Nonlocal continuum-based modeling of a nanoplate subjected to a moving nanoparticle. Part II: Parametric studies

The possible usage of nanoplates in transporting of nanovehicles encouraged the author to propose some nonlocal plate models in the companion paper where the nanovehicle (i.e., moving nanoparticle) was modeled by a moving point load by considering its friction with the upper surface of the nanoplate. In this paper, a comprehensive parametric study is carried out to study the effects of length to thickness ratio of the nanoplate, small-scale parameter, and velocity (or angular velocity) of the moving nanoparticle on dynamic response of nonlocal Kirchhoff, Mindlin, and higher-order plates subjected to a moving nanoparticle. Herein, dynamic response of the nanoplate covers both time histories and dynamic amplitude factors of the in- and out-of-plane displacements. The capabilities of various nonlocal plate models in predicting the displacement field caused by friction and mass weight of the moving nanoparticle are then explored through various numerical analyses for two cases: (i) the moving nanoparticle moves along a diagonal of the nanoplate; (ii) the moving nanoparticle orbits on an ellipse path whose center is coincident with the nanoplate's center. The obtained results indicate that due to the incorporation of small-scale effect into shear strain energy of the nanoplate, an appropriate nonlocal plate model should be used. The results show that the choice of the nanoplate model to use relies on the small-scale parameter, geometrical properties of the nanoplate, and velocity of the moving nanoparticle.     

Nonlocal vibration of SWBNNT embedded in bundle of CNTs under a moving nanoparticle

In this study, an analytical method of the small scale parameter on the vibration of single-walled Boron Nitride nanotube (SWBNNT) under a moving nanoparticle is presented. SWBNNT is embedded in bundle of carbon nanotubes (CNTs) which is simulated as Pasternak foundation. Using Euler–Bernoulli beam (EBB) model, Hamilton's principle and nonlocal piezoelasticity theory, the higher order governing equation is derived. The effects of electric field, elastic medium, slenderness ratio and small scale parameter are investigated on the vibration behavior of SWBNNT under a moving nanoparticle. Results indicate the importance of using surrounding elastic medium in decrease of normalized dynamic deflection. Indeed, the normalized dynamic deflection decreases with the increase of the elastic medium stiffness values. The electric field has significant role on the nondimensional fundamental frequencies, as a smart controller. The results of this work is hoped to be of use in design and manufacturing of smart nano-electro-mechanical devices in advanced medical applications such as drug delivery systems with great applications in biomechanics.     

Small-scale effect on the vibration of thin nanoplates subjected to a moving nanoparticle via nonlocal continuum theory

The vibration of elastic thin nanoplates traversed by a moving nanoparticle involving Coulomb friction is investigated using the nonlocal continuum theory of Eringen. The eigen function technique and the Laplace transform method are employed to solve the governing equations of the nanoplate. The explicit expressions of the in-plane and transverse displacements are obtained when the moving nanoparticle traverses the nanoplate on an arbitrary straight line. In a special case, the obtained results are also compared with those of other researchers and a reasonably good agreement is achieved. The effects of small-scale parameters and velocity of the moving nanoparticle on the dynamic response as well as the dynamic amplitude factors (DAFs) of the in-plane and transverse displacements are then explored in some detail. The results indicate that the magnitude of DAF of the transverse displacement of the nanoplate (i.e., DAF_w) increases with the first small-scale effect parameter, irrespective of the values of the second small-scale effect parameter and the velocity of the moving nanoparticle. As the first small-scale effect parameter grows, the maximum values of DAF_w as a function of the moving nanoparticle velocity increase and generally occur in the lower levels of the moving nanoparticle velocity.     

Adventures of a Theoretical Physicist, Part I: Europe

I was born in Budapest, Hungary, on July 7, 1907, and this first part of my interview with Andor Frenkel focuses on my life and work in Europe. After my elementary and secondary education I studied mathematics at the University of Budapest for two years. I went to the University of G?ttingen in 1928 where I attended Max Born’s lectures on quantum mechanics, which influenced me to change from mathematics to physics, and as a consequence I focused on filling the gaps in my physics background. When ready to turn to research work I followed the advice of my friend Edward Teller and spent three months in Werner Heisenberg’s group at the University of Leipzig in the summer of 1930. That fall I returned to the University of Budapest, where I received my Ph.D.degree in the summer of 1932. Two months later, because I had become entangled in the illegal Communist Party, I was arrested and sentenced to fourteen months in prison. Fifteen months after my release, I joined Lev Landau’s group at the Ukrainian Physical-Technical Institute in Kharkov, passed Landau’s so-called “theorminimum” program on my second attempt, began research on the theory of liquid helium, and lost my faith in communism following Stalin’s repressive measures. I obtained an exit visa through the Hungarian Legation and returned to Budapest in June 1937. That September, again with the help of my friend Edward Teller, I attended a conference in Paris where I met Fritz London and Edmond Bauer, who arranged for me a small scholarship and an association with the Langevin laboratory at the Collège de France. Four months later, in January 1938 Kapitza, and John F. Allen and A. Donald Misener reported their independent discovery of the superfluidity of helium, which London and I explored theoretically and I explained with my two-fluid theory later in 1938. Following the German invasion of France, my wife and I left Paris for Toulouse in June 1940, obtained exit visas to enter Spain and Portugal in February 1941, and boarded a Portuguese ship for New York the following month. The second part of this interview, covering my life and work in America, will appear in the next issue.     

Forced vibration of a damped sandwich beam subjected to moving forces

The response of a sandwich beam subjected to moving forces (constant as well as pulsating) is analyzed by the use of Fourier and Laplace transforms and compared with the response of an equivalent elastic beam. The results indicate that the critical speed of force on a sandwich beam is always greater than that on an elastic beam of identical mass per unit length and flexural rigidity, and depends on its geometric and shear parameters. For subcritical speeds, the maximum deflection of a sandwich beam is shown to occur earlier than that of an equivalent elastic beam. An increase in the core shear stiffness is shown to be beneficial in reducing the dynamic magnification of the central deflection of the sandwich beam.     

Experimental investigations of a multi-span flexible structure subjected to moving masses

This paper is concerned with the dynamic response of multi-span flexible structures excited by moving masses. A four-span beam on simple supports was built and the deflections at eight locations along the structure produced by one or two steel balls rolling over it at various speeds are measured by laser displacement transducers. The travelling speeds of the moving masses are also measured by laser sensors. A dynamic (theoretical) model of the structure is established and a statistical assessment of the error variability presented. The numerical results are compared with the experimental results and good agreement is achieved.     

Theoretical study of electromechanical property in a p-type silicon nanoplate for mechanical sensors

Electromechanical property of a p-type single-crystal silicon nanoplate is modelled by a microscopic approach where the hole quantization effect and the spin-orbit coupling effect are taken into account. The visible anisotropic subband structures are calculated by solving self-consistently the stress-dependent 6×6 k.p Schrodinger equation with the Poisson equation. The strong mixing among heavy, light, and split-off holes is quantitatively assessed. The influences of the thickness and the temperature on the piezoresistive coefficient are quantitatively investigated by using the hole concentrations and the effective masses from the complex dispersion structure of the valence band with and without stresses. Our results show that the stress determines the extent to which the band is mixed. The hole quantization effect increases as the thickness decreases, and therefore the valence band is strongly reshaped, resulting in the size-dependent piezoresistivity of the silicon nanoplate. The piezoresistive coefficient increases almost 4 times as the thickness reduces from the bulk to 3 nm, exhibiting a promising application in mechanical sensors.     

Theoretical studies of excitation dynamics in a peridinin-chlorophyll-protein coupled to a metallic nanoparticle

In this work we study the influence of plasmon excitations on the excitation dynamics within a protein complex embedding two chlorophyll molecules coupled to a gold nanosphere. Small separation between the chlorophylls and metallic nanoparticle allows us to simplify the calculations of the Förster energy transfer rate and non-radiative processes by replacing a spherical nanoparticle with a metallic surface. Our results show modifications of all relevant processes and the energy transfer pathways within the system as well as the radiative processes. Plasmon induced changes result in strong qualitative effects of the fluorescence of the studied light-harvesting complex.     

Supporting theory of a new magnetic separator and classifier. Equations and modeling: Part I – Non-magnetic particles

Conventional magnetic separators are only able to split the feeding stream into three different outcome streams. This work presents the theoretical principles of a new device, named MAGCLA™, which is capable to separate and classify particles according to their magnetic susceptibility. This first part of the work reports the equations of movement for non-magnetic particles. The equations for magnetic particles and the limiting conditions for both situations will be given in the remaining parts of this work.A coefficient (T_CG1) was introduced to measure the deviations between the experimental and theoretical values.     

Dynamic analysis of a rectangular plate subjected to multiple forces moving along a circular path

A multi-degree-of-freedom (m.d.o.f.) system excited by a rough moving surface has been developed to study friction-induced oscillations. The normal degrees of freedom allow for oscillatory normal forces, while the normal-tangential coupling of friction produces parametric excitation in the slipping equations of motion. After a modal change of variables, first order averaging has been used to produce a set of autonomous equations of motion. Eigenvalue analysis of the averaged equations has produced stability predictions for the steady sliding position. Numerical integration of the original system of equations has verified the existence of locally unstable oscillations for a system excited by a rough surface input. The combination of velocity-dependent friction and a harmonically varying normal force have been shown to produce large-amplitude oscillations, in some cases leading to stick-slip responses.     

Magnetic susceptibility curves of a nanoparticle assembly, I: Theoretical model and analytical expressions for a single magnetic anisotropy energy

We study a model system made of non-interacting monodomain ferromagnetic nanoparticles, considered as macrospins, with a randomly oriented uniaxial magnetic anisotropy. We derive a simple differential equation governing the magnetic moment evolution in an experimental magnetic susceptibility measurement, at low field and as a function of temperature, following the well-known Zero-Field Cooled/Field Cooled (ZFC/FC) protocol. Exact and approximate analytical solutions are obtained, together for the ZFC curve and the FC curve. The notion of blocking temperature is discussed and the influence of various parameters on the curves is investigated. A crossover temperature is defined and a comparison is made between our progressive crossover model (PCM) and the crude “two states” or abrupt transition model (ATM), where the particles are assumed to be either fully blocked or purely superparamagnetic. We consider here the case of a single magnetic anisotropy energy (MAE), which is a prerequisite before considering the more realistic and experimentally relevant case of an assembly of particles with a MAE distribution (cf. part II that follows).     

Nonlinear traveling wave vibration of a circular cylindrical shell subjected to a moving concentrated harmonic force

This is a study of nonlinear traveling wave response of a cantilever circular cylindrical shell subjected to a concentrated harmonic force moving in a concentric circular path at a constant velocity. Donnell's shallow-shell theory is used, so that moderately large vibrations are analyzed. The problem is reduced to a system of ordinary differential equations by means of the Galerkin method. Frequency-responses for six different mode expansions are studied and compared with that for single mode to find the more contracted and accurate mode expansion investigating traveling wave vibration. The method of harmonic balance is applied to study the nonlinear dynamic response in forced oscillations of this system. Results obtained with analytical method are compared with numerical simulation, and the agreement between them bespeaks the validity of the method developed in this paper. The stability of the period solutions is also examined in detail.     

Dynamic stability of thermoelastic coupling moving plate subjected to follower force

The dynamic characteristics and stability of the moving thermoelastic coupling rectangular plate subjected to uniformly distributed tangential follower force are investigated. Based on the heat conduction equation containing the thermoelastic coupling term and the thin plate theory, the thermoelastic coupling differential equation of motion of the rectangular plate under the action of uniformly distributed tangential follower force is established. Dimensionless complex frequencies of the moving thermoelastic coupling rectangular plate with four edges simply supported, two opposite edges simply supported and other two edges clamped are calculated by the differential quadrature method. The effects of the dimensionless thermoelastic coupling factor and dimensionless moving speed on the stability and critical load of the moving plate are analyzed. The results show that the divergence loads of the first order mode increase with the increase of the dimensionless thermoelastic coupling factor, and decrease with increasing the dimensionless moving speed.     

Vibration analyses of an inclined flat plate subjected to moving loads

The object of this paper is to present a moving mass element so that one may easily perform the dynamic analysis of an inclined plate subjected to moving loads with the effects of inertia force, Coriolis force and centrifugal force considered. To this end, the mass, damping and stiffness matrices of the moving mass element, with respect to the local coordinate system, are derived first by using the principle of superposition and the definition of shape functions. Next, the last property matrices of the moving mass element are transformed into the global coordinate system and combined with the property matrices of the inclined plate itself to determine the effective overall property matrices and the instantaneous equations of motion of the entire vibrating system. Because the property matrices of the moving mass element have something to do with the instantaneous position of the moving load, both the property matrices of the moving mass element and the effective overall ones of the entire vibrating system are time-dependent. At any instant of time, solving the instantaneous equations of motion yields the instantaneous dynamic responses of the inclined plate. For validation, the presented technique is used to determine the dynamic responses of a horizontal pinned–pinned plate subjected to a moving load and a satisfactory agreement with the existing literature is achieved. Furthermore, extensive studies on the inclined plate subjected to moving loads reveal that the influences of moving-load speed, inclined angle of the plate and total number of the moving loads on the dynamic responses of the inclined plate are significant in most cases, and the effects of Coriolis force and centrifugal force are perceptible only in the case of higher moving-load speed.     

Contribution to mathematical modeling of electro-magnetic phenomena in a moving rarefied gas

A new scalar field w, termed a quotient field, is introduced, based on a physical investigation of the question of inertia, into the electrodynamics of material media. The solutions of the generalized system of Maxwell's equations give the dependence of the velocity of the field on the velocity of its source. In the particular case of a dense medium, for which w = 1, the standard theory obtains. For this reason the principle that the velocity of light must be a constant is interpreted as a sufficient condition in an incomplete electromagnetic theory.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 54–58, October, 1990.