Dimensional Analysis and Self-Similarity Methods for Engineers and Scientists

Zohuri, Bahman

doi:10.1007/978-3-319-13476-5

Cited by 77 publications

(69 citation statements)

References 18 publications

(7 reference statements)

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“…There are really 2 directions in a line --backward and forward --and infinitely many in the plane. Actually there are 2 linearly independent directions in the plane [9]. Of course, it is right.…”

Section: Fractal Dimensionmentioning

confidence: 99%

A Review of Fractals Properties: Mathematical Approach

Nurujjaman¹,

Hossain²,

Ahmed³

2017

SJAMS

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Abstract:In this article, we will discuss some spectacularly beautiful images known as Fractals such as Sierpiński Triangle, Koch Curve, Dragon Curve, Koch Island, H Fractal, The Levy Curve Fractal, Box Fractal etc. We will investigate and calculate the area, perimeter and self-similar dimension of fractals. Observing the results we see some similarities about the said properties for some fractals those are generated by particular method. Our attention is restricted to find the mathematical behavior of Fractals so that we can establish mathematical formulas concerning the fractals.

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Section: Fractal Dimensionmentioning

confidence: 99%

A Review of Fractals Properties: Mathematical Approach

Nurujjaman¹,

Hossain²,

Ahmed³

2017

SJAMS

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“…All analyses in this study were carried out for a one‐quarter length scale model. Other basic scale factors based on appropriate similitude rules are time scale factor = ½ and acceleration scale factor = 1:1. Applying these rules, the model block dimensions are h = 5 m and b = 2.5 m and the model horizontal spring stiffness corresponds to T x = 1.5 s. Table summaries the prototype and scaled model BLS‐CMRD designed properties.…”

Section: Design Properties Of Bls‐cmrd For Vertical Isolationmentioning

confidence: 99%

Displacement/velocity‐based control of a liquid spring—MR damper for vertical isolation

Eltahawy

Ryan

Çeşmeci

et al. 2019

Struct Control Health Monit

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Seismic isolation is an effective technique used to mitigate effects of shaking and helps to achieve higher seismic performance. Recent researches have suggested that vertical excitation has significant effects on structures behavior during earthquake. In this study, three-dimensional (3D) isolation is proposed that combines an elastomeric bearing to resist horizontal ground shaking in series with a bilinear liquid spring (BLS)-controllable magnetorheological fluid damper (CMRD) to resist vertical shaking. A numerical model of a simplified rigid 2D block was developed to predict BLS-CMRD response under earthquake loading. The response of the BLS-CMRDs was simulated through a combination of nonlinear stiffness and viscous and hysteretic (semi-active) damping. A Disp/Vel-based control strategy was proposed that adjusts the input current according to the instantaneous vector combination of feedback displacement and velocity of the damper. Two variations of the control strategy were explored. First, with linear current variation, the current is activated when a threshold lower bound vector magnitude is reached, and maximum current is applied when threshold upper bound magnitude is exceeded. Second, the simplified ON-OFF strategy uses single threshold vector magnitude that triggers the maximum current to turn on when the instantaneous vector magnitude exceeds the threshold, and turn off otherwise. Results show that for ground motions that exceed the design level, Disp/Vel-based Control is effective to moderate the level of energy dissipation, keep the device vertical displacement within the design stroke limit, and attenuate vertical acceleration below PGA. In addition, Disp/Vel-based control reduces all responses relative to the well-known clipped optimal strategy used for structural control.

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“…Similar processes will produce corresponding physics but in reality the scaling of complex processes is not so easy and it is seldom possible to match exactly the dimensionless quantities. Similarity can be categorised in three parts: geometric similarity; kinematic similarity and; kinetic similarity [4,5]. Scaling proportionally is seldom a major difficulty but clearly a requirement of geometric similarity.…”

Section: Introductionmentioning

confidence: 99%

Scaled metal forming experiments: A transport equation approach

Davey

Darvizeh

Al-Tamimi

2017

International Journal of Solids and Structures

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The focus of this paper is on a method for the design of bespoke small-scale pilot, metalforming processes and models that accurately represent corresponding industrial-scale processes. Introducing new complex metal forming processes in industry commonly involves a trial and error approach to ensure that the final product requirements are met. Detailed process modelling, analysis and small-scale feasibility trials could be carried out instead. A fundamental concern of scaled experiments, however, is whether the results obtained can be guaranteed to be representative of the associated industrial processes. Presently, this is not the case with classical approaches founded on dimensional analysis providing little direction for the design of scaled metal-forming experiments. The difficulty is that classical approaches often focus predominantly on constitutive equations (which indirectly represent micro-structural behaviour) and thus focus on aspects that invariably cannot be scaled. This paper introduces a new approach founded on scaled transport equations that describe the physics involved on a finite domain. The transport approach however focuses on physical quantities that do scale and thus provides a platform on which bulk behaviour is accurately represented across the length scales. The new approach is trialled and compared against numerically obtained results to reveal a new powerful technique for scaled experimentation.

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Dimensional Analysis and Self-Similarity Methods for Engineers and Scientists

Cited by 77 publications

References 18 publications

A Review of Fractals Properties: Mathematical Approach

A Review of Fractals Properties: Mathematical Approach

Displacement/velocity‐based control of a liquid spring—MR damper for vertical isolation

Scaled metal forming experiments: A transport equation approach

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