Nonlinear finite element analysis for vibrations of double-walled carbon nanotubes

The large-amplitude free vibration analysis of double-walled carbon nanotubes embedded in an elastic medium is investigated by means of a finite element formulation. A double-beam model is utilized in which the governing equations of layers are coupled with each other via the van der Waals interlayer forces. Von-Karman type nonlinear strain-displacement relationships are employed where the ends of the nanotube are constrained to move axially. The amplitude-frequency response curves for large-amplitude free vibrations of single-walled and double-walled carbon nanotubes with arbitrary boundary conditions are graphically illustrated. The effects of material constant of the surrounding elastic medium and the geometric parameters on the vibration characteristics are investigated. For a double-walled carbon nanotube with different boundary conditions between inner and outer tubes, the nonlinear frequencies are obtained apparently for the first time. Comparison of the results with those from the open literature is made for the amplitude-frequency curves where possible. This comparison illustrates that the present scheme yields very accurate results in predicting the nonlinear frequencies.     

Effect of the Stone–Wales defect on the structure and mechanical properties of single-wall carbon nanotubes in axial stretch and twist

The effect of the Stone–Wales defect due to the rotation of a pair of neighboring atoms on the equilibrium structure and mechanical properties of single-wall carbon nanotubes in axial stretch and twist is considered. The position of carbon atoms in a test section consisting of a number of repeated units hosting a solitary Stone–Wales defect is computed by minimizing the Tersoff–Brenner potential. The energy invested in the defect is found to decrease as the radius of the nanotube becomes smaller. Numerical computations for nanotubes with zigzag and armchair chiralities show that inclined, axial, and circumferential defect orientations have a strong influence on the mechanical response in axial stretch and twist. Stretching may cause the defect energy to become negative, revealing the possibility of spontaneous defect formation leading to failure. In some cases, stretching may eliminate the defect and purify the nanotube. When the tube is twisted around its axis, a neck develops at the location of the defect, signaling possible disintegration.     

Assessment of structural integrity and durability—a task of experimental mechanics

The necessity of health-monitoring and supervising structures will be justified under aspects of reliability and safety as well as with regard to economical reasons. Considering the achievements in measurement techniques combined with computer techniques, the requirements on the evolution of efficient monitoring systems will be indicated. The prerequisite will be pointed out, to conceive such systems in close co-ordination with the mathematical modelling of the structure. This is inalienable with concern to system-identification, as generally the control-parameters cannot be measured directly; they are to calculate on the basis of the mathematical model and the measurable structural response symptoms. This requires mathematical complicate solution of inverse problems. During service/operation many effects give rise for degradation of the structural resistance, reducing the safety and the life-time as well. The results of system identification enable the determination of damage indicators, which provide information on the scale of degradation in the course of time to estimate the limit of service-life and the residual life-time.     

A new Lyapunov approach for global synchronization of non-autonomous chaotic systems

This paper proposes a new approach for finding the Lyapunov function to study the sufficient global synchronization criterion of master-slave non-autonomous chaotic systems via linear state error feedback control. The approach is first demonstrated in a synchronization scheme for the second-order non-autonomous chaotic systems and then generalized to the schemes for the nth-order non-autonomous chaotic systems. Some algebraic synchronization criteria for the second-order chaotic systems are obtained. The sharpness of the new criteria is compared with that of the existing criteria of the same type by numerical examples.     

Growth limit of carbon onions – A continuum mechanical study

The growth of carbon onions is simulated using continuum mechanical shell models. With this models it is shown that, if a carbon onion has grown to a critical size, the formation of an additional layer leads to the occurrence of a structural instability. This instability inhibits further growth of carbon onions and, thus, can be a reason for the limited size of such particles. The loss of stability is mainly evoked by van der Waals interactions between misfitting neighboring layers leading to self-equilibrating stress states in the layers due to mutual accommodation. The influence of the curvature induced surface energy and its consequential stress state is investigated and found to be rather negligible. Furthermore, it is shown that the nonlinear character of the van der Waals interactions has to be considered to obtain maximum layer numbers comparable to experimental observations. The proposed model gives insight into mechanisms which are assumed to limit the size of carbon onions and can serve as basis for further investigations, e.g., of the formation of nanodiamonds in the center of carbon onions.     

An evolutionary approach for the motion planning of redundant and hyper-redundant manipulators

The trajectory planning of redundant robots is an important area of research and efficient optimization algorithms are needed. The pseudoinverse control is not repeatable, causing drift in joint space which is undesirable for physical control. This paper presents a new technique that combines the closed-loop pseudoinverse method with genetic algorithms, leading to an optimization criterion for repeatable control of redundant manipulators, and avoiding the joint angle drift problem. Computer simulations performed based on redundant and hyper-redundant planar manipulators show that, when the end-effector traces a closed path in the workspace, the robot returns to its initial configuration. The solution is repeatable for a workspace with and without obstacles in the sense that, after executing several cycles, the initial and final states of the manipulator are very close.     

On the dynamic mechanical properties of open-cell metal foams – A re-assessment of the ‘simple-shock theory’

Metal foams are increasingly used for energy absorption especially in lightweight structures and to resist blast and impact loads. This requires an understanding of the dynamic response of these materials for modelling purposes. As a supplement to Tan et al., 2005a, Tan et al., 2005b, hereinafter referred to as T–L for brevity, this paper provides experimental data for the dynamic mechanical properties of open-cell Duocel® foams having a three-dimensional (3D) distribution of cells. These confirm significant enhancement of the foam’s compressive strength, accompanied by changes in their deformation pattern in certain loading régimes, particularly what has come to be described as the ‘shock’ régime by Zheng et al. (2012). This paper examines experimentally, in a similar fashion as T–L, how the structural response of the individual cell walls is affected by cell-shape anisotropy at the cell (meso)-scale and how this, in turn, alters the pattern of cell crushing and the dynamic, mechanical properties. The distinctive role of cell microinertia and ‘shock’ formation are discussed in relation to the mechanical properties measured for these 3D cylindrical specimens. For consistency the same procedures described in T–L are used. The features identified are shown to be consistent with those observed in finite-element simulations of two-dimensional (2D) honeycombs as estimated by the one-dimensional (1D) steady-shock theory summarised in T–L. The different deformation patterns that develop in the various loading régimes are categorised according to the compression rate/impact speed. Critical values of impact velocity, corresponding to the transition from one pattern to the other, are quantified and predictive formulae for the compressive uniaxial strengths in the directions of two of the principal axes of the material in each loading régime are derived and discussed. The accuracy of the predictive formula in T–L is shown to critically depend on the ‘densification strain’ of the foam specimens. This parameter and the discussion that follows could assist the formulation and validation of alternative theoretical/computational models on the dynamic deformation of such materials.     

Effect of process conditions on the synthesis of carbon nanotubes by catalytic decomposition of methane

A new dual-composition catalyst based on Ni-Mo/MgO with high efficiency of producing carbon nanotubes （CNTs） from methane was reported recently. In the present article, with this type of catalyst, the impact of such experimental parameters as reaction temperature, reaction time, concentration of H2, flow rate ratio of CH4 to H2 on yield and graphitization were investigated, leading to the following optimal growth conditions： reaction time 60min, reaction temperature 900℃, CH4：H2 about 100：20mL/min, under which high-yield multi-walled CNTs bundles were synthesized. Raman measurement indicated that the as-synthesized product was well-graphitized, and the purity was estimated over 95% by TG-DSC analysis. In terms of the above results, an explanation of high-efficiency formation of CNTs bundles and the co-catalysis mechanism of Ni-Mo/MgO were suggested. 2007 Chinese Societv of Particuology and Institute of Process Engineering, Chinese Academy of Sciences. Published by Elsevier B.V.     

Investigation on the mechanical properties of sintered porous copper compacts

In line with recent attention on porous metals having low and medium porosities in the range of 20-50%, this paper studies the effect of porosity on the mechanical properties of sintered copper compacts. Experiments were designed to investigate the effect of porosity, applied stress and sliding velocity on the wear rate of copper compacts, leading to the finding that the effects of both porosity and applied stress of the wear test on the wear rate are approximately similar and higher than that of sliding velocity. The investigation concerning the effect of porosity on compressive strength indicated that the stress-strain curve of high-porosity compact exhibited identifiable ultimate strength points, though low-porosity compact showed distinct stages of elastic plastic behavior.     

A symbolic algorithm for the automatic computation of multitone-input harmonic balance equations for nonlinear systems

A symbolic algorithm is developed for the automatic generation of harmonic balance equations for multitone input for a class of nonlinear differential systems with polynomial nonlinearities. Generalized expressions are derived for the construction of balance equations for a defined multitone signal form. Procedures are described for determining combinations for a given output frequency from the desired set obtained from box truncated spectra and their permutations to automate symbolic algorithm. An application of method is demonstrated using the well-known Duffing–Van der Pol equation. Then the obtained analytical results are compared with numerical simulations to show the accuracy of the approach. The computation times for both the numerical solutions of equations versus the number of frequency components and the symbolic generation of the equations versus the power of nonlinearity are also investigated.     

A semi-analytical solution for the confined compression of hydrated soft tissue

Confined compression is a common experimental technique aimed at gaining information on the properties of biphasic mixtures comprised of a solid saturated by a fluid, a typical example of which are soft hydrated biological tissues. When the material properties (elastic modulus, permeability) are assumed to be homogeneous, the governing equation in the axial displacement reduces to a Fourier equation which can be solved analytically. For the more realistic case of inhomogeneous material properties, the governing equation does not admit, in general, a solution in closed form. In this work, we propose a semi-analytical alternative to Finite Element analysis for the study of the confined compression of linearly elastic biphasic mixtures. The partial differential equation is discretised in the space variable and kept continuous in the time variable, by use of the Finite Difference Method, and the resulting system of ordinary differential equations is solved by means of the Laplace Transform method.     

Describing function based methods for predicting chaos in a class of fractional order differential equations

This paper deals with two different methods for predicting chaotic dynamics in fractional order differential equations. These methods, which have been previously proposed for detecting chaos in classical integer order systems, are based on using the describing function method. One of these methods is constructed based on Genesio–Tesi conjecture for existence of chaos, and another method is introduced based on Hirai conjecture about occurrence of chaos in a nonlinear system. These methods are restated to use in predicting chaos in a fractional order differential equation of the order between 2 and 3. Numerical simulation results are presented to show the ability of these methods to detect chaos in two fractional order differential equations with quadratic and cubic nonlinearities.     

Mechanical behaviour of carbon nanotubes under combined twisting–bending

The main objective of this paper is to investigate the mechanical behaviour (strength and stiffness) of carbon nanotubes (CNTs) under combinations of bending and twisting. In order to achieve this goal, molecular dynamics (MD) simulations of bended and twisted CNTs are performed. The LAMMPS code is used, the AIREBO potential is considered for CC bonds, the temperature is kept at 300 K and incremental bending and twisting rotations are imposed to the CNT. Two types of CNTs are analyzed, including zig-zag (8,0) and armchair (5,5) CNTs with similar radius and length. The CNTs are also analyzed for pure bending and pure twisting. The main results are shown in the form of diagrams of energy and moment against imposed rotations. Some relevant conclusions are drawn concerning the influence of loading (bending and twisting) on the stiffness, strength and failure of CNTs: namely, it is concluded that armchair CNTs possess higher strength and fracture toughness under twisting–bending loading than zigzag CNTs; additionally, it is found that both CNTs (armchair and zigzag) still support moderate-to-high bending levels without failure after being extremely twisted and torsionally buckled, even for twisting angles four times those corresponding to torsional buckling; finally, the results prove that CNTs, mostly armchair ones, exhibit very high twisting–bending stiffness and strength and can be used with confidence as torsional spring elements in nanoelectromechanical systems (NEMS).     

Control of iron nanoparticle size by manipulating PEG–ethanol colloidal solutions and spin-coating parameters for the growth of single-walled carbon nanotubes

Iron catalyst nanoparticles were prepared on silicon wafers by spin-coating colloidal solutions containing iron nitrate, polyethylene glycol (PEG) and absolute ethanol. The effects of various spin-coating conditions were investigated. The findings showed that the size of the iron particles was governed by the composition of the colloidal solution used and that a high angular speed was responsible for the formation of a thin colloidal film. The effect of angular acceleration on the size and distribution of the iron particles were found to be insignificant. It was observed that a longer spin-coating duration provoked the agglomeration of iron particles, leading to the formation of large particles. We also showed that single-walled carbon nanotubes could be grown from the smallest iron catalyst nanoparticles after the chemical vapor deposition of methane.     

A micro–macro method for predicting the shear strength of brittle rock under compressive loading

Microcracks have great significance for shear strength of brittle rock in compression. A major challenge of this area is to establish the correlation of microcracks and macroscopic shear strength. A new micro–macro method is presented to predict the shear strength of brittle rock in compression. This method incorporates the microcrack model suggested by Ashby, Mohr–Coulomb failure criterion and a crack-strain relation. This crack–strain relation is presented to link the crack growth and axial strain by combining the micro and macro definitions from rock damage. The shear strength and stress–strain relationship of Jinping marble are theoretically investigated in detail. The rationality of this suggested method is verified by using the experimental results founded on Jinping marble. Effects of the initial microcrack size, friction coefficient and confining pressure on internal friction angle, cohesion, and shear strength are also discussed.     

A three-scale FE approach to reliability analysis of MEMS sensors subject to impacts

In this paper the effects of accidental impacts on polysilicon MEMS sensors are investigated within the framework of a three-scale finite element approach. By allowing for the very small ratio (on the order of 10⁻⁴) between the inertia of the MEMS and the inertia of the whole device, macro-scale analyses at the package length-scale are run to obtain the loading conditions at the sensor anchor points. These loading conditions are successively adopted in meso-scale analyses at the MEMS length-scale to detect where the stress level tends to be amplified by sensor layout. To foresee failure of polysilicon in these domains, as caused by the propagation of inter- as well as trans-granular cracks up to percolation, representative crystal topologies are handled in micro-scale analyses. In case of a uni-axial MEMS accelerometer falling from a reference drop height, results show that the crystal structure within the failing sensor detail can have a remarkable effect on the failure mode and on the time to failure. Conversely, through comparison with simulations where the MEMS is assumed to fall anchored to the naked die, it is assessed that packaging only slightly modifies failure details, without significantly reducing the shock loading on the sensor. F. Fachin is currently with: Technology Laboratory for Advanced Materials and Structures, Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139-4307 (USA). F. Cacchione is currently with: ABB SACE, Viale dell’Industria 18, Vittuone, 20010 (Italy).     

A comparative experimental study on the use of three denoising methods for bearing defect detection

In the conditional maintenance of mechanical components by vibratory analysis, one distinguishes two types of analyses which are necessary for obtaining a reliable diagnosis. The first analysis lies in the detection of potential defects; there are currently various succeeded methods based on the treatment of the vibratory signals allowing the localization of a defect. One can quote among these methods the analysis of spectrum (with constant resolution (RC) or percentage of bands constant (PCB)), the analysis of envelope, the analysis cepstrale, the analysis time-frequencies or the analysis time-scales (wavelet). The second analysis is interested in the determination and the evaluation of severity of a defect detected to estimate the influence of this defect on the operation of a mechanism. The scalar indicators which make it possible to estimate the gravity of a defect are indicators known as total which are based on the statistical analysis of a temporal signal. However, the signals resulting from accelerometer sensors are the results of a mixture of sources of vibrations, sources being able to be allotted to one or more defects and are generally polluted by noise. This work presents the three principal methods of denoising and the study of their influence on the scalar parameters (kurtosis, factor peak, value rms) and this within the framework of the detection of defects of the chippings types of bearings.     

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.     

A model establishment and numerical simulation of dynamic coupled hydraulic–mechanical–electric–structural system for hydropower station

Nonlinear Dynamics - A nonlinear dynamic coupled model for hydropower station system, which contains the model of water-carriage system, water turbine system, speed governor system,...     

Poincaré and the shortcomings of the Hamilton-Jacobi method for classical or quantized mechanics

A great theorem was proven by H. Poincaré in celestial mechanics. It states that, in the most general problems of mechanics, the total energy of the system is the only well behaved first integral of the system, while other so-called integrals cannot be represented by uniform and convergent series. This very important result can be explained and visualized by comparison with standard methods of discussion, as, for example, the Hamilton-Jacobi procedure. The discussion shows that there are serious limitations to the use of this procedure, which collapses in the most general problems (Poincaré theorem) and can be used only for “almost separated” variables. The Poincaré theorem appears to provide the distinction between determinism in mechanics and statistical mechanics according to Boltzmann. The research presented here done under Contract Nonr 266(56) and was first described in a Quarterly Report dated July 31, 1959.