A structural mechanics approach for predicting the mechanical properties of carbon nanotubes

Based on molecular mechanics, a structural mechanics model of carbon nanotubes (CNTs) was developed with special consideration given to the bending stiffness of the graphite layer. The potentials associated with the atomic interactions within a CNT were evaluated by the strain energies of beam elements which serve as structural substitutions of covalent bonds in a CNT. In contrast to the original model developed by Li and Chou (Int. J. Solids Struct. 40(10):2487–2499, 2003), in the current model the out-of-plane deformation (inversion) of the bond was distinguished from the in-plane deformation by considering a rectangular cross-section for the beam element. Consequently, the model is able to study problems where the effect of local bending of the graphite layer in a carbon nanotube is significant. A closed-form solution of the sectional properties of the beam element was derived analytically. The model was verified through the analysis of rolling a graphite sheet into a carbon nanotube. Using the present model, the buckling behavior of nanotubes under bending is simulated. The predicted critical bending angle agrees well with molecular dynamics simulations.     

Extension of Lagrangian–Hamiltonian mechanics for continuous systems—investigation of dynamics of a one-dimensional internally damped rotor driven through a dissipative coupling

In this paper, the extended Lagrangian formulation for a one-dimensional continuous system with gyroscopic coupling and non-conservative fields has been developed. Using this formulation, the dynamics of an internally and externally damped rotor driven through a dissipative coupling has been studied. The invariance of the extended or so-called umbra-Lagrangian density is obtained through an extension of Noether’s theorem. The rotor shaft is modeled as a Rayleigh beam. The dynamic behavior of the rotor shaft is obtained and validated through simulation studies. Results show an interesting phenomenon of limiting behavior of the rotor shaft with internal damping beyond certain threshold speeds which are obtained theoretically and affirmed by simulations. It is further observed that there is entrainment of whirling speeds at natural frequencies of the rotor shaft primarily depending on the damping ratio.     

Realization of a new experimental setup for magnetostrictive actuators

A new setup for the prospective investigation of the active damping properties of magnetostrictive (MST) actuators has been realized. A dynamical finite element analysis has been carried out to meet the design requirements concerning the eigenvalues spectra and the mode shapes of the setup: experimental and numerical results match satisfactorily. The setup has given a clear evidence of the damping capabilities of a MST actuator developed by our group and utilized as a compensator of external harmonic excitations.     

Fifty years of finite elements — a solid mechanics perspective

The finite element method has been considered as one of the most significant engineering advances of the twentieth century. This computational methodology has made substantial impact on many fields in science and also has profoundly changed engineering design procedures and practice. This paper, mainly from a solid mechanics perspective, and the Swansea viewpoint in particular, describes very briefly the origin of the methodology, then summaries selected milestones of the technical developments that have taken place over the last fifty years and illustrates their application to some practical engineering problems.     

Mathematical modeling and experimental investigation of an embedded vibro-impact system

The subject of this work is the experimental investigation and the mathematical modeling of the impact force behavior in a vibro-impact system, where a hammer is mounted on a cart that imposes a prescribed displacement. By changing the hammer stiffness and the impact gap it is possible to investigate the impact force behavior under different excitation frequencies. The experimental data will be used to validate the mathematical model. The hammer behavior is studied in more detail using a nonlinear analysis, which shows the various responses of the hammer, such as dynamical jumps, bifurcations and chaos.     

Unsteady and transient flow of compressible fluids in pipelines—a review of theoretical and some experimental studies

The mathematical modelling of highly compressible unsteady flows has been of interest for some years. In order to obtain tractable solutions of the governing equations, investigators have made various simplifying assumptions such as presuming isothermal or isentropic flow of ideal gases, etc. The present review, with dense phase gas tranmission systems of particular interest, briefly develops the basic equations without such assumptions and includes the effects of wall friction and heat transfer. After re-expressing the equations in terms of the measurable quantities of pressure, temperature and velocity, previously published work is reviewed for their solution. Relevant experimental work is somewhat limited but contributions from 20 references are included.     

Global dynamics and integrity of a two-dof model of?a?parametrically excited cylindrical shell

In this paper the global dynamics and topological integrity of the basins of attraction of a parametrically excited cylindrical shell are investigated through a two-degree-of-freedom reduced order model. This model, as shown in previous authors?? works, is capable of describing qualitatively the complex nonlinear static and dynamic buckling behavior of the shell. The discretized model is obtained by employing Donnell shallow shell theory and the Galerkin method. The shell is subjected to an axial static pre-loading and then to a harmonic axial load. When the static load is between the buckling load and the minimum post-critical load, a three potential well is obtained. Under these circumstances the shell may exhibit pre- and post-buckling solutions confined to each of the potential wells as well as large cross-well motions. The aim of the paper is to analyze in a systematic way the bifurcation sequences arising from each of the three stable static solutions, obtaining in this way the parametric instability and escape boundaries. The global dynamics of the system is analyzed through the evolution of the various basins of attraction in the four-dimensional phase space. The concepts of safe basin and integrity measures quantifying its magnitude are used to obtain the erosion profile of the various solutions. A detailed parametric analysis shows how the basins of the various solutions interfere with each other and how this influences the integrity measures. Special attention is dedicated to the topological integrity of the various solutions confined to the pre-buckling well. This allows one to evaluate the safety and dynamic integrity of the mechanical system. Two characteristic cases, one associated with a sub-critical parametric bifurcation and another with a super-critical parametric bifurcation, are considered in the analysis.     

Multi-scale experimental analysis of rate dependent metal–elastomer interface mechanics

A remarkable high fracture toughness is sometimes observed for interfaces between materials with a large elastic mismatch, which is reported to be caused by the fibrillar microstructure appearing in the fracture process zone. In this work, this fibrillation mechanism is investigated further to investigate how this mechanism is dissipating energy. For that purpose, thermoplastic urethane (TPU)-copper interfaces are delaminated at various rates in a peel test experimental setup. The fracture process zone is visualized in situ at the meso-scale using optical microscopy and at the micro-scale using Environmental Scanning Electron Microscopy (ESEM). It is shown that the geometry of the fracture process zone is insensitive to the delamination rate, while the interface traction scales logarithmically with the rate. This research has revealed that, the interface roughness is shown to be pivotal in initiating the fibrillation delamination process, which facilitates the high fracture toughness. The multi-scale experimental approach identified two mechanisms responsible for this high fracture toughness. Namely, the viscous dissipation of the TPU at the high strain levels occurring in the fibrils and the loss of stored elastic energy which is disjointed from the propagation due to the size of the process zone.     

The influences of both offset and mass moment of inertia of a tip mass on the dynamics of a centrifugally stiffened visco-elastic beam

The present study is concerned with the out-of-plane vibrations of a rotating, internally damped (Kelvin-Voigt model) Bernoulli-Euler beam carrying a tip mass. The centroid of the tip mass, possessing also a mass moment of inertia is offset from the free end of the beam and is located along its extended axis. This system can be thought of as an extremely simplified model of a helicopter rotor blade or a blade of an auto-cooling fan. The differential eigenvalue problem is solved by using Frobenius method of solution in power series. The characteristic equation is then solved numerically. The simulation results are tabulated for a variety of the nondimensional rotational speeds, tip mass, tip mass offset, mass moment of inertia and internal damping parameters. These are compared with the results of a conventional finite element modeling as well, and excellent agreement is obtained. Some numerical results are given in graphical form. The numerical results obtained, indicate clearly that the tip mass offset and mass moment of inertia are important parameters on the eigencharacteristics of rotating beams so that they have to be included in the modeling process.     

Flow and heat transfer of a slightly rarefied gas over a stretching surface

This work deals with the study of the boundary layer flow and mass transfer of a visco-elastic fluid immersed in a porous medium over a stretching surface in the presence of surface slip, chemical reaction and variable viscosity. The partial differential equations governing the flow have been transformed by similarity transformation into a system of coupled nonlinear ordinary differential equations which is solved numerically by means of the fourth order Runge-Kutta integration scheme coupled with the shooting technique. The effects of various involved interesting parameters on the velocity fields and concentration fields are shown graphically and investigated. In addition, tabulated results for the local skin-friction coefficient and the local Sherwood number are presented and discussed.     

Vibration reduction of a nonlinear spring pendulum under multi external and parametric excitations via a longitudinal absorber

The vibration of a ship pitch-roll motion described by a non-linear spring pendulum system (two degrees of freedom) subjected to multi external and parametric excitations can be reduced using a longitudinal absorber. The method of multiple scale perturbation technique (MSPT) is applied to analyze the response of this system near the simultaneous primary, sub-harmonic and internal resonance. The steady state solution near this resonance case is determined and studied applying Lyapunov’s first method. The stability of the system is investigated using frequency response equations. Numerical simulations are extensive investigations to illustrate the effects of the absorber and some system parameters at selected values on the vibrating system. The simulation results are achieved using MATLAB 7.0 programs. Results are compared to previously published work.     

Simulation and hybrid fuzzy-PID control for positioning of a hydraulic system

Accuracy and precision of position control of hydraulic systems are key parameters for engineering applications in order to set more economical and quality systems. In this context, this paper presents modeling and position control of a hydraulic actuation system consisting of an asymmetric hydraulic cylinder driven by a four way, three position proportional valve. In this system model, the bulk modulus is considered as a variable. In addition, the Hybrid Fuzzy-PID Controller with Coupled Rules (HFPIDCR) is proposed for position control of the hydraulic system and its performance is tested by simulation studies. The novel aspect of this controller is to combine fuzzy logic and PID controllers in terms of a switching condition. Simulation results of the HFPIDCR based controller are compared with the results of classical PID, Fuzzy Logic Controller (FLC), and Hybrid Fuzzy-PID controller (HFPID). As a result, it is demonstrated that Hybrid Fuzzy PID Controller with Coupled Rules is more effective than other controllers.     

Bifurcation of periodic solutions and invariant tori for a four-dimensional system

In this paper, a four-dimensional system of autonomous ordinary differential equations depending on a small parameter is considered. Suppose that the unperturbed system is composed of two planar systems: one is a Hamiltonian system and another system has a focus. By using the Poincaré map and the integral manifold theory, sufficient conditions for the existence of periodic solutions and invariant tori of the four-dimensional system are obtained. An application of our results to a nonlinearly coupled Van der Pol–Duffing oscillator system is given.     

Meshfree modelling of fracture—a comparative study of different methods

Different fracture methods in meshfree methods are studied and compared. Our studies focuses on the elementfree Galerkin (EFG) method though similar results were obtained with SPH and MPM. Three major fracture approaches are tested: Natural fracture, smeared crack method and discrete crack method. In the latter method, the crack is represented as continuous line and as set of discrete crack segment. Natural fracture is a key feature of meshfree methods. In some numerical examples, we will show that natural fracture criterion cannot handle even simple fracture adequately. Moreover, we will show in our numerical examples that smeared crack models can capture global behavior appropriately for simple examples but not for complex examples involving branching cracks. The most accurate methods are discrete fracture methods.     

Adaptive control for synchronization of a four-dimensional chaotic system via a single variable

This paper studies the control for synchronization of a four-dimensional system via a single variable, and a linear feedback controller and an adaptive controller are proposed. Based on the Lyapunov stability theory, the correctness of the proposed methods is strictly demonstrated. The numerical simulations further show their effectiveness.     

Stability and control of random rocking motion of a multidimensional structure: the Melnikov approach

This paper investigates the controlled dynamics of a structure consisting of a free standing rigid block with an attached chain of uniaxially moving point masses. Rocking motion is excited by motion of the ground; instability is associated with overturning of the structure as a whole. The control task is to minimize the probability of overturning. The stochastic Melnikov method is used to obtain a necessary condition of instability, estimate an upper bound to the probability of overturning, and find a convenient control strategy. The paper is restricted to the consideration of seismic vulnerability of the structure. A similar approach can be applied to systems with wind or wave excitations.     

Full- and reduced-order synchronization of a class of time-varying systems containing uncertainties

Investigation on chaos synchronization of autonomous dynamical systems has been largely reported in the literature. However, synchronization of time-varying, or nonautonomous, uncertain dynamical systems has received less attention. The present contribution addresses full- and reduced-order synchronization of a class of nonlinear time-varying chaotic systems containing uncertain parameters. A unified framework is established for both the full-order synchronization between two completely identical time-varying uncertain systems and the reduced-order synchronization between two strictly different time-varying uncertain systems. The synchronization is successfully achieved by adjusting the determined algorithms for the estimates of unknown parameters and the linear feedback gain, which is rigorously proved by means of the Lyapunov stability theorem for nonautonomous differential equations together with Barbalat’s lemma. Moreover, the synchronization result is robust against the disturbance of noise. We illustrate the applicability for full-order synchronization using two identical parametrically driven pendulum oscillators and for reduced-order synchronization using the parametrically driven second-order pendulum oscillator and an additionally driven third-order Rossler oscillator.     

Order reduction and nonlinear behaviors of a continuous rotor system

An isotropic flexible shaft, acted by nonlinear fluid-induced forces generated from oil-lubricated journal bearings and hydrodynamic seal, is considered in this paper. Dimension reductions of the rotor system were carried out by both the standard Galerkin method and the nonlinear Galerkin method. Numerical simulations provide bifurcation diagrams, spectrum cascade, orbits of the disk center and Poincaré maps, to demonstrate the dynamical behaviors of the system. The results reveal transitions, or bifurcations, of the rotor whirl from being synchronous to non-synchronous as the unstable speed is exceeded. The non-synchronous oil/seal whirl is a quasi-periodic motion. In the regime of quasi-periodic motion, the “windows” of multi-periodic motion were found. The investigation shows that the nonlinear Galerkin method has an advantage over the standard one with the same order of truncations, because the influences of higher modes are considered by the former.     

The Theory of Thin-Walled Rods of Open Profile as a Result of Asymptotic Splitting in the Problem of Deformation of a Noncircular Cylindrical Shell

A new asymptotic approach to the theory of thin-walled rods of open profile is suggested. For the problem of linear static deformation of a noncircular cylindrical shell we consider solutions, which are slowly varying along the axial coordinate. A small parameter is introduced in the equations of the modern theory of shells. Conditions of compatibility for the shell strain measures are employed. The principal terms of the series expansion of the solution are determined from the conditions of solvability for the minor terms. We conclude the procedure with the subsequent solution for the field of displacements. The analysis shows that the known equations of thin-walled rods, which were previously obtained with some approximate methods using hypotheses and approximations of displacements, are asymptotically exact. The presented semi-numerical analysis of the shell equations allows us to estimate the accuracy of the obtained solution. The results of the paper constitute a sound basis to the equations of the theory of thin-walled rods and provide trustworthy information concerning the distribution of stresses in the cross-section.     

Optimization of an acoustic test chamber involving the fluid-structure interaction by FEM and experimental validation

The aim of this work is to determine the optimal design of two acoustic test chambers using systems of optimization by means of finite elements. In this way, we have modelled a set of tests composed of a source chamber and a receiving chamber according to the basic requirements of the standard rule. The constructive element whose acoustical behaviour is being evaluated is placed between both chambers. Applying the finite element method (FEM), a two-dimensional coupled finite element model with fluid-structure interaction has been made, using finite elements of the fluid-type both for the air and fluid-structure interface, and finite elements of solid-type with its elastic properties for a multilayered wall. The geometry of the chambers has been parameterized as design variables (DVs) and an objective function has been defined from the absolute value of the difference between the transmission loss (TL) values of the laboratory test and the TL of the numerical simulation in order to minimize it. To find an optimal design of the geometry of the acoustic chamber, a new cascade optimization procedure has been successfully developed. Finally, the numerical simulation results are compared with the acoustic laboratory results, and conclusions are exposed.