Multibody Systems with Flexible Elements

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Computer".

Deadline for manuscript submissions: closed (30 April 2021) | Viewed by 39430

Printed Edition Available!
A printed edition of this Special Issue is available here.

Special Issue Editors


E-Mail Website
Guest Editor
Department of Mathematics and Computer Science, Transilvania University of Brasov, 500093 Brasov, Romania
Interests: differential equations; partial differential equations; equations of evolution; integral equations; mixed initial-boundary value problems for PDE; termoelasticity; media with microstretch; environments goals; nonlinear problems
Special Issues, Collections and Topics in MDPI journals

E-Mail Website
Guest Editor
Department of Mechanics, “Transilvania” University of Brasov, Brasov, Romania
Interests: mechanics; vibrations; elasticity; composite materials; analytical mechanics
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Multibody systems with flexible elements represent mechanical systems made by many elastic (and rigid) bodies interconnected meeting a functional, technical or biological assembly. The displacements of each or some of the elements of the system are generally large and cannot be neglected in mechanical modeling. The study of these multibody systems covers many industrial fields but also has applications in medicine, sports, and art. The systematic treatment of the dynamic behavior of interconnected bodies has led to an important number of formalisms for multibody systems within mechanics. At present, this formalism is used in large engineering fields, especially in robotics and vehicle dynamics. The formalism of multicorp systems offers a means of algorithmic analysis, assisted by the computer, and a means of simulating and optimizing an arbitrary movement of a possible high number of elastic bodies in the connection. The domain where researchers apply these methods are robotics, simulation in the dynamics of vehicles, biomechanics, aerospace engineering (helicopters, the behavior of cars in the gravitational field), engines with internal combustion, gearboxes, transmissions, mechanisms, the cellulose industry, simulation of particle behavior (granulated particles and molecules), dynamic simulation, military applications, computer games, medicine, and rehabilitation.

Isotropy and homogeneity of the Euclidian space and the homogeneity of the time leads to conservation laws and symmetry of differential evolution equations that describe the behavior of such mechanical systems.

Prof. Dr. Marin Marin
Prof. Dr. Dumitru Baleanu
Prof. Dr. Sorin Vlase
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Symmetry is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • multibody systems
  • flexible elements
  • robotics
  • vehicle dynamics
  • dynamic simulation
  • military applications
  • aerospatial engineering

Published Papers (16 papers)

Order results
Result details
Select all
Export citation of selected articles as:

Editorial

Jump to: Research

5 pages, 220 KiB  
Editorial
Multibody Systems with Flexible Elements
by Marin Marin, Dumitru Băleanu and Sorin Vlase
Symmetry 2021, 13(8), 1359; https://doi.org/10.3390/sym13081359 - 27 Jul 2021
Viewed by 1142
Abstract
The formalism of multibody systems offers a means of computer-assisted algorithmic analysis and a means of simulating and optimizing an arbitrary movement of a possible high number of elastic bodies in the connection [...] Full article
(This article belongs to the Special Issue Multibody Systems with Flexible Elements)

Research

Jump to: Editorial

12 pages, 6489 KiB  
Article
Experimental Dynamic Rigidity of an Elastic Coupling with Bolts
by Marilena Ghitescu, Ion-Marius Ghitescu, Sorin Vlase and Paul Nicolae Borza
Symmetry 2021, 13(6), 989; https://doi.org/10.3390/sym13060989 - 02 Jun 2021
Cited by 3 | Viewed by 2280
Abstract
The paper presents an elastic coupling with bolts and intermediary non-metallic elements, which allows for radial and axial deviation and can absorb shocks and torsional vibrations. The designed bolts have a particular shape of a circular area of a length equal to the [...] Read more.
The paper presents an elastic coupling with bolts and intermediary non-metallic elements, which allows for radial and axial deviation and can absorb shocks and torsional vibrations. The designed bolts have a particular shape of a circular area of a length equal to the width of the non-metallic element, a cylindrical area larger than the diameter of the cylindrical groove where the non-metallic elements are mounted, and a cylindrical area smaller than the threaded area to avoid stress concentrators and bolt breakage. The coupling represents a symmetrical piece, having two planes of symmetry. Therefore, the study of such a mechanical system can be considerably simplified considering the design and description of the repeating elements. The novelty of this coupling consists in the existence of an intermediate disc between two half-couplings (driving and driven half-coupling). The non-metallic elements with different shapes are made of different types of rubber, mounted on cylindrical bolts fixed by the driving half-coupling, transmitting the motion in both directions. Full article
(This article belongs to the Special Issue Multibody Systems with Flexible Elements)
Show Figures

Figure 1

13 pages, 285 KiB  
Article
Symmetries for Nonconservative Field Theories on Time Scale
by Octavian Postavaru and Antonela Toma
Symmetry 2021, 13(4), 552; https://doi.org/10.3390/sym13040552 - 26 Mar 2021
Cited by 4 | Viewed by 1330
Abstract
Symmetries and their associated conserved quantities are of great importance in the study of dynamic systems. In this paper, we describe nonconservative field theories on time scales—a model that brings together, in a single theory, discrete and continuous cases. After defining Hamilton’s principle [...] Read more.
Symmetries and their associated conserved quantities are of great importance in the study of dynamic systems. In this paper, we describe nonconservative field theories on time scales—a model that brings together, in a single theory, discrete and continuous cases. After defining Hamilton’s principle for nonconservative field theories on time scales, we obtain the associated Lagrange equations. Next, based on the Hamilton’s action invariance for nonconservative field theories on time scales under the action of some infinitesimal transformations, we establish symmetric and quasi-symmetric Noether transformations, as well as generalized quasi-symmetric Noether transformations. Once the Noether symmetry selection criteria are defined, the conserved quantities for the nonconservative field theories on time scales are identified. We conclude with two examples to illustrate the applicability of the theory. Full article
(This article belongs to the Special Issue Multibody Systems with Flexible Elements)
33 pages, 684 KiB  
Article
Controlling Wolbachia Transmission and Invasion Dynamics among Aedes Aegypti Population via Impulsive Control Strategy
by Joseph Dianavinnarasi, Ramachandran Raja, Jehad Alzabut, Michał Niezabitowski and Ovidiu Bagdasar
Symmetry 2021, 13(3), 434; https://doi.org/10.3390/sym13030434 - 08 Mar 2021
Cited by 6 | Viewed by 1806
Abstract
This work is devoted to analyzing an impulsive control synthesis to maintain the self-sustainability of Wolbachia among Aedes Aegypti mosquitoes. The present paper provides a fractional order Wolbachia invasive model. Through fixed point theory, this work derives the existence and uniqueness results for [...] Read more.
This work is devoted to analyzing an impulsive control synthesis to maintain the self-sustainability of Wolbachia among Aedes Aegypti mosquitoes. The present paper provides a fractional order Wolbachia invasive model. Through fixed point theory, this work derives the existence and uniqueness results for the proposed model. Also, we performed a global Mittag-Leffler stability analysis via Linear Matrix Inequality theory and Lyapunov theory. As a result of this controller synthesis, the sustainability of Wolbachia is preserved and non-Wolbachia mosquitoes are eradicated. Finally, a numerical simulation is established for the published data to analyze the nature of the proposed Wolbachia invasive model. Full article
(This article belongs to the Special Issue Multibody Systems with Flexible Elements)
Show Figures

Figure 1

15 pages, 2253 KiB  
Article
New Command Mechanism of Flaps and Wings of a Light Sport Aircraft
by Ion-Marius Ghiţescu, Maria Luminita Scutaru, Marilena Ghiţescu, Paul Nicolae Borza and Marin Marin
Symmetry 2021, 13(2), 221; https://doi.org/10.3390/sym13020221 - 29 Jan 2021
Cited by 4 | Viewed by 2977
Abstract
Commercial aircraft have well-designed and optimized systems, the result of a huge experience in the field, due to the large fleet of aircraft in operation. For light, utility, or sports aircraft, with a multitude of shapes, tasks, and construction types, there are different [...] Read more.
Commercial aircraft have well-designed and optimized systems, the result of a huge experience in the field, due to the large fleet of aircraft in operation. For light, utility, or sports aircraft, with a multitude of shapes, tasks, and construction types, there are different solutions that seek to best meet the requirements of the designed aircraft. In this sense, for a sport plane, an increased maneuverability is desired, and the system that controls flaps and wing must be properly designed. A new flap mechanism command solution is proposed and justified in the paper, for use in sports and recreational aviation, in order to achieve angles of braking greater than 40°, take-off and landing in a shorter time and over a shorter distance, as well as the gliding of the aircraft in critical flight conditions or when fuel economy is needed. A finite element model is used to verify the optimized command system for the flap and wing and to check if the strength structure of the aircraft is properly designed. The main result consists of the new design command system for flaps and wings and in verifying, by calculation, the acceptability of the new mechanism proposed from the point of view of the strength of the materials. Full article
(This article belongs to the Special Issue Multibody Systems with Flexible Elements)
Show Figures

Figure 1

16 pages, 5360 KiB  
Article
A New Optimized Solution for a Flexible Coupling with Bolts Used in the Mechanical Transmissions
by Marilena Ghiţescu, Ion-Marius Ghiţescu, Paul Nicolae Borza and Sorin Vlase
Symmetry 2021, 13(2), 171; https://doi.org/10.3390/sym13020171 - 22 Jan 2021
Cited by 3 | Viewed by 1639
Abstract
The paper presents a new constructive and functional solution of flexible coupling with bolts and nonmetallic intermediary elements. The bolts have a special shape in the sense that they have a milled area on a certain length equal to the width of the [...] Read more.
The paper presents a new constructive and functional solution of flexible coupling with bolts and nonmetallic intermediary elements. The bolts have a special shape in the sense that they have a milled area on a certain length equal to the width of the non-metallic element, a cylindrical area that reduces the stress concentrators at the diameter passages. The novelty of this coupling consists of the existence of one intermediary disk between two semi couplings (driver and driven semi couplings). This is fixed by the semi-coupling on the right side, the intermediary disc having milled four locations in which to mount the left, as the right has a metal plate with a special shape of eight metallic plates that are mounted with screws in the four milled places processed on the intermediate disc. The nonmetallic elements have various forms and can be made from different qualities of rubber mounted on the bolts. Eight milled bolts (four on each semi-coupling) allow the transmission of the torsion moment in both directions of rotation, in one direction becoming rigid and thus behaving like a safety coupling. Finite element method is used to obtain the mechanical response of this new type of coupling. Full article
(This article belongs to the Special Issue Multibody Systems with Flexible Elements)
Show Figures

Figure 1

22 pages, 11359 KiB  
Article
Design and Analysis of Inertial Platform Insulation of the ELI-NP Project of Laser and Gamma Beam Systems
by Calin Itu, Polidor Bratu, Paul Nicolae Borza, Sorin Vlase and Dorin Lixandroiu
Symmetry 2020, 12(12), 1972; https://doi.org/10.3390/sym12121972 - 28 Nov 2020
Cited by 13 | Viewed by 1652
Abstract
All the installations, devices, and annexes within the laser and the gamma ray production system within the ELI-NP project from Magurele are installed on an inertial platform that weighs over 54,000 tons. The platform is made of concrete, is insulated from the outside [...] Read more.
All the installations, devices, and annexes within the laser and the gamma ray production system within the ELI-NP project from Magurele are installed on an inertial platform that weighs over 54,000 tons. The platform is made of concrete, is insulated from the outside environment, and is supported by spring batteries and shock absorbers. The flatness of this platform respects some very strict standards, and, taking into account the processes that take place on the platform, the transmission of the different trepidations of the environment to the inertial mass must be extremely low. For this reason, a static study and a vibration analysis of the platform, performed in this paper, are required. The static analysis verifies if the flatness of the platform can be observed in operating conditions, and the dynamic analysis verifies how excitations coming from the external environment can be transmitted to the measuring equipment. The finite element method is used both to determine the deformability of the concrete platform for different loads, placed at different points and to determine its eigenvalues and its eigenmodes of vibration. The obtained results are analyzed and constructive solutions are proposed to improve the realized system, through a judicious placement of the installations and the distribution of the masses on the platform. Full article
(This article belongs to the Special Issue Multibody Systems with Flexible Elements)
Show Figures

Figure 1

11 pages, 2623 KiB  
Article
Multibody System with Elastic Connections for Dynamic Modeling of Compactor Vibratory Rollers
by Polidor Bratu
Symmetry 2020, 12(10), 1617; https://doi.org/10.3390/sym12101617 - 29 Sep 2020
Cited by 5 | Viewed by 1655
Abstract
The dynamic model of the system of bodies with elastic connections substantiates the conceptual basis for evaluating the technological vibrations of the compactor roller as well as of the parameters of the vibrations transmitted from the vibration source to the remainder of the [...] Read more.
The dynamic model of the system of bodies with elastic connections substantiates the conceptual basis for evaluating the technological vibrations of the compactor roller as well as of the parameters of the vibrations transmitted from the vibration source to the remainder of the equipment components. In essence, the multi-body model with linear elastic connections consists of a body in vertical translational motion for vibrating roller with mass m1, a body with composed motion of vertical translation and rotation around the transverse axis passing through its weight center for the chassis of the car with mass m and the moment of mass inertia J and a body of mass m’ representing the traction tire-wheel system located on the opposite side of the vibrating roller. The study analyzes the stationary motion of the system of bodies that are in vibrational regime as a result of the harmonic excitation of the m mass body, with the force F(t)= m0rω2sinωt, generated by the inertial vibrator located inside the vibrating roller. The vibrator is characterized by the total unbalanced m0 mass in rotational motion at distance r from the axis of rotation and the angular velocity or circular frequency ω. Full article
(This article belongs to the Special Issue Multibody Systems with Flexible Elements)
Show Figures

Figure 1

21 pages, 8730 KiB  
Article
Parameterized Design and Dynamic Analysis of a Reusable Launch Vehicle Landing System with Semi-Active Control
by Chen Wang, Jinbao Chen, Shan Jia and Heng Chen
Symmetry 2020, 12(9), 1572; https://doi.org/10.3390/sym12091572 - 22 Sep 2020
Cited by 5 | Viewed by 6272
Abstract
Reusable launch vehicles (RLVs) are a solution for effective and economic transportation in future aerospace exploration. However, RLVs are limited to being used under simple landing conditions (small landing velocity and angle) due to their poor adaptability and the high rocket acceleration of [...] Read more.
Reusable launch vehicles (RLVs) are a solution for effective and economic transportation in future aerospace exploration. However, RLVs are limited to being used under simple landing conditions (small landing velocity and angle) due to their poor adaptability and the high rocket acceleration of current landing systems. In this paper, an adaptive RLV landing system with semi-active control is proposed. The proposed landing system can adjust the damping forces of primary strut dampers through semi-actively controlled currents in accordance with practical landing conditions. A landing dynamic model of the proposed landing system is built. According to the dynamic model, an light and effective RLV landing system is parametrically designed based on the response surface methodology. Dynamic simulations validate the proposed landing system under landing conditions including the highest rocket acceleration and the greatest damper compressions. The simulation results show that the proposed landing system with semi-active control has better landing performance than current landing systems that use passive liquid or liquid–honeycomb dampers. Additionally, the flexibility and friction of the structure are discussed in the simulations. Compared to rigid models, flexible models decrease rocket acceleration by 51% and 54% at the touch down moments under these two landing conditions, respectively. The friction increases rocket acceleration by less than 1%. However, both flexibility and friction have little influence on the distance between the rocket and ground, or the compression strokes of the dampers. Full article
(This article belongs to the Special Issue Multibody Systems with Flexible Elements)
Show Figures

Figure 1

21 pages, 8021 KiB  
Article
A Multibody Inertial Propulsion Drive with Symmetrically Placed Balls Rotating on Eccentric Trajectories
by Attila Gerocs, Gilbert-Rainer Gillich, Dorian Nedelcu and Zoltan-Iosif Korka
Symmetry 2020, 12(9), 1422; https://doi.org/10.3390/sym12091422 - 26 Aug 2020
Cited by 4 | Viewed by 3820
Abstract
Starting with the last century, a lot of enthusiastic researchers have invested significant time and energy in proposing various drives capable to generate linear propulsion force. Regrettably, only a few of these devices passed the patent phase and have been practically materialized. The [...] Read more.
Starting with the last century, a lot of enthusiastic researchers have invested significant time and energy in proposing various drives capable to generate linear propulsion force. Regrettably, only a few of these devices passed the patent phase and have been practically materialized. The aim of this paper was to simulate the dynamic behavior of an inertial propulsion drive (IPD) developed by the authors, to demonstrate its functionality. The core of the IPD consists of two symmetric drivers that each performs rotation of eight steel balls on an eccentric path. We propose three solutions for the element which maintain the off-center trajectory of the balls. For the simulation, we used the multibody system approach and determine the evolution of the displacement, velocity, and power consumption. Further, we analyze the collisions between the elements of the system and the influence of this phenomenon on the dynamic behavior of the IPD. We found that collisions generate impact forces which affect the ball acceleration values achieved by simulation. We have concluded that the developed system is capable to generate linear movement. In addition, in terms of velocity and power consumption, the best constructive version of the retaining disk is that which has a cylindrical inner bore placed eccentric relative to the rotation center of the balls. Full article
(This article belongs to the Special Issue Multibody Systems with Flexible Elements)
Show Figures

Figure 1

21 pages, 3958 KiB  
Article
Experimental Assessments on the Evaluation of Wire Rope Characteristics as Helical Symmetrical Multi-body Ensembles
by Gina Diana Musca (Anghelache), Carmen Debeleac and Sorin Vlase
Symmetry 2020, 12(8), 1231; https://doi.org/10.3390/sym12081231 - 26 Jul 2020
Cited by 5 | Viewed by 1953
Abstract
The existing literature provides various computational models related to the dynamic behavior of strand wire ropes. It starts from the simple longitudinally oscillating beam, to the complex nonlinear multi-body configuration based on helical structural symmetry. The challenge is the prior availability of characteristic [...] Read more.
The existing literature provides various computational models related to the dynamic behavior of strand wire ropes. It starts from the simple longitudinally oscillating beam, to the complex nonlinear multi-body configuration based on helical structural symmetry. The challenge is the prior availability of characteristic parameters for material behavior, structural configuration, and functional capability. Experimental investigation is the main source for evaluation of these characteristics. However, tests have specifically been performed according to each case, minimizing the generalization aspect. This is the main frame of this study. Hereby, the authors propose an ensemble of spectral investigations, applied to a reduced set of experimental tests regarding wire rope dynamics. The research goal consists of wire rope characterization in terms of the flexible and adaptive groups of parameters, related to the conservative and dissipative behaviors. An experimental setup is considered here according to the rope exploitation conditions in order to enable an extension of the method application from the experimental mode to the operational mode. Experiments are conducted based on classical vibration measurement procedures. The analysis is performed using a spectral method ensemble, including discrete Fourier transform, time-frequency joint analysis, and the Prony method. The result show that the proposed assessments can provide suitable information related to a large group of wire rope models. Full article
(This article belongs to the Special Issue Multibody Systems with Flexible Elements)
Show Figures

Figure 1

15 pages, 4088 KiB  
Article
Kane’s Formalism Used to the Vibration Analysis of a Wind Water Pump
by Gabriel Leonard Mitu, Eliza Chircan, Maria Luminita Scutaru and Sorin Vlase
Symmetry 2020, 12(6), 1030; https://doi.org/10.3390/sym12061030 - 19 Jun 2020
Cited by 5 | Viewed by 1949
Abstract
The paper uses Kane’s formalism to study two degrees of freedom (DOF) mechanisms with elastic elements = employed in a wind water pump. This formalism represents an alternative, in our opinion, that is simpler and more economical to Lagrange’s equation, used mainly by [...] Read more.
The paper uses Kane’s formalism to study two degrees of freedom (DOF) mechanisms with elastic elements = employed in a wind water pump. This formalism represents an alternative, in our opinion, that is simpler and more economical to Lagrange’s equation, used mainly by researchers in this type of application. In the problems where the finite element method (FEM) is applied, Kane’s equations were not used at all. The automated computation causes it to be reconsidered in the case of mechanical systems with a high DOF. Analyzing the planar transmission mechanism, these equations were applied for the study of an elastic element. An analysis was then made of the results obtained for this type of water pump. The matrices coefficients of the obtained equations were symmetric or skew-symmetric. Full article
(This article belongs to the Special Issue Multibody Systems with Flexible Elements)
Show Figures

Figure 1

10 pages, 1866 KiB  
Article
The Effect of Fractional Time Derivative of Bioheat Model in Skin Tissue Induced to Laser Irradiation
by Aatef Hobiny, Faris Alzahrani, Ibrahim Abbas and Marin Marin
Symmetry 2020, 12(4), 602; https://doi.org/10.3390/sym12040602 - 10 Apr 2020
Cited by 101 | Viewed by 2949
Abstract
This work uses the “fractional order bio-heat model” (Fob) model of heat conduction to offer a new interpretation to study the thermal damages in a skin tissue caused by laser irradiation. The influences of fractional order and the thermal relaxation time parameters on [...] Read more.
This work uses the “fractional order bio-heat model” (Fob) model of heat conduction to offer a new interpretation to study the thermal damages in a skin tissue caused by laser irradiation. The influences of fractional order and the thermal relaxation time parameters on the temperature of skin tissue and the resulting thermal damage are studied. In the Laplace domain, the analytical solutions of temperature are obtained. Using the equation of Arrhenius, the resulting thermal injury to the tissues is assessed by the denatured protein ranges. The numerical results of the thermal damages and temperature are presented graphically. A parametric analysis is dedicated to the identifications of suitable procedures for the selection of significant design variables to achieve an effective thermal in the therapy of hyperthermia. Full article
(This article belongs to the Special Issue Multibody Systems with Flexible Elements)
Show Figures

Figure 1

22 pages, 785 KiB  
Article
Dynamic Hilbert-Type Inequalities with Fenchel-Legendre Transform
by Ahmed A. El-Deeb, Samer D. Makharesh and Dumitru Baleanu
Symmetry 2020, 12(4), 582; https://doi.org/10.3390/sym12040582 - 07 Apr 2020
Cited by 13 | Viewed by 1709
Abstract
Our work is based on the multiple inequalities illustrated in 2020 by Hamiaz and Abuelela. With the help of a Fenchel-Legendre transform, which is used in various problems involving symmetry, we generalize a number of those inequalities to a general time scale. Besides [...] Read more.
Our work is based on the multiple inequalities illustrated in 2020 by Hamiaz and Abuelela. With the help of a Fenchel-Legendre transform, which is used in various problems involving symmetry, we generalize a number of those inequalities to a general time scale. Besides that, in order to get new results as special cases, we will extend our results to continuous and discrete calculus. Full article
(This article belongs to the Special Issue Multibody Systems with Flexible Elements)
13 pages, 1557 KiB  
Article
Energy of Accelerations Used to Obtain the Motion Equations of a Three- Dimensional Finite Element
by Sorin Vlase, Iuliu Negrean, Marin Marin and Maria Luminița Scutaru
Symmetry 2020, 12(2), 321; https://doi.org/10.3390/sym12020321 - 23 Feb 2020
Cited by 25 | Viewed by 2339
Abstract
When analyzing the dynamic behavior of multi-body elastic systems, a commonly used method is the finite element method conjunctively with Lagrange’s equations. The central problem when approaching such a system is determining the equations of motion for a single finite element. The paper [...] Read more.
When analyzing the dynamic behavior of multi-body elastic systems, a commonly used method is the finite element method conjunctively with Lagrange’s equations. The central problem when approaching such a system is determining the equations of motion for a single finite element. The paper presents an alternative method of calculation theses using the Gibbs–Appell (GA) formulation, which requires a smaller number of calculations and, as a result, is easier to apply in practice. For this purpose, the energy of the accelerations for one single finite element is calculated, which will be used then in the GA equations. This method can have advantages in applying to the study of multi-body systems with elastic elements and in the case of robots and manipulators that have in their composition some elastic elements. The number of differentiation required when using the Gibbs–Appell method is smaller than if the Lagrange method is used which leads to a smaller number of operations to obtain the equations of motion. Full article
(This article belongs to the Special Issue Multibody Systems with Flexible Elements)
Show Figures

Figure 1

9 pages, 416 KiB  
Article
The Properties of a Decile-Based Statistic to Measure Symmetry and Asymmetry
by Mohammad Reza Mahmoudi, Roya Nasirzadeh, Dumitru Baleanu and Kim-Hung Pho
Symmetry 2020, 12(2), 296; https://doi.org/10.3390/sym12020296 - 18 Feb 2020
Cited by 7 | Viewed by 2609
Abstract
This paper studies a simple skewness measure to detect symmetry and asymmetry in samples. The statistic can be obviously applied with only three short central tendencies; i.e., the first and ninth deciles, and the median. The strength of the statistic to find symmetry [...] Read more.
This paper studies a simple skewness measure to detect symmetry and asymmetry in samples. The statistic can be obviously applied with only three short central tendencies; i.e., the first and ninth deciles, and the median. The strength of the statistic to find symmetry and asymmetry is studied by employing numerous Monte Carlo simulations and is compared with some alternative measures by applying some simulation studies. The results show that the performance of this statistic is generally good in the simulation. Full article
(This article belongs to the Special Issue Multibody Systems with Flexible Elements)
Show Figures

Figure 1

Back to TopTop