Predrag Kozić

Dynamics of multiple viscoelastic carbon nanotube based nanocomposites with axial magnetic field

Nanocomposites and magnetic field effects on nanostructures have received great attention in recent years. A large amount of research work was focused on developing the proper theoretical framework for describing many physical effects appearing in structures on nanoscale level. Great step in this direction was successful application of nonlocal continuum field theory of Eringen. In the present paper, the free transverse vibration analysis is carried out for the system composed of multiple single walled carbon nanotubes (MSWCNT) embedded in a polymer matrix and under the influence of an axial magnetic field. Equivalent nonlocal model of MSWCNT is adopted as viscoelastically coupled multi-nanobeam system (MNBS) under the influence of longitudinal magnetic field. Governing equations of motion are derived using the Newton second low and nonlocal Rayleigh beam theory, which take into account small-scale effects, the effect of nanobeam angular acceleration, internal damping and Maxwell relation. Explicit expres...

Influence of transverse shear on stochastic instability of viscoelastic beam

Abstract The stochastic instability problem associated with an axially loaded Timochenko beam made of viscoelastic material is formulated. The beam is treated as Voigt–Kelvin body compressed by time-dependent deterministic and stochastic forces. By using the direct Liapunov method, bounds of the almost sure instability of beams as a function of retardation time, variance of the stochastic force, mode number, section shape factor and intensity of the deterministic component of axial loading, are obtained. Calculations are performed for the Gaussian process with a zero mean and variance σ2 as well as for harmonic process with an amplitude A.

Moment Lyapunov exponents and stochastic stability of moving narrow bands

Stochastic stability of narrow moving bands under random tension fluctuation is investigated within the concept of the Lyapunov exponent. The moment Lyapunov exponents and Lyapunov exponents are important characteristics determining the moment and almost-sure stability boundaries of a stochastic dynamical system. Galerkin’s method is used to reduce the partial differential equation of motion to a corresponding ordinary differential equation with randomly varying stiffness. We obtain explicit stability conditions based on the asymptotic expansion series for the moment Lyapunov exponent g(p), and the Lyapunov exponent λ for a two-dimensional linear stochastic system.

Influence of Transverse Shear on Stochastic Instability of the Elastic Beam

In the case when Kirchhoff–Love hypotheses do not give satisfactory results, we have to take the rotatory inertia and transverse shear into account. This paper studies the elastic beam subjected to stochastic axial load, when transverse shear is taken into account. By using the direct Liapunov method, the bounds of the almost sure instability of beams as the function of the damping coefficient, variance of the stochastic force, geometric parameters, mode number, section shape factor and intensity of the deterministic component of axial loading, are obtained. Calculations are performed for the Gaussian process with zero mean and variance σ2, as well as for the harmonic process with amplitude A.

THERMAL EFFECT ON FREE VIBRATION AND BUCKLING OF A DOUBLE-MICROBEAM SYSTEM

The paper investigates the problem of free vibration and buckling of an Euler-Bernoulli double-microbeam system (EBDMBS) under the compressive axial loading with a temperature change effect. The system is composed of two identical, parallel simply-supported microbeams which are continuously joined by the Pasternak’s elastic layer. Analytical expressions for the critical buckling load, critical buckling temperature, natural frequencies and frequencies of transverse vibration of the EBDMBS represented by the ratios are derived and validated by the results found in the literature. Also analytical expressions are obtained for various buckling states and vibration-phase of the EBDMBS. The temperature change effect is assumed to have an influence on both the microbeams. The length scale parameter, temperature change effect, critical buckling load, thickness/material parameter, Pasternak’s parameter and Poisson’s effect are discussed in detail. Also, as a clearer display of the thermo-mechanical response of EBDMBS, the paper introduces a critical scale load ratio of the modified and the local critical buckling loads in low-temperature environs. Numerical results show that the critical buckling temperatures for classical theories are always higher than the critical buckling temperature for MCST systems.

Effects of Axial Compression Forces, Rotary Inertia and Shear on Forced Vibrations of the System of Two Elastically Connected Beams

This chapter covers the solution for forced vibrations of two elastically connected beams of Rayleigh’s, Timoshenko’s and Reddy-Bickford’s type under the influence of axial forces. Scientific contribution is presented through the analytical solutions in forms of three cases of forced vibrations - Harmonic arbitrarily continuous excitation, the continuous uniform harmonic excitation and harmonic concentrated excitation. Analytical solutions were obtained by using the modal analysis method. Based on the results derived in this chapter, it can be made a conclusion that the differences in the approximations of the solutions depending of the used model gave a good solutions just in cases of Timoshenko’s and Reddy-Bickford’s theory for thick beams in higher modes also in forced vibrations regime and must be taken into account.

Free Vibrations and Stability of an Elastically Connected Double-Beam System

Free oscillations and static stability of two elastically connected beams are considered in Chapter 2. At various examples it is shown analytically obtained results and impacts of some mechanical parameters of the system on the natural frequencies and amplitudes. Verification of obtained results is shown by comparison with results of the existed classical models. New scientific contribution in this chapter is formulation of the new double-beam model described with new derived equations of motion with rotational inertia effects and with inertia of rotation with transverse shear (Rayleigh’s model, Timoshenko’s model, Reddy - Bickford’s model). It is formulized the static stability condition of the two elastically connected beams of different types with analytical expressions for the various values of critical forces. Numerical experiments confirmed the validity of the analytical results obtained by comparing the results of the models existing in the literature. From chapter 2 it can be concluded that the effects of rotational inertia and transverse shear must be taken into account in the model of thick beams because errors that occur by ignoring them are increasing with the increasing the mode of vibration.

The Effects of Rotary Inertia and Transverse Shear on Vibrations and Stability of the System of Elastically Connected Reddy-Bickford Beams on Elastic Foundation

Chapters 6 analyzed free vibration of the multiple elastically connected beam system of Reddy-Bickford’s type on an elastic foundation under the influence of axial forces with the comparison of the frequency and stability theoretical research for all four types of the beam’s theory. Analytical solutions for the natural frequencies and the critical buckling forces are determined by the trigonometric method and verified numerically as in case in the previous chapter. In the case of the Reddy-Bickford’s model, it is shown that the natural frequency provides the best solution approximation.

Geometrically Non-linear Vibrations of Timoshenko Damaged Beams Using the New p-Version of Finite Element Method

Chapter 7 presents geometrically nonlinear forced vibrations of damaged Timoshenko beams. In the study it is developed new p-version of finite element method for damaged beams. The advantage of the new method is compared with the traditional p-version of finite element method and provides better approximations of solutions with a small number of degrees of freedom used in numerical analysis.

The Effects of Rotary Inertia and Transverse Shear on the Vibration and Stability of the Elastically Connected Timoshenko Beam-System on Elastic Foundation

Chapter 5 analyzed free vibration of the multiple elastically connected beams of Timoshenko’s type on an elastic foundation under the influence of axial forces. Analytical solutions for the natural frequencies and the critical buckling forces are determined by the trigonometric method and verified numerically. It is shown that the fundamental natural frequency in the first mode of the multiple beam system tends to the value of the natural frequency of the system with one beam resting on an elastic foundation with the tendency of increasing the number of connected beams with the same stiffness of the layers between.