scholarly journals CRITERIA OF MINIMUM MATERIALS CONSUMPTION FOR BARS WITH RECTANGULAR CROSS-SECTION AND RESTRICTIONS ON STABILITY OR LIMITATIONS ON THE VALUE OF THE FIRST NATURAL FREQUENCY

2017 ◽  
Vol 13 (1) ◽  
pp. 9-22 ◽  
Author(s):  
Leonid S. Lyakhovich ◽  
Pavel A. Akimov ◽  
Boris A. Tukhfatullin
Keyword(s):  
Mathematical Programming ◽  
Natural Frequency ◽  
Cross Section ◽  
Rectangular Cross Section ◽  
Optimal Solutions ◽  
Material Consumption ◽  
Variable Parameters ◽  
Special Cases ◽  
The Stability ◽  
Minimal Consumption

Apparatus of mathematical programming is normally used in the most part of research works, dealing with structural optimization. However, the special properties of optimal systems have been identified in several studies. Besides, corresponding criteria, which have been formulated as well, can be used for assessments of proximity of optimal solutions to minimal material consumption. Particularly relevant criteria for bars with rectangular cross-section and restrictions on the stability or limitations on the value of the first natural frequency have been formulated. However, not all the features of some of the criteria have been observed. In addition it seems appropriate to identify relevant criteria for special cases set variable parameters. The distinctive paper contains additional property proximity criterion of optimal solutions to minimal consumption of materials for the bars with a rectangular cross-section and limitations on the value of the first natural frequency, modification of one of the previously proposed criteria and formulation of appropriate criterion for the case where one of the parameters of variable rectangular cross-section is constant along the length of the bar.

scholarly journals CRITERION OF MINIMUMMATERIAL CONSUMPTIONOF FLANGE OF I-SHAPED BAR WITH A VARIATION IN ITS THICKNESS ANDOUTLINE OF THE WIDTH, WITH RESTRICTION TO THE VALUE OF THE CRITICALFORCE OR RESTRICTIONTO THE VALUE OF THEFIRSTNATURAL FREQUENCY INTWO PRINCIPAL PLANESO

2018 ◽  
Vol 14 (2) ◽  
pp. 96-108
Author(s):  
Leonid S. Lyakhovich ◽  
Pavel A. Akimov ◽  
Boris A. Tukhfatullin
Keyword(s):  
Natural Frequency ◽  
Cross Section ◽  
Critical Force ◽  
Principal Plane ◽  
Material Consumption ◽  
The Cross ◽  
The Stability

We have already presented original criterion of minimum material consumption within the design of the outline of the width of the I-shaped bar and the stability constraints or restriction to the value of the first natu­ral frequency in one principal plane of inertia of the cross-section. This paper is devoted in its turn to a criterion for the minimum material capacity of the I-shaped bar with a variation in its thickness and outline of the width, with restrictions to the value of the critical force or restriction to the value of the first natural frequency in two principal planes of inertia of the section

scholarly journals ASSESSMENT CRITERIA OF OPTIMAL SOLUTIONS FOR CREATION OF RODS WITH PIECEWISE CONSTANT CROSS-SECTIONS WITH STABILITY CONSTRAINTS OR CONSTRAINTS FOR VALUE OF THE FIRST NATURAL FREQUENCY. PART 1: THEORETICAL FOUNDATIONS

2019 ◽  
Vol 15 (4) ◽  
pp. 88-100 ◽  
Author(s):  
Leonid Lyakhovich ◽  
Pavel Akimov ◽  
Boris Tukhfatullin
Keyword(s):  
Natural Frequency ◽  
Cross Section ◽  
Cross Sections ◽  
Optimization Methods ◽  
Optimal Solutions ◽  
Continuous Change ◽  
Material Consumption ◽  
Piecewise Constant ◽  
Ideal Object ◽  
The Cross

The special properties of optimal systems have been already identified. Besides, criteria has been for­mulated to assess the proximity of optimal solutions to the minimal material consumption. In particular, the cri­teria were created for rods with rectangular and I-beam cross-section with stability constraints or constraints for the value of the first natural frequency. These criteria can be used for optimization when the cross sections of a bar change continuously along its length. The resulting optimal solutions can be considered as an idealized ob­ject in the sense of the limit. This function of optimal design allows researcher to assess the actual design solu­tion by the criterion of its proximity to the corresponding limit (for example, regarding material consumption). Such optimal project can also be used as a reference point in real design, for example, implementing a step-by­step process of moving away from the ideal object to the real one. At each stage, it is possible to assess the changes in the optimality index of the object in comparison with both the initial and the idealized solution. One of the variants of such a process is replacing the continuous change in the size of the cross sections of the rod along its length with piecewise constant sections. Boundaries of corresponding intervals can be selected based on an ideal feature, and cross-section dimensions can be determined by one of the optimization methods. The dis­tinctive paper is devoted to criteria that allow researcher providing reliable assessment of the endpoint of the op­timization process.

scholarly journals ASSESSMENT CRITERIA OF OPTIMAL SOLUTIONS FOR CREATION OF RODS WITH PIECEWISE CONSTANT CROSS-SECTIONS WITH STABILITY CONSTRAINTS OR CONSTRAINTS FOR VALUE OF THE FIRST NATURAL FREQUENCY. PART 2: NUMERICAL EXAMPLES

2019 ◽  
Vol 15 (4) ◽  
pp. 101-110 ◽  
Author(s):  
Leonid Lyakhovich ◽  
Pavel Akimov ◽  
Boris Tukhfatullin
Keyword(s):  
Natural Frequency ◽  
Cross Section ◽  
Cross Sections ◽  
Optimal Solutions ◽  
Continuous Change ◽  
Material Consumption ◽  
Piecewise Constant ◽  
Numerical Examples ◽  
Ideal Object ◽  
The Cross

The special properties of optimal systems have been already identified. Besides, criteria has been for­mulated to assess the proximity of optimal solutions to the minimal material consumption. In particular, the cri­teria were created for rods with rectangular and I-beam cross-section with stability constraints or constraints for the value of the first natural frequency. These criteria can be used for optimization when the cross sections of a bar change continuously along its length. The resulting optimal solutions can be considered as an idealized ob­ject in the sense of the limit. This function of optimal design allows researcher to assess the actual design solu­tion by the criterion of its proximity to the corresponding limit (for example, regarding material consumption). Such optimal project can also be used as a reference point in real design, for example, implementing a step-by­step process of moving away from the ideal object to the real one. At each stage, it is possible to assess the changes in the optimality index of the object in comparison with both the initial and the idealized solution. One of the variants of such a process is replacing the continuous change in the size of the cross sections of the rod along its length with piecewise constant sections. Boundaries of corresponding intervals can be selected based on an ideal feature, and cross-section dimensions can be determined by one of the optimization methods. The dis­tinctive paper is devoted to criteria that allow researcher providing reliable assessment of the endpoint of the op­timization process, and the second part of the material presented contains corresponding numerical examples, prepared in accordance with the theoretical foundations given in the first part.

Experimental Analysis of Vortex Induced Vibration in the Bladeless Small Wind Turbine

2019 ◽  
Author(s):  
Micha Premkumar Thomai ◽  
Lasoodawanki Kharsati ◽  
Nakandhrakumar Rama Samy ◽  
Seralathan Sivamani ◽  
Hariram Venkatesan
Keyword(s):  
Energy Conversion ◽  
Wind Turbine ◽  
Natural Frequency ◽  
Cross Section ◽  
Vortex Shedding ◽  
Rectangular Cross Section ◽  
The Body ◽  
Test Facility ◽  
Vortex Induced Vibration ◽  
Small Wind Turbine

Abstract Vortex-induced vibration is one of the predominant fundamental concepts for forced oscillation which attracts considerable practical engineering application for energy conversion. In this work, an oscillation of a mast arising as a result of wind force is utilized for energy conversion. The paradigm for energy conversion from vortex-induced vibration in the mast is the bladeless wind turbine. It consists of a rigid mass known as a mast, fixed in the spring of stiffness (k) and allowed to oscillate along the direction of the flow. In this work, four different types of mast have been fabricated and tested. The first is uniform tapered hollow conical mast (MAST1), the cross-section of the second is uniform tapered plus symbol (MAST2), the third is uniform tapered inversed plus symbol (MAST3) and the fourth is uniform tapered simple rectangular cross-section (MAST4). All the masts were fabricated using fiber carbon. The experiments were conducted in a versatile small wind turbine testing facility of Hindustan Institute of Technology and Science, Chennai. This test facility contained an open jet wind tunnel with variable frequency drive and other measuring instruments. The vibration sensor was located in the mast where it experienced a large oscillation in a free stream. In this experiment, an increase in wind velocity led to a terrible change in the amplitude of vibration. A vigorous oscillation was experienced in this mast at this critical frequency, when the natural frequency of the mast was synchronized with the frequency of the vortex shedding and the frequency of the oscillation of the mast. The total force in this oscillation was a summation of the body force due to the mass of the mast and vorticity force that is mainly which was the result of the shedding of the vortices. In this work, extensive studies have been carried out for Reynolds number ranging from 2.5 × 105 to 5.0 × 105. The mast length to diameter ratio of 13 was exposed to various speeds of wind and response was measured. The occurrence of the maximum oscillation in a simple rectangular mast was seen where vortex shedding due to the bluff body was large for constant mass and spring stiffness. The frequency of the oscillation at maximum amplitude of the rectangular cross-section mast was equal to the natural frequency, due to vortices shedding at critical velocity. This demonstrated the appropriateness of the simple rectangular cross-section for harnessing the low rated wind energy and its suitability for renewable energy conversion in the small bladeless wind turbine.

Rectangular Cross Section Beams Calculation on the Stability of a Flat Bending Shape Taking into Account the Initial Imperfections

2019 ◽  
Vol 974 ◽  
pp. 551-555 ◽  
Author(s):  
I.M. Zotov ◽  
Anastasia P. Lapina ◽  
Anton S. Chepurnenko ◽  
B.M. Yazyev
Keyword(s):  
Cross Section ◽  
Basic Equation ◽  
Applied Load ◽  
Rectangular Cross Section ◽  
Twist Angle ◽  
Stability Loss ◽  
Lateral Buckling ◽  
Initial Imperfections ◽  
Beam Stability ◽  
The Stability

The article presents the derivation of the resolving equation for the calculation of lateral buckling of rectangular beams. When deriving the basic equation, the initial imperfections of the beam are taken into account, which are specified in the form of the eccentricity of the applied load, the initial deflection in the plane of least stiffness and the initial twist angle. The influence of initial imperfections on the process of beam stability loss is investigated.

scholarly journals Calculation of wooden beams on the stability of a flat bending shape enhancement

2018 ◽  
Vol 196 ◽  
pp. 01003 ◽  
Author(s):  
Anton Chepurnenko ◽  
Vera Ulianskaya ◽  
Serdar Yazyev ◽  
Ivan Zotov
Keyword(s):  
Differential Equation ◽  
Cross Section ◽  
Stability Problem ◽  
Secular Equation ◽  
Rectangular Cross Section ◽  
Center Of Gravity ◽  
Critical Force ◽  
Distributed Load ◽  
Matlab Package ◽  
The Stability

Flat bending stability problem of constant rectangular cross section wooden beam, loaded by a distributed load is considered. Differential equation is provided for the cases when load is located not in the center of gravity. The solution of the equation is performed numerically by the method of finite differences. For the case of applying a load at the center of gravity, the problem reduces to a generalized secular equation. In other cases, the iterative algorithm developed by the authors is implemented, in the Matlab package. A relationship between the value of the critical force and the position of the load application point is obtained. A linear approximating function is selected for this dependence.

On the stability of liquid ridges

1999 ◽  
Vol 391 ◽  
pp. 293-318 ◽  
Author(s):  
R. VALÉRY ROY ◽  
LEONARD W. SCHWARTZ
Keyword(s):  
Contact Angle ◽  
Cross Section ◽  
Energy Functional ◽  
Liquid Region ◽  
Contact Lines ◽  
Property A ◽  
Cross Sectional ◽  
Elliptical Cross ◽  
Special Cases ◽  
The Stability

We consider the stability of a rectilinear liquid region whose boundary is composed of a solid cylindrical substrate of arbitrary shape and a free surface whose cross-section, in the absence of gravity, is a circular arc. The liquid–solid contact angle is a prescribed material property. A variational technique, using an energy functional, is developed that predicts the minimum wavelength for transverse instability under the action of capillarity. Conversely, certain configurations are absolutely stable and a simple stability criterion is derived. Stability is guaranteed if, for given substrate geometry and given contact angle, the unperturbed meniscus pressure is an increasing function of the liquid cross-sectional area. The analysis is applied to a variety of liquid/substrate configurations including (i) a liquid ridge with contact lines pinned to the sharp edges of a slot or groove, (ii) liquid ridges with free contact lines on flat and wedge-shaped substrates as well as substrates of circular or elliptical cross-section. Results are consistent with special cases previously treated including those that employ a slope-small-slope approximation.

Recommendations for Designing Wooden Arches on Metal-toothed Plates

2021 ◽  
Author(s):  
Bohdan Demchyna ◽  
◽  
Yaroslav Shydlovskyi
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Laboratory Testing ◽  
Horizontal Plane ◽  
Thrust Force ◽  
Rectangular Cross Section ◽  
Rectangular Section ◽  
Pilot Studies ◽  
Different Types ◽  
The Stability

This paper presents the findings of the pilot studies and recommendations for designing of two-hinged wooden arches. The prototype models of wooden arches with the span of 6mand the rise of 1m were designed. The models had a rectangular cross-section of 180x40mm and a T-section of 180x40mm with a plywood plate with the thickness of 6 mm and the width of 500mm. The main objective of the T-section was to ensure the stability of the arch. Each arch was composed of six segments –boards joined by clamping plates. The bowstring truss including two inclined tie bars enables carrying asymmetric loads and provides in-plane stability of the arch. A methodology for laboratory testing of the prototype models of wooden arches subjected to different types of loads was developed. Two prototypes of wooden arches were tested with rectangular cross-sections and two T-section ones subjected to the loading across the span, and two prototypes subjected to the half-span loading. In total, eight arches were tested. Deflections of arches, cross-section deformations and arch thrust force were recorded. The arches were tested until failure. The results of testing revealed insufficient stability of the arches with rectangular cross-section in the horizontal plane. For the arches with T-section the whole arch rib was damaged, the in-plane stability was ensured by the T-section. The collapsing force of the T-section arch was about 1.3 times greater than the collapsing force of the rectangular section arches.

On Sensitivity of Capacitive Microresonators Near Three Half Natural Frequency

2010 ◽  
Author(s):  
Dumitru I. Caruntu ◽  
Martin Knecht
Keyword(s):  
Natural Frequency ◽  
Cross Section ◽  
Rectangular Cross Section ◽  
Constant Thickness ◽  
Microcantilever Sensors ◽  
Electrostatically Actuated ◽  
Resonance Frequencies ◽  
Parametric Oscillations ◽  
Deposition Thickness ◽  
Beam Dimension

This paper deals with sensitivity of electrostatically actuated micro resonator sensors near three half natural frequency. Mass deposition changes resonance frequencies of structures. Resonator sensitivity, defined as a fraction of change in frequency per unit deposited mass, can be found for microcantilever sensors electrostatically actuated to include fringe and Casimir effects. These actuation forces produce nonlinear parametric oscillations. Constant thickness mass deposition on all four lateral surfaces of the cantilever of rectangular cross-section was assumed. The Euler-Bernoulli theory was used under the assumption that the beams are slender. Mass deposition on the free end surface of the cantilever was neglected. The deposition thickness was considered uniform and very small compared to any beam dimension. The deposited mass had no contribution to the stiffness, only to the mass. Analytical expression of the sensitivity of electrostatically actuated uniform microcantilever resonators sensor near natural frequency can be determined.

Sign in / Sign up

Export Citation Format

Share Document