scholarly journals Conceptual design decision support of a mechatronic system using analytical approach with Modelica

2018 ◽  
Vol 19 (1) ◽  
pp. 103 ◽  
Author(s):  
Ghazoi Hamza ◽  
Moncef Hammadi ◽  
Maher Barkallah ◽  
Jean-Yves Choley ◽  
Alain Riviere ◽  
...  
Keyword(s):  
Boundary Conditions ◽  
Conceptual Design ◽  
Mode Shapes ◽  
Design Stage ◽  
System Response ◽  
Flexible Beam ◽  
Design Decision ◽  
Mechatronic Systems ◽  
Arbitrary Boundary ◽  
Simply Supported

During conceptual design phase, system architects pre-validate architectures following different constrains. This paper proposes a new pre-designing method applied to a flexible multibody system to characterize its vibrational behavior analytically with Dymola/Modelica language. We study the vibration interaction between perturbations sources (motors) and receivers (electronic cards) through a flexible beam with arbitrary boundary conditions. In fact, a lot of mechatronic systems may have their natural frequencies and mode shapes dependent on their spatial configuration, which affect the dynamic response of the system. This methodology shows that using Modelica, we can implement different boundary conditions, making the element suitable for any multibody simulation. This model can help system architects to study the influence of the boundary conditions on the system response. Two types of boundary conditions are considered in this study, simply supported–simply supported (S-S) and clamped–clamped (C-C). The solution for this issue would be a pre-positioning procedure which targets to provide a support for decision-making on the feasibility of a given system architecture at an early design stage, before proceeding to the detailed design. The simulation results have been validated with respect to the literature and by a comparison with those obtained by the model based on the Beam component which belongs to the Modelica flexible Bodies Library.

A Levy-Type Solution for a Rectangular Plate of Variable Thickness

1958 ◽  
Vol 25 (2) ◽  
pp. 297-298
Author(s):  
H. D. Conway
Keyword(s):  
Boundary Conditions ◽  
Rectangular Plate ◽  
Variable Thickness ◽  
Thickness Variation ◽  
Type Solution ◽  
Arbitrary Boundary ◽  
Simply Supported ◽  
Arbitrary Boundary Conditions ◽  
Plate Of Variable Thickness

Abstract A solution is given for the bending of a uniformly loaded rectangular plate, simply supported on two opposite edges and having arbitrary boundary conditions on the others. The thickness variation is taken as exponential in order to make the solution tractable, and thus closely approximates to uniform taper if the latter is small.

scholarly journals Wave Based Method for Free Vibration Analysis of Ring Stiffened Cylindrical Shell with Intermediate Large Frame Ribs

2013 ◽  
Vol 20 (3) ◽  
pp. 459-479 ◽  
Author(s):  
Meixia Chen ◽  
Jianhui Wei ◽  
Kun Xie ◽  
Naiqi Deng ◽  
Guoxiang Hou
Keyword(s):  
Cylindrical Shell ◽  
Free Vibration ◽  
Boundary Conditions ◽  
Natural Frequencies ◽  
Free Vibration Analysis ◽  
Structure Type ◽  
Vibration Characteristics ◽  
Mode Shapes ◽  
Arbitrary Boundary ◽  
Stiffened Cylindrical Shell

Wave based method which can be recognized as a semi-analytical and semi-numerical method is presented to analyze the free vibration characteristics of ring stiffened cylindrical shell with intermediate large frame ribs for arbitrary boundary conditions. According to the structure type and the positions of discontinuities, the model is divided into different substructures whose vibration field is expanded by wave functions which are exactly analytical solutions to the governing equations of the motions of corresponding structure type. Boundary conditions and continuity equations between different substructures are used to form the final matrix to be solved. Natural frequencies and vibration mode shapes are calculated by wave based method and the results show good agreement with finite element method for clamped-clamped, shear diaphragm – shear diaphragm and free-free boundary conditions. Free vibration characteristics of ring stiffened cylindrical shells with intermediate large frame ribs are compared with those with bulkheads and those with all ordinary ribs. Effects of the size, the number and the distribution of intermediate large frame rib are investigated. The frame rib which is large enough is playing a role as bulkhead, which can be considered imposing simply supported and clamped constraints at one end of the cabin and dividing the cylindrical shell into several cabins vibrating separately at their own natural frequencies.

Three-Dimensional Vibrations of Truncated Hollow Cones

1995 ◽  
Vol 1 (2) ◽  
pp. 145-158 ◽  
Author(s):  
Arthur W. Leissa ◽  
Jinyoung So
Keyword(s):  
Boundary Conditions ◽  
Cross Sections ◽  
Ritz Method ◽  
Three Dimensional ◽  
Mode Shapes ◽  
Vibration Frequencies ◽  
Arbitrary Boundary ◽  
Conical Shells ◽  
Hole Radius ◽  
Geometric Boundary

This work presents a three-dimensional (3-D) method of analysis for determining the free vibration frequencies and corresponding mode shapes of truncated hollow cones of arbitrary thickness and having arbitrary boundary conditions. It also supplies the first known numerical results from 3-D analysis for such problems. The analysis is based upon the Ritz method. The vibration modes are separated into their Fourier components in terms of the circumferential coordinate. For each Fourier component, displacements are expressed as algebraic polynomials in the thickness and slant length coordinates. These polynomials satisfy the geometric boundary conditions exactly. Because the displacement functions are mathematically complete, upper bound values of the vibration frequencies are obtained that are as close to the exact values as desired. This convergence is demonstrated for a representative truncated hollow cone configuration where six-digit exactitude in the frequencies is achieved. The method is then used to obtain accurate and extensive frequencies for two sets of completely free, truncated hollow cones, one set consisting of thick conical shells and the other being tori having square-generating cross sections. Frequencies are presented for combinations of two values of apex angles and two values of inner hole radius ratios for each set of problems.

Mechatronic Multicriteria Profile (MMP) for Conceptual Design of a Robotic Visual Servoing System

2014 ◽  
Author(s):  
Abolfazl Mohebbi ◽  
Sofiane Achiche ◽  
Luc Baron
Keyword(s):  
Conceptual Design ◽  
Visual Servoing ◽  
Design Thinking ◽  
Choquet Integral ◽  
Design Stage ◽  
Physical Aspect ◽  
Mechatronic Systems ◽  
Robotic Visual Servoing ◽  
And Control

Mechatronic systems are a combination of cooperative mechanical, electronics and control components. The high number of their components, their multi-physical aspect, the couplings between the different domains involved and the interacting design objectives makes the design task very tedious ad complex. Due to this inherent complexity, a concurrent systematic and multi-objective design thinking methodology is crucial to replace the often used sequential design approach that tends to deal with the different domains separately. In this research we present a new multi-criteria profile for mechatronic system performance evaluation in conceptual design stage. The newly introduced Mechatronic Multi-criteria Profile (MMP) includes various quantitative members such as intelligence, reliability, complexity, flexibility and cost. A nonlinear fuzzy integral called 2-additive Choquet Integral will be used for the aggregation of criteria and fitting the intuitive requirements for decision-making in the presence of interacting criteria. Finally, the effectiveness of the proposed method will be validated via a case study of designing a robotic visual servoing system.

Reliability-Based Topology Optimization Considering Multicriteria Using Frame Elements

2005 ◽  
Author(s):  
Katsuya Mogami ◽  
Kazuhiro Izui ◽  
Shinji Nishiwaki ◽  
Masataka Yoshimura ◽  
Nozomu Kogiso
Keyword(s):  
Decision Making ◽  
Topology Optimization ◽  
Conceptual Design ◽  
Environmental Changes ◽  
Mechanical Design ◽  
Optimization Method ◽  
Design Stage ◽  
Design Decision ◽  
Discrete Elements ◽  
Detailed Design

Since decision-making at the conceptual design stage critically affects final design solutions at the detailed design stage, conceptual design support techniques are practically mandatory if the most efficient realization of optimal designs is desired. Topology optimization methods using discrete elements such as frame elements enable a useful understanding of the underlying mechanics principles of products, however the possibility of changing prior assumptions concerning utilization environments exists since the detailed design process starts after the completion of conceptual design decision-making. In order to avoid product performance reductions due to such later-stage environmental changes, this paper discusses a reliability-based topology optimization method that can secure specified design goals even in the face of environmental factor uncertainty. This method can optimize mechanical structures with respect to two principal characteristics, namely structural stiffness and eigen-frequency. Several examples are provided to illustrate the utility of the method presented here for mechanical design engineers.

A Set of Orthogonal Plate Functions for Flexural Vibration of Regular Polygonal Plates

1991 ◽  
Vol 113 (2) ◽  
pp. 182-186 ◽  
Author(s):  
K. M. Liew ◽  
K. Y. Lam
Keyword(s):  
Boundary Conditions ◽  
Vibration Analysis ◽  
Mixed Boundary ◽  
Flexural Vibration ◽  
Mixed Boundary Conditions ◽  
Mode Shapes ◽  
Two Dimensional ◽  
Computationally Efficient ◽  
Simply Supported ◽  
Free Boundary Conditions

A computationally efficient and very accurate numerical method is proposed for vibration analysis of regular polygonal plates with any combinations of clamped, simply-supported and free boundary conditions. The method involves the use of two-dimensional orthogonal polynomials generated by the Gram-Schmidt recurrence procedure. For the cases of simply supported and fully clamped hexagonal and octagonal plates, the results obtained agreed very well with those existing in the literature. The frequencies and mode shapes for several hexagonal and octagonal plates subjected to mixed boundary conditions are also presented.

An Extended Separation-of-Variable Method for Free Vibration of Rectangular Mindlin Plates

2021 ◽  
pp. 2150154
Author(s):  
Gen Li ◽  
Yufeng Xing ◽  
Zekun Wang
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Closed Form ◽  
Natural Frequencies ◽  
Mode Shapes ◽  
Arbitrary Boundary ◽  
Unknown Variable ◽  
Closed Form Solutions ◽  
Solution Methods ◽  
Separation Of Variable

For rectangular thick plates with non-Levy boundary conditions, it is important to explore analytical free vibration solutions because the classical inverse and semi-inverse exact solution methods are not applicable to this category of problems. This work is to develop an extended separation-of-variable (SOV) method to find closed-form analytical solutions for the free vibration of rectangular Mindlin plates with arbitrary homogeneous boundary conditions. In the extended SOV method, characteristic differential equations and boundary conditions in two directions are obtained by employing the Rayleigh principle and the assumption that the mode functions are in the SOV form, and two transcendental eigenvalue equations are achieved through boundary conditions. But these two eigenvalue equations cannot be solved simultaneously since there are two equations and only the natural frequency is the unknown variable. Considering this, the second assumption in this method is that the natural frequencies corresponding to two-direction mode functions are independent of each other in the mathematical sense, thus there are two unknowns in two transcendental eigenvalue equations, and the closed-form solutions for plates with arbitrary boundary conditions can be obtained non-iteratively. From the physical sense, the natural frequencies pertaining to different direction mode functions should be the same, and this conclusion is validated analytically and numerically. The present natural frequencies and mode shapes agree well with those obtained by other analytical and numerical methods. Especially, for the plates with at least two opposite sides simply supported, the present solutions are exact.

An Incidence Matrix Support for Conceptual Design Based on Port Ontology

2009 ◽  
Vol 419-420 ◽  
pp. 49-52 ◽  
Author(s):  
Dong Xing Cao ◽  
Zhan Wei Li ◽  
Hong Lai Li ◽  
Kai Cheng Qi
Keyword(s):  
Conceptual Design ◽  
Incidence Matrix ◽  
Product Information ◽  
Design Stage ◽  
Design Decision ◽  
Physical Domain ◽  
Levels Of Abstraction ◽  
Conceptual Design Stage ◽  
Different Levels

Existing conceptual design methods mainly focus on component modeling and representation, which makes them insufficient to help in the conceptual design stage. Port ontology, as an approach to formally expressing product design, has been effectively applied to concept description of a product. An incidence matrix support for product conceptual design based on port ontology is given in this paper. It formally represents and organizes product information in both functional ontology and physical domain in a hierarchy. Port compatibilities are used to map and link the two components. This makes it possible to build incidence matrix and decompose it into an independence matrix, and allow designers from different backgrounds with various interests to access the design ontology. A multilevel matrix is constructed to generate principle schemes of products at different levels of abstraction, which facilitates design decision-making through the whole conceptual design stage. A case study is also given to demonstrate the proposed approach.

Vibration of Stiffened Plates

1964 ◽  
Vol 15 (3) ◽  
pp. 285-298 ◽  
Author(s):  
Thein Wah
Keyword(s):  
Boundary Conditions ◽  
Orthotropic Plate ◽  
Natural Frequencies ◽  
General Procedure ◽  
The Other ◽  
Stiffened Plates ◽  
Rectangular Plates ◽  
Arbitrary Boundary ◽  
Simply Supported ◽  
Arbitrary Boundary Conditions

SummaryThis paper presents a general procedure for calculating the natural frequencies of rectangular plates continuous over identical and equally spaced elastic beams which are simply-supported at their ends. Arbitrary boundary conditions are permissible on the other two edges of the plate. The results are compared with those obtained by using the orthotropic plate approximation for the system

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