomb friction law in a set-valued form. Horizontal ground motion induces movement of both structures which can cause a destroying pounding effect. Energy brought to the system consisting of two structures connected by a friction damper dissipates by work done by viscoelastic and friction forces. Ground excitation is modeled by a simplified earthquake model by means of Ricker's waves.

Research paper thumbnail of The influence of foundation nonlinearity on the post-buckling behavior of a shearable rod near double eigenvalues

International Journal of Solids and Structures, 2020

The post-buckling behavior of a compressed, simply supported, shearable elastic rod on a nonlinea... more The post-buckling behavior of a compressed, simply supported, shearable elastic rod on a nonlinear elastic foundation is studied. For the critical values of auxiliary parameter the eigenvalues are double so that the Liapunov-Schmidt method leads to two bifurcation equations. These equations describe the postbuckling behavior for the values of auxiliary parameter near the critical ones. The occurrence of secondary bifurcations, depending on the nonlinearity of foundation and shear rigidity, is investigated. It is shown that these effects have a significant influence on the post-buckling behavior of the rod. The type of bifurcations, stability, mode interactions and asymptotic expansions of primary and secondary branches are determined. It is shown that the secondary branches can be stable for the nonlinear hardening elastic foundation. The complex bifurcation analysis reveals that for every critical value of the auxiliary parameter, there are eleven different post-buckling behaviors, depending on the nonlinearity of foundation and shear rigidity.

Research paper thumbnail of The increasing doses of methotrexate pharmacokinetics after intravenous administration in rats - model selection

Vojnosanitetski pregled, 2019

Background/Aim. Methotrexate (MTX) plays a significant role in the treatment of various diseases,... more Background/Aim. Methotrexate (MTX) plays a significant role in the treatment of various diseases, but the toxicity remains the main issue of its use, especially when administered in high doses. Considering altered pharmacokinetics of MTX as a factor strongly implicated in the large interpatient variability and unexpected toxicity in certain patients, the accurate description of MTX pharmacokinetic behaviour of both low and high doses is of the utmost importance. Therefore, the objective of this study was to determine the pharmacokinetics of MTX after intravenous (iv) administration in ascending doses of 5, 40, 80 and 160 mg/kg in rats and to select the appropriate mathematical model describing MTX pharmacokinetics. Methods. Plasma concentrations of MTX were measured using the liquid chromatography - mass spectrometry (LC/MS) method. Pharmacokinetic parameters were calculated by non-compartmental and two-compartmental integer-order analyses. Results. MTX showed linear pharmacokinetic...

Research paper thumbnail of Dinamički Odziv Konstrukcije Na Zemljotresnu Pobudu

Zbornik radova Građevinskog fakulteta, 2017

Behavior of a column like structure during earthquake excitation is studied. The structure consis... more Behavior of a column like structure during earthquake excitation is studied. The structure consists of rigid blocks which move translatory during a horizontal ground motion. Fractional derivatives are used within a constitutive model of а viscoelastic damper. Dry friction damping during relative motion of the blocks is also considered. Governing equations of motion of the structure subjected to a single component horizontal ground acceleration are derived. The posed problem is solved by use of mathematical tools for dealing with non-smooth mechanical systems containing fractional derivatives.

Research paper thumbnail of Secondary bifurcation of a shearable rod with nonlinear spring supports

European Journal of Mechanics - A/Solids, 2017

The postbuckling behavior of a compressed elastic rod is studied. The rod is supported by two ide... more The postbuckling behavior of a compressed elastic rod is studied. The rod is supported by two identical hardening spring supports at clamped ends. The constitutive equations of the rod take into account the effect of shear. For local bifurcation analysis the Liapunov-Schmidt method is used. It is shown that for the critical value of auxiliary parameter the lowest eigenvalue becomes double. This fact and double Z 2 symmetry lead to the occurrence of secondary bifurcations for the values of auxiliary parameter near the critical one. For primary and secondary branches asymptotic expansions are constructed. Depending on the values of parameters of nonlinear spring supports and shear rigidity five different groups of bifurcation diagrams are found.

Research paper thumbnail of Earthquake response of adjacent structures with viscoelastic and friction dampers

Theoretical and Applied Mechanics, 2015

We study the seismic response of two adjacent structures connected with a dry friction damper. Ea... more We study the seismic response of two adjacent structures connected with a dry friction damper. Each of them consists of a viscoelastic rod and a rigid block, which can slide without friction along the moving base. A simplified earthquake model is used for modeling the horizontal ground motion. Energy dissipation is taken by the presence of the friction damper, which is modeled by the set-valued Coulomb friction law. Deformation of viscoelastic rods during the relative motion of the blocks represents another way of energy dissipation. The constitutive equation of a viscoelastic body is described by the fractional Zener model, which includes fractional derivatives of stress and strain. The problem merges fractional derivatives as non-local operators and theory of set-valued functions as the non-smooth ones. Dynamical behaviour of the problem is governed by a pair of coupled multi-valued differential equations. The posed Cauchy problem is solved by use of the Gr?nwald-Letnikov numerica...

Research paper thumbnail of Seismic response of a column like structure with both fractional and dry friction type of dissipation

Konstrukcija u obliku stuba koja se sastoji od donjeg bloka (osnova) i gornjeg bloka, b) Uvećan d... more Konstrukcija u obliku stuba koja se sastoji od donjeg bloka (osnova) i gornjeg bloka, b) Uvećan detalj B 1 , c) Dekomponovani sistem.. .. .. .. .. . 2.2 Dinamiµ cki modeli neglatkog sistema u zavisnosti od relativne brzine bloka. 2.3 Faze kretanja neglatkog sistema tokom vremena.

Research paper thumbnail of On Impact Scripts with Both Fractional and Dry Friction Type of Dissipation

International Journal of Bifurcation and Chaos, 2012

We study the dynamics of a mass, sliding on a dry surface and impacting against a rigid wall thro... more We study the dynamics of a mass, sliding on a dry surface and impacting against a rigid wall through a viscoelastic body, that we model as a straight rod of negligible mass. The problem comprises a constitutive model of the viscoelastic body with fractional derivatives of stress and strain, restrictions on the coefficients that follow from Clausius–Duhem inequality, and discontinuous inequality constraint conditions imposed by the Coulomb friction model. We show that the dynamics of the problem is governed by a single integro-differential inclusion. By use of the slack variable algorithm the problem was solved numerically. The predictions of the model concerning the duration of the impact, maximal values of the impacting force and deformation, as well as the restitution coefficient are determined for several values of system parameters. Depending on the dry friction coefficient three different impact scripts are identified: rebound after the impact, capture in the approaching phase,...

Research paper thumbnail of Numerical algorithm for rigid body position estimation using the quaternion approach

Acta Mechanica Sinica, 2017

This paper deals with rigid body attitude estimation on the basis of the data obtained from an in... more This paper deals with rigid body attitude estimation on the basis of the data obtained from an inertial measurement unit mounted on the body. The aim of this work is to present the numerical algorithm, which can be easily applied to the wide class of problems concerning rigid body positioning, arising in aerospace and marine engineering, or in increasingly popular robotic systems and unmanned aerial vehicles. Following the considerations of kinematics of rigid bodies, the relations between accelerations of different points of the body are given. A rotation matrix is formed using the quaternion approach to avoid singularities. We present numerical procedures for determination of the absolute accelerations of the center of mass and of an arbitrary point of the body expressed in the inertial reference frame, as well as its attitude. An application of the algorithm to the example of a heavy symmetrical gyroscope is presented, where input data for the numerical procedure are obtained from the solution of differential equations of motion, instead of using sensor measurements.

Research paper thumbnail of Application of Fractional Calculus to Frontal Crash Modeling

Mathematical Problems in Engineering, 2017

Fractional derivative viscoelastic model is used in the analysis of a frontal impact of a vehicle... more Fractional derivative viscoelastic model is used in the analysis of a frontal impact of a vehicle against a rigid obstacle. The frontal part of the vehicle is first modeled as a viscoelastic fractional rod and then it is modeled as two different viscoelastic fractional rods with a different length. In the second model also the friction is taken into account. A motion is analyzed during several phases because of both different lengths of the rods and the presence of a dry friction force in the later model. Governing systems of differential equations together with the corresponding initial conditions are derived. Parameter identification is done on the basis of the existing experimental results using the solution of a posed impact problem. What makes the problem more complex, regarding the second model, is the fact that it belongs to the class of nonsmooth fractional order systems, which require special treatment when dealing with deformation history during different motion phases.