Nanometric transverse displacement metrology in range of hundreds of micrometers with polarization-encoded metasurface

A long range, high precision and compact transverse displacement metrology method is of crucial importance in many research areas. We propose and experimentally demonstrate the first prototype polarization-encoded metasurface for ultrasensitive transverse displacement metrology. The transverse displacement of the metasurface is encoded into the polarization direction of the outgoing light via the Pancharatnam-Berry phase. By measuring the output light polarization direction, the metasurface’s position can be readout directly according to the Malus law. We experimentally demonstrate nanometer displacement resolution with the uncertainty on the order of 100 pm for a large measurement range of 200 µm with the total area of the metasurface being within 900 µm x 900 µm. The measurement range can be extended further using a larger metasurface. Our work largely broadens the existing application areas of metasurface and opens new avenue of applying metasurface in the field of ultrasensitive optical transverse displacement metrology.

Influence of the position of the center of mass of a trailer category O1 on the stability of the road train

In a number of operational properties of motor vehicle (ATZ) at the tendency of increase of speeds of movement the most important indicators of the kept quality, in any modes, are stability and controllability. The choice of constructive parameters of ATZ providing these properties increases active safety of operation and reduces probability of road accidents during the execution of transport operations. From the point of view of practical purposes at operation of ATZ not only the reason of infringement of stability becomes important, and reaction of ATZ to it and control actions of the driver which are ambiguous and unstable. Therefore, it is assumed that the stability and controllability of the ATZ movement should be provided by the design parameters of the machine itself. The result of the analysis of the course stability of the road train was the expression of the critical speed of rectilinear motion. According to the developed mathematical model, the critical velocity is determined. Calculations were made for a road train consisting of a VAZ-2107 car and the uniaxial trailer for different loads of the trailer and different location of its center of mass. According to the initial data inherent in the nominal load of the car and the maximum load of the trailer and the location of the center of mass of the trailer on the longitudinal axis and in the center of mass of the loading platform, the critical speed is about 36 m/s (129.6 km/h). In transient modes of movement, such as "entering the circle and moving in a circle", "jerk of the steering wheel", "shift", "snake", displacement of the center of mass of the trailer in both the longitudinal and transverse planes, the critical speed decreases, and more significantly reduction occurs when the transverse displacement of the center of mass. Thus, if at the maximum displacement of the center of mass of the trailer on the x-axis (x = -0.75 m) the rate of oscillation instability decreases by 36.4% (Gn = 350 kg), 38.4% (Gn = 500 kg) and 44.3% (Gn = 750 kg) in comparison with this speed in the absence of displacement, then at the maximum displacement along the y -axis in the rate of oscillation instability decreases by 45.4%, 55.2% and 63.6%, respectively. In the case of such a trailer loading, the center of mass of the trailer shifts along both the x-axis and the y-axis, there is a further decrease in both the critical speed of the road train and the rate of oscillation instability. This must be taken into account when loading the trailer.

Axisymmetric Free Vibration of Layered Cylindrical Shell Filled with Fluid

The aim of the study is to analyse the axisymmetric free vibration of layered cylindrical shells filled with a quiescent fluid. The fluid is assumed to be incompressible and inviscid. The equations of axisymmetric vibrations of layered cylindrical shell filled with fluid, on the longitudinal and transverse displacement components are obtained using Love’s first approximation theory. The solutions of displacement functions are assumed in a separable form to obtain a system of coupled differential equations in terms of displacement functions. The displacement functions are approximated by Bickley-type splines. A generalized eigenvalue problem is obtained and solved numerically for a frequency parameter and an associated eigenvector of spline coefficients. Two layered shells with three different types of materials under clamped-clamped boundary conditions are considered. Parametric studies are made on the variation of the frequency parameter with respect to length-to-radius ratio and length-to-thickness ratio.

A New Beam Finite Element for Static Bending Analysis of Slender Transversely Cracked Beams on Two-Parametric Soils

This paper derives an original finite element for the static bending analysis of a transversely cracked uniform beam resting on a two-parametric elastic foundation. In the simplified computational model based on the Euler–Bernoulli theory of small displacements, the crack is represented by a linear rotational spring connecting two elastic members. The derivations of approximate transverse displacement functions, stiffness matrix coefficients, and the load vector for a linearly distributed load along the entire beam element are based on novel cubic polynomial interpolation functions, including the second soil parameter. Moreover, all derived expressions are obtained in closed forms, which allow easy implementation in existing finite element software. Two numerical examples are presented in order to substantiate the discussed approach. They cover both possible analytical solution forms that may occur (depending on the problem parameters) from the same governing differential equation of the considered problem. Therefore, several response parameters are studied for each example (with additional emphasis on their convergence) and compared with the corresponding analytical solution, thus proving the quality of the obtained finite element.

Transverse Response of an Axially Moving Beam with Intermediate Viscoelastic Support

This study presented the transverse vibration of an axially moving beam with an intermediate nonlinear viscoelastic foundation. Hamilton’s principle was used to derive the nonlinear equations of motion. The finite difference and state-space methods transform the partial differential equations into a system of coupled first-order regular differential equations. The numerical modeling procedures are utilized for evaluating the effects of parameters, such as axial translation velocity, flexure rigidities of the beam, damping, and stiffness of the support on the transverse response amplitude and frequencies. It is observed that the dimensionless fundamental frequency and magnitude of axial speed had an inverse correlation. Furthermore, increasing the flexure rigidity of the beam reduced the transverse displacement, but at the same instant, fundamental frequency rises. Vibration amplitude is found to be significantly reduced with higher damping of support. It is also observed that an increase in the foundation damping leads to lower fundamental frequencies, whereas increasing the foundation stiffness results in higher frequencies.

The Question of Drawing a Design Scheme of a Wagon with a Non-Symmetrically Located Freight

Violations of the stability of a wagon with an asymmetrically positioned freight can lead to a threat to the safety of train traffic, the safety of freight on the route and transport facilities. The design diagram of a wagon with an asymmetrically located freight drawn up in the article and the equations obtained in an analytical way, oscillations of the sprung mass of a wagon with an asymmetric arrangement of the freight, characterizing the longitudinal and transverse displacement of the center of mass of the freight, can be used for mathematical modeling of forced vibrations and impact on the track of a wagon with asymmetrically located freight in various operating conditions.

EXPONENTIAL STABILITY OF LAMINATED BEAM WITH CONSTANT DELAY FEEDBACK

In this article, we consider a system of laminated beams with an internal constant delay term in the transverse displacement. We prove that the dissipation through structural damping at the interface is strong enough to exponentially stabilize the system under suitable assumptions on delay feedback and coefficients of wave propagation speed.

First-order VEM for Reissner–Mindlin plates

In this paper, a first-order virtual element method for Reissner–Mindlin plates is presented. A standard displacement-based variational formulation is employed, assuming transverse displacement and rotations as independent variables. In the framework of the first-order virtual element, a piecewise linear approximation is assumed for both displacement and rotations on the boundary of the element. The consistent term of the stiffness matrix is determined assuming uncoupled polynomial approximations for the generalized strains, with different polynomial degrees for bending and shear parts. In order to mitigate shear locking in the thin-plate limit while keeping the element formulation as simple as possible, a selective scheme for the stabilization term of the stiffness matrix is introduced, to indirectly enrich the approximation of the transverse displacement with respect to that of the rotations. Element performance is tested on various numerical examples involving both thin and thick plates and different polygonal meshes.

Plane wave in non-local semiconducting rotating media with Hall effect and three-phase lag fractional order heat transfer

This paper deals with the propagation of the plane wave in a nonlocal magneto-thermoelastic semiconductor solid with rotation. The fractional-order three-phase lag theory of thermoelasticity with two temperatures has been applied. When a longitudinal wave is incident on the surface z = 0, four types of reflected coupled longitudinal waves (the coupled longitudinal displacement wave, the coupled thermal wave, coupled carrier density wave, and coupled transverse displacement wave) are identified. The plane wave characteristics such as phase velocities, specific loss, attenuation coefficient, and penetration depth of various reflected waves are computed. The effects of two temperatures, non-local parameter, fractional order parameter, and Hall current on these wave characteristics are illustrated graphically with the use of MATLAB software.

Structural Dynamic Response of a Shield Tunnel under Aircraft Taxiing Load

Dynamic load is an important factor affecting the safety and stability of subway tunnel structures. To obtain the variation law of shield tunnel structure dynamic response under aircraft taxiing load, a three-dimensional numerical simulation of such tunnel under the action of aircraft taxiing load is performed on the basis of a project involving a shield tunnel orthogonal underpass taxiway. The effects of sliding speed and tunnel depth on the structure of the shield tunnel are also analyzed. The results show that the transverse displacement and acceleration response of tunnel segment exhibit evident time-space effect under the action of aircraft taxiing load. The transverse displacement and arch waist acceleration of the shield segment increase first and then decrease. The transverse displacement of the arch waist reaches its maximum when the aircraft taxis directly above the tunnel. The sliding speed exhibits an evident influence on the dynamic response of shield tunnel structure. The vertical and convergence displacements of tunnel segments increase with the increase in sliding speed. The dynamic response of tunnel structure is significantly affected by the factors of tunnel buried depth. The vertical and convergence displacements of tunnel segments decrease with the increase in tunnel buried depth. Therefore, the safety of the shield tunnel structure can be ensured by controlling the taxiing speed when the aircraft taxis directly above the tunnel. The measures of increasing the buried depth of the tunnel or strengthening the tunnel structure need to be considered when the taxiing speed is large.