scholarly journals A Camera Intrinsic Matrix-Free Calibration Method for Laser Triangulation Sensor

Sensors ◽  
2021 ◽  
Vol 21 (2) ◽  
pp. 559
Author(s):  
Xuzhan Chen ◽  
Youping Chen ◽  
Bing Chen ◽  
Zhuo He ◽  
Yunxiu Ma ◽  
...  
Keyword(s):  
Closed Form Solution ◽  
Calibration Method ◽  
Industrial Applications ◽  
Form Solution ◽  
Displacement Measurement ◽  
Necessary Condition ◽  
Laser Triangulation ◽  
Depth Information ◽  
One Dimensional ◽  
Matrix Free

Laser triangulation sensors (LTS) are widely used to acquire depth information in industrial applications. However, the parameters of the components, e.g., the camera, of the off-the-shelf LTS are typically unknown. This makes it difficult to recalibrate the degenerated LTS devices during regular maintenance operations. In this paper, a novel one-dimensional target-based camera intrinsic matrix-free LTS calibration method is proposed. In contrast to conventional methods that calibrate the LTS based on the precise camera intrinsic matrix, we formulate the LTS calibration as an optimization problem taking all parameters of the LTS into account, simultaneously. In this way, many pairs of the camera intrinsic matrix and the equation of the laser plane can be solved and different pairs of parameters are equivalent for displacement measurement. A closed-form solution of the position of the one-dimensional target is proposed to make the parameters of the LTS optimizable. The results of simulations and experiments show that the proposed method can calibrate the LTS without knowing the camera intrinsic matrix. In addition, the proposed approach significantly improves the displacement measurement precision of the LTS after calibration. In conclusion, the proposed method proved that the precise camera intrinsic matrix is not the necessary condition for LTS displacement measurement.

Free Vibration of a Multilayered One-Dimensional Quasi-Crystal Plate

2014 ◽  
Vol 136 (4) ◽  
Author(s):  
Natalie Waksmanski ◽  
Ernian Pan ◽  
Lian-Zhi Yang ◽  
Yang Gao
Keyword(s):  
Free Vibration ◽  
Natural Frequencies ◽  
Closed Form Solution ◽  
Form Solution ◽  
Crystal Plate ◽  
Mode Shapes ◽  
Sandwich Plates ◽  
One Dimensional ◽  
Propagator Matrix ◽  
Multilayered Plates

An exact closed-form solution of free vibration of a simply supported and multilayered one-dimensional (1D) quasi-crystal (QC) plate is derived using the pseudo-Stroh formulation and propagator matrix method. Natural frequencies and mode shapes are presented for a homogenous QC plate, a homogenous crystal plate, and two sandwich plates made of crystals and QCs. The natural frequencies and the corresponding mode shapes of the plates show the influence of stacking sequence on multilayered plates and the different roles phonon and phason modes play in dynamic analysis of QCs. This work could be employed to further expand the applications of QCs especially if used as composite materials.

scholarly journals The generalized viscoelastic spring

2020 ◽  
Vol 476 (2236) ◽  
pp. 20190881
Author(s):  
Kostas P. Soldatos
Keyword(s):  
Viscous Flow ◽  
A Priori ◽  
Closed Form Solution ◽  
Form Solution ◽  
Viscoelastic Deformation ◽  
One Dimensional ◽  
Flow Formation ◽  
Inelastic Material ◽  
Flow Potential ◽  
Well Posed

A spring/rod model is presented that describes one-dimensional behaviour of solids susceptible to large or small viscoelastic deformation. Derivation of its constitutive equation is underpinned by the fact that the internal energy, which the elastic part of deformation stores in the spring, changes in time with the observed strain as well as with some, unknown part of the strain-rate. The latter emerges through the action of a viscous flow potential and is the source of inelastic deformation. Thus, unlike its conventional viscoelasticity counterparts, the model does not postulate a priori a rule that relates strain with viscous flow formation. Instead, it considers that such a rule, as well as other important features of combined elastic and inelastic material response, should become known a posteriori through the solution of a relevant, well-posed boundary value problem. This paper begins with considerations compatible with large viscoelastic deformations and gradually progresses through simpler modelling situations. The latter also include the case of small viscoelastic strain that underpins formulation of classical, spring-dashpot viscoelastic models. In an example application, a relevant closed-form solution is obtained for a spring undergoing small viscoelastic deformation under the influence of a viscous flow potential which is quadratic in the stress.

scholarly journals MHD Nanofluids in a Permeable Channel with Porosity

Symmetry ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 378 ◽  
Author(s):  
Ilyas Khan ◽  
Aisha Alqahtani
Keyword(s):  
Magnetic Parameter ◽  
Flow Direction ◽  
Perturbation Technique ◽  
Closed Form Solution ◽  
Form Solution ◽  
Convection Flow ◽  
Temperature Profiles ◽  
Uniform Temperature ◽  
One Dimensional ◽  
Physical Conditions

This paper introduces a mathematical model of a convection flow of magnetohydrodynamic (MHD) nanofluid in a channel embedded in a porous medium. The flow along the walls, characterized by a non-uniform temperature, is under the effect of the uniform magnetic field acting transversely to the flow direction. The walls of the channel are permeable. The flow is due to convection combined with uniform suction/injection at the boundary. The model is formulated in terms of unsteady, one-dimensional partial differential equations (PDEs) with imposed physical conditions. The cluster effect of nanoparticles is demonstrated in the C 2 H 6 O 2 , and H 2 O base fluids. The perturbation technique is used to obtain a closed-form solution for the velocity and temperature distributions. Based on numerical experiments, it is concluded that both the velocity and temperature profiles are significantly affected by ϕ . Moreover, the magnetic parameter retards the nanofluid motion whereas porosity accelerates it. Each H 2 O -based and C 2 H 6 O 2 -based nanofluid in the suction case have a higher magnitude of velocity as compared to the injections case.

New exact results for the defective square lattice

1976 ◽  
Vol 80 (2) ◽  
pp. 365-381 ◽  
Author(s):  
G. Ronca
Keyword(s):  
Closed Form Solution ◽  
Exact Result ◽  
Form Solution ◽  
Square Lattice ◽  
Zero Temperature ◽  
Real Crystal ◽  
One Dimensional ◽  
Resonance Modes ◽  
The One ◽  
Dimensional Crystal

Since the publication of the fundamental papers by Lifshitz (1, 2) and Montroll and Potts (3, 4) many authors have investigated the effect of an isotopic impurity on the lattice vibrations of a harmonic crystal at zero temperature. A fairly broad knowledge is now available on scattering amplitudes, localized modes and resonance modes (6, 7). Nevertheless, as pointed out by Maradudin and Montroll (see (7), p. 430), a closed form solution to the problem has been found only for the one-dimensional crystal, the work done on two and three-dimensional crystals being predominantly numerical. Unfortunately the one-dimensional crystal, as an approximation for a real crystal is an oversimplified model, incapable as it is of exhibiting resonance modes. To the author's knowledge the most significant exact result concerning the classical behaviour at zero temperature of crystals having a dimensionality higher than one is the connexion, calculated by Mahanty et al. (5) between localized mode frequency and impurity mass for the case of a square lattice undergoing planar vibrations.

Fracture behavior of periodically bonded interface of piezoelectric bi-material under compressive–shear loading

2019 ◽  
Vol 24 (10) ◽  
pp. 3216-3230 ◽  
Author(s):  
S Kozinov ◽  
A Sheveleva ◽  
V Loboda
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Fracture Behavior ◽  
Compressive Loading ◽  
Closed Form Solution ◽  
Industrial Applications ◽  
Shear Loading ◽  
Form Solution ◽  
Applied Loading

A closed-form solution is constructed for a bi-material consisting of two piezoelectric (or piezoelectric and dielectric) half-planes, which are periodically bonded along the interface and can partially contact along the initially unbonded parts. Under compressive loading, the size of the frictionless contact zone is usually quite large; in some cases the interface is completely closed. Such a situation is frequently observed in industrial applications. Since the periodic bonding of two different materials is extremely widespread, it is very important to study the influence of the mutual material properties of the composite and the applied loading on the size and shape of the opened regions, as well as the stress intensity factor at the bonding points. To formulate the problem, the electromechanical factors are presented through piecewise analytic functions, so that the problem in question is reduced to the combined periodic Dirichlet–Riemann problem, which is solved exactly. The obtained solution provides explicit formulas for the mechanical stresses and displacements along the interface and allows one to find the dependence of the contact zones and the stress intensity factor on the ratio of the bonded parts of the interface to the period for the different values of applied loading and materials.

On the Numerical Solution of One-Dimensional Continuum Problems Using the Theory of a Cosserat Point

1985 ◽  
Vol 52 (2) ◽  
pp. 373-378 ◽  
Author(s):  
M. B. Rubin
Keyword(s):  
Numerical Solution ◽  
Body Force ◽  
Closed Form Solution ◽  
Form Solution ◽  
Element Approximation ◽  
One Dimensional ◽  
Linear Elastic ◽  
Elastic Bar ◽  
Cosserat Point ◽  
Nonlinear Elastic

The theory of a Cosserat point is specialized to describe the motion of a one-dimensional continuum. Attention is focused on two problems of an elastic bar. Vibration of a linear-elastic bar is considered in the first problem and static deformation of a nonlinear-elastic bar subjected to a uniform body force is considered in the second problem. A closed-form solution is derived for each problem by dividing the bar into two elements, each of which is modeled as a Cosserat point. The predictions of the two-element approximation are shown to be very accurate.

Active Noise Cancellation Using Feedforward and Hybrid Controls

2001 ◽  
Author(s):  
A. R. Ohadi ◽  
E. Esmailzadeh ◽  
A. Alasty
Keyword(s):  
Active Noise Control ◽  
Closed Form Solution ◽  
Form Solution ◽  
Time Shift ◽  
One Dimensional ◽  
Acoustic Feedback ◽  
Active Noise ◽  
Adaptive Weight ◽  
Fxlms Algorithm ◽  
Overall Performance

Abstract The exact closed-form solution of a one-dimensional wave equation including the viscous damping effect has been obtained from the Green’s function. Accurate models for the error sensor and secondary loudspeaker, which includes the electro-mechanical and mechano-acoustical couplings, have been used and the transfer function of the primary, secondary and acoustic feedback paths of the active noise control system have been obtained. The generalized form of the classical FXLMS algorithm, referred to G-FXLMS algorithm, has been developed. In contrast to the FXLMS algorithm, G-FXLMS algorithm does not neglect the time shift of the filter coefficients and employs a more general recursive adaptive weight update equation, which can improve the performance of FXLMS algorithm. Simulation results presented to compare the performance of the feedforward and hybrid ANC systems and to study the effect of acoustical feedbacks and boundary conditions on the overall performance of ANC systems.

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