A survey of Hopf bifurcation analysis in nonlinear railway wheelset dynamics

This article attempts to analyze the Hopf bifurcation behavior of a railway wheelset in the presence of dead-zone and yaw damper nonlinearities. A model that is more precise than Yang and Ahmadian is investigated. Using Bogoliubov-Mitropolsky averaging method and critical speed, the amplitude of the limit cycle in the presence of the mentioned nonlinearities is taken into consideration. To solve these nonlinear equations analytically, the integration interval has been divided into three sub-domains. Two-dimensional bifurcation diagrams are provided to illustrate the mechanism of formation of Hopf bifurcation. These diagrams can be used for design of stable wheelset systems

Analytical approximation of nonlinear frequency of cantilever beam vibrations

This research presents the application of modern analytical approaches for the nonlinear vibrations of cantilever beams. These methods are Homotopy Analysis Method, Parameter Expansion Method and Bubnov-Galerkin Weighted Residual Method. Powerful analytical methods are used to obtain frequency-amplitude relationship of dynamic behavior of the mentioned system. It is demonstrated that one term in series expansions of all methods are sufficient to obtain a highly accurate solution. Finally, a comparison with numerical methods is provided in order to confirm the soundness of the obtained results

Dynamic analysis of preload nonlinearity in nonlinear beam vibration

The objective of this paper is to propose a novel exact equivalent function (EF) for preload nonlinearity. The nonlinear preloaded spring force, which is exerted on the cantilever beam has been rewritten with a definite force-displacement relationship using new EF. This approach permits us to overcome severe computational issues that are encountered in the analytical investigations of nonlinear problems. Highly nonlinear equation of beam vibration under the influence of preloaded spring at its end with cubic nonlinearity is considered and the related analytical solution is obtained through Parameter-expansion Method (PEM). Finally, the soundness of the introduced EF would be verified by comparison of the results with the obtained solutions using numerical method

Thermomagnetic behavior of a semiconductor material heated by pulsed excitation based on the fourth-order MGT photothermal model

This article proposes a photothermal model to reveal the thermo-magneto-mechanical properties of semiconductor materials, including coupled diffusion equations for thermal conductivity, elasticity, and excess carrier density. The proposed model is developed to account for the optical heating that occurs through the semiconductor medium. The Moore–Gibson–Thompson (MGT) equation of the fourth-order serves as the theoretical framework to establish the photothermal model. It is well-known that the optical and heat transfer properties of such materials behave as random functions of photoexcited-carrier density; therefore, the current model is remarkably more reliable compared to the earlier closed-form theories which are limited to a single form. The constructed theoretical framework is able to investigate the magneto-photo-thermoelastic problems in a semiconductor medium due to laser pulse excitation as a case study. Some parametric studies are used to exhibit the impact of thermal parameters, electromagnetic fields, laser pulses and thermoelectric coupling factors on the thermomagnetic behavior of physical variables. Finally, several numerical examples have been presented to draw the distributions of the examined field variables

On a 3D material modelling of smart nanocomposite structures

Smart composites (SCs) are utilized in electro-mechanical systems such as actuators and energy harvesters. Typically, thin-walled components such as beams, plates, and shells are employed as structural elements to achieve the mechanical behavior desired in these composites. SCs exhibit various advanced properties, ranging from lower order phenomena like piezoelectricity and piezomagneticity, to higher order effects including flexoelectricity and flexomagneticity. The recently discovered flexomagneticity in smart composites has been investigated under limited conditions. A review of the existing literature indicates a lack of evaluation in three-dimensional (3D) elasticity analysis of SCs when the flexomagnetic effect (FM) exists. To address this issue, the governing equations will incorporate the term ∂/∂z, where z represents the thickness coordinate. The variational technique will guide us in further developing these governing equations. By using hypotheses and theories such as a 3D beam model, von Kármán's strain nonlinearity, Hamilton's principle, and well-established direct and converse FM models, we will derive the constitutive equations for a thick composite beam. Conducting a 3D analysis implies that the strain and strain gradient tensors must be expressed in 3D forms. The inclusion of the term ∂/∂z necessitates the construction of a different model. It should be noted that current commercial finite element codes are not equipped to accurately and adequately handle micro- and nano-sized solids, thus making it impractical to model a flexomagnetic composite structure using these programs. Therefore, we will transform the derived characteristic linear three-dimensional bending equations into a 3D semi-analytical Polynomial domain to obtain numerical results. This study demonstrates the importance of conducting 3D mechanical analyses to explore the coupling effects of multiple physical phenomena in smart structures

Strain-Rate Dependency of a Unidirectional Filament Wound Composite under Compression

This article presents the results of experimental studies concerning the dynamic deformation and failure of a unidirectional carbon fiber reinforced plastic (T700/LY113) under compression. The test samples were manufactured through the filament winding of flat plates. To establish the strain rate dependencies of the strength and elastic modulus of the material, dynamic tests were carried out using a drop tower, the Split Hopkinson Pressure Bar method, and standard static tests. The samples were loaded both along and perpendicular to the direction of the reinforcing fiber. The applicability of the obtained samples for static and dynamic tests was confirmed through finite element modeling and the high-speed imaging of the deformation and failure of samples during testing. As a result of the conducted experimental studies, static and dynamic stress-strain curves, time dependencies of deformation and the stress and strain rates of the samples during compression were obtained. Based on these results, the strain rate dependencies of the strength and elasticity modulus in the strain rate range of 0.001–600 1/s are constructed. It is shown that the strain rate significantly affects the strength and deformation characteristics of the unidirectional carbon fiber composites under compression. An increase in the strain rate by 5 orders of magnitude increased the strength and elastic modulus along the fiber direction by 42% and 50%, respectively. Perpendicular loading resulted in a strength and elastic modulus increase by 58% and 50%, respectively. The average strength along the fibers at the largest studied strain rate was about 1000 MPa. The obtained results can be used to design structural elements made of polymer composite materials operating under dynamic shock loads, as well as to build models of mechanical behavior and failure criteria of such materials, taking into account the strain rate effects

Static and Free Vibration Analyses of Single-Walled Carbon Nanotube (SWCNT)-Substrate Medium Systems

This paper proposes a novel nanobar-substrate medium model for static and free vibration analyses of single-walled carbon nanotube (SWCNT) systems embedded in the elastic substrate medium. The modified strain-gradient elasticity theory is utilized to account for the material small-scale effect while the Gurtin-Murdoch surface theory is employed to represent the sur-face-energy effect. The Winkler-foundation model is assigned to consider interactive mechanism between the nanobar and its surrounding substrate medium. Hamilton’s principle is called for to consistently derive the system governing equation, initial conditions, and classical as well as non-classical boundary conditions. Two numerical simulations are employed to demonstrate the essence of the material small-scale effect, the surface-energy effect, and the surrounding substrate medium on static and free vibration responses of single-walled carbon nanotube (SWCNT)-substrate medium systems. The simulation results show that the material small-scale effect, the surface-energy effect, and the interaction between the substrate and the structure lead to a system-stiffness enhancement both in static and free vibration analyses

Nonlinear transversely vibrating beams by the homotopy perturbation method with an auxiliary term

This paper presents the high order frequency-amplitude relationship for nonlinear transversely vibrating beams with odd and even nonlinearities using Homotopy Perturbation Method with an auxiliary term (HPMAT). The governing equations of vibrating buckled beam, beam carrying an intermediate lumped mass and quintic nonlinear beam are investigated to exhibit the reliability and ability of the proposed asymptotic approach. It is demonstrated that two terms in series expansions are sufficient to obtain a highly accurate periodic solutions. The integrity of the analytical solutions is verified by numerical results. It is clearly demonstrated that this asymptotic approach is very effective and straightforward to study the nonlinear oscillator systems include odd and even nonlinear terms

The effect of small scale on the vibrational behavior of single-walled carbon nanotubes with a moving nanoparticle

In this paper, free and forced vibration of simply-supported Single-walled carbon nanotube is investigated under the moving nanoparticle by considering nonlocal cylindrical shell model. To validate the theoretical results, modal analysis of nanotube is conducted using ANSYS commercial software. Excellent agreement is exhibited between the results of two different methods. Furthermore, the dynamic response of SWCNT under moving nanoparticle is also studied. It is assumed that the nanoparticle travels along the center of nanotube with constant velocity and the van der Waals force between CNT and particle is taken into account. The dynamic response of the SWCNT under the influence of C60 particle obtained using dynamic Green’s function and modal expansion. The obtained results show that the nonlocal scale effect decreases the natural frequency and dynamic displacement of the CNT