Effects of van der Waals force on nonlinear vibration of electromechanical integrated electrostatic harmonic actuator

An electromechanical integrated electrostatic harmonic actuator is promising for the miniaturization of electromechanical devices. As the dimensions of the actuator decrease, the effects of the van der Waals force become obvious. In this study, by considering the nonlinearity of electrostatic and van der Waals forces, nonlinear vibration equations of the flexible ring of an electrostatic harmonic actuator are deduced. Using these equations, the nonlinear free vibration and nonlinear forced response of the actuator are investigated. The effects of the van der Waals force on the nonlinear vibration of the flexible ring are analyzed. Results show that these effects of the van der Waals force are relatively obvious under some conditions and should be considered.     

Bifurcation and pull-in voltages of primary resonance of electrostatically actuated SWCNT cantilevers to include van der Waals effect

In this work the voltage response of primary resonance of electrostatically actuated single wall carbon nano tubes (SWCNT) cantilevers over a parallel ground plate is investigated. Three forces act on the SWCNT cantilever, namely electrostatic, van der Waals and damping. While the damping is linear, the electrostatic and van der Waals forces are nonlinear. Moreover, the electrostatic force is also parametric since it is given by AC voltage. Under these forces the dynamics of the SWCNT is nonlinear parametric. The van der Waals force is significant for values less than 50 nm of the gap between the SWCNT and the ground substrate. Reduced order model method (ROM) is used to investigate the system under soft excitation and weak nonlinearities. The voltage-amplitude response and influences of parameters are reported for primary resonance (AC near half natural frequency).     

A cohesive law for carbon nanotube/polymer interfaces based on the van der Waals force

We have established the cohesive law for interfaces between a carbon nanotube (CNT) and polymer that are not well bonded and are characterized by the van der Waals force. The tensile cohesive strength and cohesive energy are given in terms of the area density of carbon nanotube and volume density of polymer, as well as the parameters in the van der Waals force. For a CNT in an infinite polymer, the shear cohesive stress vanishes, and the tensile cohesive stress depends only on the opening displacement. For a CNT in a finite polymer matrix, the tensile cohesive stress remains the same, but the shear cohesive stress depends on both opening and sliding displacements, i.e., the tension/shear coupling. The simple, analytical expressions of the cohesive law are useful to study the interaction between CNT and polymer, such as in CNT-reinforced composites. The effect of polymer surface roughness on the cohesive law is also studied.     

Parametric variational principle and quadratic programming method for van der Waals force simulation of parallel and cross nanotubes

A parametric variational principle for van der Waals force simulation between any two adjacent nonbonded atoms and the corresponding improved quadratic programming method for numerical simulation of mechanical behaviors of carbon nanotubes are developed. Carbon nanotubes are modeled and computed based on molecular structural mechanics model. van der Waals force is simulated by the network of bars (called bar network) with a special nonlinear mechanical constitutive law (called generalized parametric constitutive law) in the finite element analysis. Compared with conventional numerical methods, the proposed method does not depend on displacement and stress iteration, but on the base exchanges in the solution of a standard quadratic programming problem. Thus, the model and method developed present very good convergence behavior in computation and provide accurate predictions of the mechanical behaviors and displacement distributions in the nanotubes. Numerical results demonstrate the validity and the efficiency of the proposed method.     

Effects of layer number and initial pressure on continuum-based buckling analysis of multi-walled carbon nanotubes accounting for van der Waals interaction

The structural instability of multi-walled carbon nanotubes (MWCNTs) has captured extensive attention due to the unique characteristic of extremely thin hollow cylinder structure. The previous studies usually focus on the buckling behavior without considering the effects of the wall number and initial pressure. In this paper, the axial buckling behavior of MWCNTs with the length-to-outermost radius ratio less than 20 is investigated within the framework of the Donnell shell theory. The governing equations for the infinitesimal buckling of MWCNTs are established, accounting for the van der Waals (vdW) interaction between layers. The effects of the wall number, initial pressure prior to buckling, and aspect ratio on the critical buckling mode, buckling load, and buckling strain are discussed, respectively. Specially, the four-walled and twenty-walled CNTs are studied in detail, indicating the fact that the buckling instability may occur in other layers besides the outermost layer. The obtained results extend the buckling analysis of the continuum-based model, and provide theoretical support for the application of CNTs.     

An investigation into the effects of electrostatic and squeeze-film non-linearities on the shock spectrum of microstructures

We present an investigation into the effects of some of the common microelectromechanical systems (MEMS) non-linearities on their shock response and shock spectrum. As a case study, a capacitive accelerometer is selected to investigate theoretically and experimentally the effect of non-linearities due to squeeze film damping (SQFD) and electrostatic actuation. For the theoretical investigation, a non-linear single-degree-of-freedom model is used to simulate the response of the device. It is shown that, in the case of light damping, the electrostatic forces soften the microstructure and raise its deflection significantly. Dynamic pull-in instability is predicted near the dynamic range zone of the shock spectrum. On the other hand, SQFD is found to highly suppress the deflection of the microstructure in the dynamic range, while it is of less effect in the quasi-static range. Experimentally, the capacitive accelerometer is powered with a DC load and then subjected to acceleration pulses generated by a shaker. Tests are conducted while the accelerometer is operated in air, where the squeeze film effect is significant, and while placed inside a vacuum chamber. Simulation results are compared to experimental data showing excellent agreement.     

Effects of anti-symmetric nonlinear viscous damping on the force transmissibility of multi-degree of freedom structures

In the present study, the concept of the output frequency response function is applied to theoretically investigate the force transmissibility of multi-degree of freedom (MDOF) structures with a nonlinear anti-symmetric viscous damping. The results reveal that an anti-symmetric nonlinear viscous damping can significantly reduce the transmissibility over all resonance regions for MDOF structures while it has almost no effect on the transmissibility over non-resonant and isolation regions. The results indicate that the vibration isolators with an anti-symmetric damping characteristic have great potential to overcome the dilemma in the design of linear viscously damped vibration isolators where an increase of the damping level reduces the force transmissibility over resonant region but increases the transmissibility over non-resonant regions.     

Nonlinear dynamics and control of a variable order oscillator with application to the van der Pol equation

We investigate the dynamics and control of a nonlinear oscillator that is described mathematically by a Variable Order Differential Equation (VODE). The dynamic problem in question arises from the dynamical analysis of a variable viscoelasticity oscillator. The dynamics of the model and the behavior of the variable order differintegrals are shown in variable phase space for different parameters. Two different controllers are developed for the VODEs under study in order to track an arbitrary reference function. A generalization of the van der Pol equation using the VODE formulation is analyzed under the light of the methods introduced in this work.     

Nonlinear dynamics of self-, parametric,and externally excited oscillator with time delay: van der Pol versus Rayleigh models

The regular and chaotic vibrations of a nonlinear structure subjected to self-, parametric, and external excitations acting simultaneously are analysed in this study. Moreover, a time delay input is added to the model to control the system response. The frequency-locking phenomenon and transition to quasi-periodic oscillations via Hopf bifurcation of the second kind (Neimark–Sacker bifurcation) are determined analytically by the multiple time scales method up to the second-order perturbation. Approximate solutions of the quasi-periodic motion are determined by a second application of the multiple time scales method for the slow flow, and then, slow–slow motion is obtained. The similarities and differences between the van der Pol and Rayleigh models are demonstrated for regular, periodic, and quasi-periodic oscillations, as well as for chaotic oscillations. The control of the structural response, and modifications of the resonance curves and bifurcation points by the time delay signal are presented for selected cases.

     

Nonlinear dynamics, stability and control of the scan process in noncontacting atomic force microscopy

The nonlinear equations of motion for the scan process in noncontacting atomic force microscopy are consistently derived using the extended Hamilton’s principle. A modal dynamical system obtained from the continuum model reveals that scan control appears in the form of parametric excitation. The system is analyzed asymptotically and numerically to yield escape bounds limiting the noncontacting mode of operation. Approximate stability bounds are deduced from both a global Melnikov integral and a local Moon–Chirikov overlap criterion. The Melnikov–Holmes stability curve and the overlap criterion are found to be similar for small damping. However, for very small damping, typical of ultra-high vacuum conditions, where the Melnikov bound becomes trivial, the Moon–Chirikov criterion yields an improved stability threshold.     

Effect of changes of surface tension and contact angle on normal force measurement with the Weissenberg rheogoniometer

Summary In experiments with water and dilute aqueous solutions of polyacrylamide spurious normal forces were observed. This phenomenon was traced to changes in contact angle between the test liquid and the plates brought about by starting and stopping shear. There are circumstances in which contact angle and surface tension changes with shear could be indistinguishable from true normal forces.

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Zusammenfassung In Versuchen mit Wasser und verdünnten wässerigen Lösungen von Polyacrylamid wurden falsche Normal-Kräfte beobachtet. Diese Erscheinung wird durch die Änderung des Kontaktwinkels zwischen der Versuchsflüssigkeit und den Platten erklärt. Diese Änderungen werden an sich durch den Anfang und die Beendigung der Bewegung erzeugt. Unter Umständen können die Änderungen des Kontaktwinkels und der Oberflächenspannung mit der Scherung nicht von den Normal-Kräften zu unterscheiden sein.

     

Effects of contact angle on condensate topology, drainage and efficiency of a condenser with minichannels

Epoxy coatings with good adhesion characteristics have been developed that are suitable for large-scale manufacturing and application in compact heat exchangers. Two of them, with a static contact angle for water of 105° and 79° have been tested in a finned-tube condenser comparing flat plate minichannels on the gas-side. Contrary to the expectation, the thermal efficiency of the 105° condenser is slightly less than that of the 79° one. This is due to a reduction of condensate drop size at detachment, resulting in relatively small dry paths after drainage. In the present study, geometry and coating thickness of the two coated exchangers used have not been optimized, since emphasis has been on the effect of contact angle. The finned-tube geometry is shown to be less favourable, for a condenser, than the compact cross-flow plate geometry with minichannels on both the gas- and coolant side that was tested previously.     

Effects of compressive load and support damping on the propagation of flexural waves in beams resting on elastic foundation

The contributions of compressive load and support damping are included into the formulation of flexural wave motion in beams lying on elastic (Winkler) foundation. The beam is modeled by both Euler–Bernoulli’s and Timoshenko’s theories. First, dispersion analysis is performed, which reveals that, for a fixed wavenumber, phase velocity decreases as the intensity of the compressive force or the value of the support damping is increased. Secondly, the transverse displacement of a semi-infinite beam excited by a velocity step pulse at its finite end is examined in the transient regime by adopting Laplace transform approach. This latter study sustains the validity of the dispersion analysis outcomes and shows that compressive load and support damping cause an amplification and a diminution, respectively, of the displacement amplitudes at the various positions of the beam.     

Determination of the inertial,stiffness, and damping parameters of a solid resting on nonlinear shock absorbers

Institute of Mechanics, Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 29, No. 8, pp. 78–84, August, 1993.     

The effect of the VOF–CSF static contact angle boundary condition on the dynamics of sliding and bouncing ellipsoidal bubbles

The static contact angle is the only empiricism introduced in a Volume of Fluid–Continuum Surface Force (VOF–CSF) model of bubbly flow. Although it has previously been shown to have a relatively limited effect on the accuracy of velocity and shape predictions in the case of large gas bubbles sliding under inclined walls (e.g. Cook and Behnia, 2001), it may have a more determining influence on the numerical prediction of the dynamics of smaller ellipsoidal bubbles which were shown by Tsao and Koch (1997) to bounce repeatedly when sliding under inclined walls at certain wall inclinations. The present paper reports on the influence of surface tension and the static contact angle on the dynamics of an ellipsoidal air bubble of equivalent diameter D_e = 3.4 mm. The bubble Eötvös and Morton numbers are Eo = 1.56 and Mo = 2 × 10⁻¹¹ respectively. The computational results are achieved with a Piecewise Linear Construction (PLIC) of the interface and are reviewed with reference to experimental measurements of bubble velocity and interface shape oscillations recorded using a high speed digital camera. Tests are performed at plate inclination angles θ ∈ {10°, 20°, 30°, 45°} to the horizontal and computational models consider three static contact angles θ_c ∈ {10°, 20°, 30°}. The static contact angle has been found to have a significant effect on the bubble dynamics but to varying degree depending on the plate inclination. It is shown to promote lift off and bouncing when the plate inclination angle reaches 30° in a way that does not necessarily reflect experimental observations.     

Study of the effect of contact force model on the dynamic response of mechanical systems with dry clearance joints: computational and experimental approaches

The main objective of this work is to present a computational and experimental study on the contact forces developed in revolute clearance joints. For this purpose, a well-known slider-crank mechanism with a revolute clearance joint between the connecting rod and slider is utilized. The intra-joint contact forces that are generated at these clearance joints are computed by considering several different elastic and dissipative approaches, namely those based on the Hertz contact theory and the ESDU tribology-based cylindrical contacts, along with a hysteresis-type dissipative damping. The normal contact force is augmented with the dry Coulomb’s friction force. In addition, an experimental apparatus is used to obtained some experimental data in order to verify and validate the computational models. From the outcomes reported in this paper, it is concluded that the selection of the appropriate contact force model with proper dissipative damping plays a significant role in the dynamic response of mechanical systems involving contact events at low or moderate impact velocities.     

Effects of control measures on the dynamics of COVID-19 and double-peak behavior in Spain

Nonlinear Dynamics - The COVID-19 disease significantly has threatened the human lives and economy. It is a dynamic system with transmission and control as factors. Modeling the dynamics of the...     

An overview of the formulation,existence and uniqueness issues for the initial value problem raised by the dynamics of discrete systems with unilateral contact and dry friction

In the end of the seventies, Schatzman and Moreau undertook to revisit the venerable dynamics of rigid bodies with contact and dry friction in the light of more recent mathematics. One claimed objective was to reach, for the first time, a mathematically consistent formulation of an initial value problem associated with the dynamics. The purpose of this article is to make a review of the today state-of-art concerning not only the formulation, but also the issues of existence and uniqueness of solution.     

Effects of damping on the speed of increase and amplitude of limit cycle for an aircraft braking system subjected to mode-coupling instability

A nonlinear model of an aircraft braking system is presented and used to investigate the effects of damping on the stability in Chevillot et al. (Arch Appl Mech 78(12):949–963, 2008). It has been shown that the addition of damping into the equations of motion does not lead systematically to the stabilization of the system. In the case of a mode-coupling instability, there is indeed an optimal ratio between the modal damping coefficients of the two modes in coalescence, that maximize the stable area. But the stable area is not a sufficient criterion. In dynamics, the amplitude of the vibrations and the transient behavior characterized by the speed of increase of the oscillations are best indicators. In this paper, the same nonlinear model of the aircraft braking system is used to compute time-history responses by integration of the full set of the nonlinear dynamic equations. The aim of the study is to evaluate the effects of damping on the nonlinear dynamics of the brake. It is shown that damping may be very efficient to significantly reduce and slow down the increase of the friction-induced vibrations. But, in the same way as for the stability area, there exists a value of the damping ratio that optimizes the effects of damping.