Least-squares method for laminated beams with distributed braided piezoelectric composite actuators

2020 ◽  
Vol 31 (18) ◽  
pp. 2165-2176
Author(s):  
Bo Zhou ◽  
Xiao Ma ◽  
Shuai Wang ◽  
Shifeng Xue
Keyword(s):  
Least Squares ◽  
Governing Equation ◽  
Volume Fraction ◽  
Least Squares Method ◽  
Three Dimensional ◽  
Piezoelectric Actuators ◽  
Piezoelectric Composite ◽  
Laminated Beam ◽  
Composite Actuator ◽  
Driving Capability

Piezoelectric ceramics are a very popular material in the field of actuator technology due to their unique piezoelectric properties. However, the brittle behavior of ceramics endangers the reliability of piezoelectric actuators. In this article, the three-dimensional braided piezoelectric composite is utilized to ameliorate the reliability and driving capability of piezoelectric actuators. The static analysis of laminated beam with the distributed braided piezoelectric composite actuator is presented to study its driving capability. Based on the piezoelectric constitutive equations and Euler–Bernoulli beam theory, the governing equation of the piezoelectric laminated beam is derived. The least-squares method for the piezoelectric laminated beam is established to solve the derived governing equation. The current approach is validated by comparison with published results and finite element results. In the numerical examples, the effects of the number and spacing of the three-dimensional braided piezoelectric composite patches, actuator central location, actuator length, actuator thickness ratio, cantilever beam thickness, applied voltage and fiber volume fraction on the driving capability of the distributed braided piezoelectric composite actuator are investigated. This study suggests the potential use of the distributed braided piezoelectric composite actuator in intelligent structures and provides useful guidance for the design and optimization of piezoelectric actuators.

Structure cristalline et moléculaire du cyclopentadiényle dicarbonyle triphénylphosphine manganèse, MnC5H5(CO)2P(C6H5)3

1973 ◽  
Vol 51 (18) ◽  
pp. 3027-3031 ◽  
Author(s):  
Claude Barbeau ◽  
Klaus Sorrento Dichmann ◽  
Louis Ricard
Keyword(s):  
Molecular Structure ◽  
Least Squares ◽  
Least Squares Method ◽  
Three Dimensional ◽  
Triphenyl Phosphine ◽  
Triclinic Space Group ◽  
Space Group ◽  
Bond Lengths ◽  
Atomic Parameter

The crystalano molecular structure of cyclopentadienyl manganese dicarbonyl-triphenyl phosphine has been determined by means of three dimensional data obtained by a Buerger precession camera. 2931 independent intensities were utilized in the refinement of the structure using the least-squares method. The final disagreement factor is 0.11. MnC5H5(CO)2P(C6H5)3 crystallizes in the triclinic space group.[Formula: see text]The molecule shows atomic parameter almost identical to those of MnC5H5(CO)3 except for the Mn—C bond lengths which change from 1.80 to 1.73 Å. The Mn—P distance (2.236 Å) and the unchanged parameters for the Mn—C5H5 group confirm the strong donating power of the cyclopentadienyl group. [Journal translation]

A Three-Dimensional Generalization of Reuleaux’s Method Based on Line Geometry

2006 ◽  
Author(s):  
Jasem Baroon ◽  
Bahram Ravani
Keyword(s):  
Rigid Body ◽  
Least Squares ◽  
Least Squares Method ◽  
Three Dimensional ◽  
Line Geometry ◽  
Basic Form ◽  
Motion Reconstruction ◽  
Linear Solution ◽  
On Line

In kinematics, the problem of motion reconstruction involves generation of a motion from the specification of distinct positions of a rigid body. In its most basic form, this problem involves determination of a screw displacement that would move a rigid body from one position to the next. Much if not all of the previous work in this area has been based on point geometry. In this paper, we develop a method for motion reconstruction based on line geometry. An elegant geometric method is developed based on line geometry that can be considered as a generalization of the classical Reuleaux’s method used in 2D kinematics. The case of over determined system is also considered a linear solution is presented based on least squares method.

N-way partial least squares combined with new self-construction strategy—A promising approach of using near infrared spectral data for quantitative determination of multiple compounds

2019 ◽  
Vol 28 (2) ◽  
pp. 113-121
Author(s):  
Xiang-Zhi Zhang ◽  
Ai-Jun Ma ◽  
Na Feng ◽  
Bao Qiong Li
Keyword(s):  
Quantitative Analysis ◽  
Least Squares ◽  
Partial Least Squares ◽  
Near Infrared ◽  
Least Squares Method ◽  
Three Dimensional ◽  
Near Infrared Spectra ◽  
Infrared Spectral ◽  
Construction Strategy ◽  
Partial Least Squares Method

Because of the complexity of near infrared spectral data, effective strategies are necessary proposed for accurate quantitative analysis purpose. This work explores a new self-construction strategy for the arrangement of conventional near infrared two-dimensional spectra into new self-constructed three-dimensional spectra, and investigate the feasibility of N-way partial least squares combined with the new self-constructed three-dimensional near infrared spectra for obtaining accurate quantitative determination results. A proof-of-concept model system, the quantitative analysis of four components (moisture, oil, protein, and starch) in corn samples, was applied to evaluate the performance of the proposed strategy. The ability of the newly proposed approach to predict the target compounds was checked with test samples. The established models have good predictive power for the target compounds with acceptable values of Rp (range from 0.82 to 0.997) and RMSEP (range from 0.03 to 0.47). Compared with partial least squares method on pretreated near infrared spectra and N-way partial least squares method on the basis of near infrared self-constructed three-dimensional spectra, the proposed method is competitive.

Total Least-Squares Methods for Active View Registration of Three-Dimensional Line Laser Scanning Data

2004 ◽  
Vol 127 (1) ◽  
pp. 50-56 ◽  
Author(s):  
F. Xi ◽  
D. Nancoo ◽  
G. Knopf
Keyword(s):  
Least Squares ◽  
Laser Scanning ◽  
Least Squares Method ◽  
Three Dimensional ◽  
Measurement Data ◽  
Ordinary Least Squares ◽  
Total Least Squares ◽  
Position Measurement ◽  
Point Position ◽  
Ordinary Least Squares Method

In this paper a method is proposed to register three-dimensional line laser scanning data acquired in two different viewpoints. The proposed method is based on three-point position measurement by scanning three reference balls to determine the transformation between two views. Since there are errors in laser scanning data and sphere fitting, the two sets of three-point position measurement data at two different views are both subject to errors. For this reason, total least-squares methods are applied to determine the transformation, because they take into consideration the errors both at inputs and outputs. Simulations and experiment are carried to compare three methods, namely, ordinary least-squares method, unconstrained total least-squares method, and constrained total least-squares method. It is found that the last method gives the most accurate results.

Three Dimensional Simulation of the Heat Dissipation of an Automotive Radiator Based on Porous Media Method

2014 ◽  
Vol 543-547 ◽  
pp. 207-210
Author(s):  
Ning Kang ◽  
Ni Ka Mo ◽  
Wei Qi Zheng
Keyword(s):  
Porous Media ◽  
Least Squares ◽  
Heat Dissipation ◽  
Least Squares Method ◽  
Cell Model ◽  
Three Dimensional ◽  
Cell Models ◽  
Air Inlet ◽  
Dimensional Simulation ◽  
Porous Media Method

12 kinds of automotive radiator cell models were simulated at different air inlet velocities using CFD software Fluent. The distributed drag coefficients of each cell model were obtained by least squares method. Then the whole radiator model whose fins region was replaced by the porous media was simulated. The numerical results were validated by experiments which indicate that the porous media method is reliable. The study shows that the radiator heat dissipation is significantly influenced by fin structure and the model with a fin space of 1.4mm and a louver angle of 23o has the best cooling effect.

Nonlinear Analysis of Laminated Beams with Braided Fiber Piezoelectric Composite Actuators

2020 ◽  
Vol 12 (04) ◽  
pp. 2050043
Author(s):  
Bo Zhou ◽  
Xiao Ma ◽  
Shifeng Xue
Keyword(s):  
Nonlinear Analysis ◽  
Volume Fraction ◽  
Beam Theory ◽  
Piezoelectric Composite ◽  
Laminated Beams ◽  
Fiber Volume ◽  
Novel Approach ◽  
Strain Components ◽  
The Galerkin Method ◽  
Driving Capability

This paper presents a novel approach for improving the reliability and driving capability of piezoelectric actuators by developing braided fiber piezoelectric composite (BFPC) actuators. The nonlinear analysis of laminated beams integrated with the BFPC actuators under electric load is presented. According to Timoshenko beam theory and von Kármán nonlinear geometric relation, the strain components of the piezoelectric laminated beams are obtained. The nonlinear governing equations of the piezoelectric laminated beams are derived by the Galerkin method and principle of minimum potential energy, and then are solved through the direct iterative method. The accuracy of this method is demonstrated by its comparison with the published results. The driving capability of the BFPC actuator and the existing piezoelectric composite actuator is compared. The influences of the fiber volume fraction, actuator thickness, simply supported beam thickness and applied voltage on the driving capability of the BFPC actuators are discussed through a comprehensive parametric study. The numerical results illustrate that the BFPC actuators with excellent driving capability can effectively control the deformation of smart structures.

Verfeinerung der Kristallstruktur eines basaltischen Magnesio-Hastingsites

1981 ◽  
Vol 156 (3-4) ◽  
Author(s):  
E. M. Walitzi ◽  
F. Walter
Keyword(s):  
Crystal Structure ◽  
Least Squares ◽  
Least Squares Method ◽  
Three Dimensional ◽  
Full Matrix ◽  
Space Group ◽  
X Ray

AbstractThe crystal structure of the basaltic clino-amphibole magnesio-hastingsite was refined from three-dimensional photographic X-ray data by a full matrix least-squares method in the space group

Boundary least squares method with three-dimensional harmonic basis of higher order for solving linear div-curl systems with Dirichlet conditions

2019 ◽  
Vol 34 (3) ◽  
pp. 175-186 ◽  
Author(s):  
Marina B. Yuldasheva ◽  
Oleg I. Yuldashev
Keyword(s):  
Least Squares ◽  
Harmonic Functions ◽  
Least Squares Method ◽  
Three Dimensional ◽  
Approximate Solutions ◽  
Piecewise Polynomial ◽  
Dirichlet Conditions ◽  
Convergence Of Approximate Solutions ◽  
Penalty Weight ◽  
Unknown Vector

Abstract Solving linear divergence-curl system with Dirichlet conditions is reduced to finding an unknown vector function in the space of piecewise-polynomial gradients of harmonic functions. In this approach one can use the boundary least squares method with a harmonic basis of a high order of approximation formulated by the authors previously. The justification of this method is given. The properties of the bilinear form and approximating properties of the basis are investigated. Convergence of approximate solutions is proved. A numerical example with estimates of experimental orders of convergence in $\begin{array}{} {\bf V}_h^p \end{array}$-norm for different parameters h, p (p ⩽ 10) is presented. The method does not require specification of penalty weight function.

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