Determination of joint reactions in a rigid multibody system, two different approaches

U ovom radu su prikazane dve različite metode za određivanje sila i momenata reakcija idealnih veza u zglobovima. Razmatrani sistem više tela ima strukturu otvorenog kinematskog lanca. Prva metoda se odnosi na određivanje glavnih vektora i momenata reakcija veza u simboličkoj formi koja se zasniva na Rodrigezovom pristupu i pogodna je za simboličko računanje. Druga prikazana metoda je vektorska metoda koja je bazirana na vektorima momenata masa i vektorima rotatorima vezanih za pol i usmerenu osu. Oba primera su prikazana i diskutovana na sistemu tri kruta tela.In this paper two different methods for determination of frictionless joint reaction forces and moments are presented. The considered multibody system has an open kinematic chain structure. The first method refers to the determination of resultant joint reaction forces and moments based on the Rodrigues approach suitable for computation in a symbolic form. The second method presented is the method based on the so-called vectors of the body mass moments and vector rotators coupled for a pole and oriented axes. Both approaches are presented and discussed on the three- like rigid multibody system

Determination of joint reactions in a rigid multibody system, two different approaches

U ovom radu su prikazane dve različite metode za određivanje sila i momenata reakcija idealnih veza u zglobovima. Razmatrani sistem više tela ima strukturu otvorenog kinematskog lanca. Prva metoda se odnosi na određivanje glavnih vektora i momenata reakcija veza u simboličkoj formi koja se zasniva na Rodrigezovom pristupu i pogodna je za simboličko računanje. Druga prikazana metoda je vektorska metoda koja je bazirana na vektorima momenata masa i vektorima rotatorima vezanih za pol i usmerenu osu. Oba primera su prikazana i diskutovana na sistemu tri kruta tela.In this paper two different methods for determination of frictionless joint reaction forces and moments are presented. The considered multibody system has an open kinematic chain structure. The first method refers to the determination of resultant joint reaction forces and moments based on the Rodrigues approach suitable for computation in a symbolic form. The second method presented is the method based on the so-called vectors of the body mass moments and vector rotators coupled for a pole and oriented axes. Both approaches are presented and discussed on the three- like rigid multibody system

Modeling of complex fractional order hybrid structures and application in dynamics of systems of rigid and deformable bodies

Предмет ове докторске дисертације је истраживање у области моделирања и анализе динамичког понашања система крутих тела повезаних хибридним елементима фракционог типа и сложених система наноструктура чија су вискоеластична својства описана изводима фракционог реда...The research subject of this doctoral dissertation is in the field of modeling and analysis of dynamic behavior of rigid multibody systems, connected with fractional order hybrid elements, and complex nanostructure based systems with fractional order viscoelastic properties..

Equations of Motion of Robotic System With Piezo‐Modified Viscoelastic and Magnetorheological Elements of Fractional Order

In this communication, the Rodriguez method is proposed for modeling dynamics of the robotic system, where Lagrange’s equations of second kind of rigid bodies system in covariant form are used. Discrete hybrid elements with so called piezomodified Kelvin-Voight (PKV) and magnetorheological (MRD) type of viscoelastic models with fractional order derivatives are introduced in to the system of motion equations by means of generalized forces. The results obtained are illustrated by numerical examples

Generalized Forces of the Robotic System with Fractional Order Thermoviscoelastic Element

In this paper, we analyze generalized forces of a discrete fractional order Kelvin-Voigt thermoviscoelasic element connected into a multibody robotic system. An efficient numerical approximation scheme is used to approximate fractional order derivative. The effects of fractional order derivative and temperature change on generalized forces are examined through the numerical example of simple three rigid body robotic syste

Equations of Motion of Robotic System With Piezo‐Modified Viscoelastic and Magnetorheological Elements of Fractional Order

In this communication, the Rodriguez method is proposed for modeling dynamics of the robotic system, where Lagrange’s equations of second kind of rigid bodies system in covariant form are used. Discrete hybrid elements with so called piezomodified Kelvin-Voight (PKV) and magnetorheological (MRD) type of viscoelastic models with fractional order derivatives are introduced in to the system of motion equations by means of generalized forces. The results obtained are illustrated by numerical examples

Combined sub-harmonic resonances of nanobeam on fractional visco-Pasternak type foundation

In this work, we observe combined parametric and external sub-harmonic resonances of order one-third of a geometrically nonlinear nonlocal nanobeam model resting on a fractional visco- Pasternak type foundation. Euler-Bernoulli beam theory, nonlinear strain-displacement relation and nonlocal elasticity constitutive equation are employed to obtained fractional order governing equation for the transverse vibration of a system. Under the assumption of small fractional damping, we used the perturbation multiple-scales method to obtain an approximated analytical solution for the frequency-amplitude response for variable axial and transverse external loads. Several numerical examples are given to show the effects of different parameters on frequencyamplitude response

VIBRATION AND STABILITY OF A NONLINEAR NONLOCAL STRAIN-GRADIENT FG BEAM ON A VISCO-PASTERNAK FOUNDATION

This study investigates the stability of periodic solutions of a nonlinear nonlocal strain gradient functionally graded Euler–Bernoulli beam model resting on a visco-Pasternak foundation and subjected to external harmonic excitation. The nonlinearity of the beam arises from the von Kármán strain-displacement relation. Nonlocal stress gradient theory combined with the strain gradient theory is used to describe the stress-strain relation. Variations of material properties across the thickness direction are defined by the power-law model. The governing differential equation of motion is derived by using Hamilton's principle and discretized by the Galerkin approximation. The methodology for obtaining the steady-state amplitude-frequency responses via the incremental harmonic balance method and continuation technique is presented. The obtained periodic solutions are verified against the numerical integration method and stability analysis is performed by utilizing the Floquet theory

Fractal boundary value problems for integral and differential equations with local fractional operators

In the present paper we investigate the fractal boundary value problems for the Fredholm and Volterra integral equations, heat conduction and wave equations by using the local fractional decomposition method. The operator is described by the local fractional operators. The four illustrative examples are given to elaborate the accuracy and reliability of the obtained results

ENERGY ANALYSIS OF FREE TRANSVERSE VIBRATIONS OF THE VISCO-ELASTICALLY CONNECTED DOUBLE-MEMBRANE SYSTEM

The presented paper deals with the analysis of energy transfer in the visco-elastically connected circular double-membrane system for free transverse vibration of the membranes. The system motion is described by a set of two coupled non-homogeneous partial differential equations. The solutions are obtained by using the method of separation of variables. Once the problem is solved, natural frequencies and mode shape functions are found, and then the form of solution for small transverse deflections of membranes is derived. Using the obtained solutions, forms of reduced kinetic, potential and total energies, as functions of dissipation of the whole system and subsystems, are determined. The numerical examples are given as an illustration of the presented theoretical analysis as well as the possibilities to investigate the influence of different parameters and different initial conditions on the energies transfer in the system.