Journal of Engineering Mathematics最新文献_第9页

Short time angular impulse response of Rayleigh beams 瑞利梁的短时角脉冲响应

IF 1.3 4区工程技术

Journal of Engineering Mathematics Pub Date : 2023-11-21 DOI: 10.1007/s10665-023-10302-6

Bidhayak Goswami, K. R. Jayaprakash, Anindya Chatterjee

{"title":"Short time angular impulse response of Rayleigh beams","authors":"Bidhayak Goswami, K. R. Jayaprakash, Anindya Chatterjee","doi":"10.1007/s10665-023-10302-6","DOIUrl":"https://doi.org/10.1007/s10665-023-10302-6","url":null,"abstract":"<p>In the dynamics of linear structures, the impulse response function is of fundamental interest. In some cases one examines the short term response wherein the disturbance is still local and the boundaries have not yet come into play, and for such short-time analysis the geometrical extent of the structure may be taken as unbounded. Here we examine the response of slender beams to angular impulses. The Euler–Bernoulli model, which does not include rotary inertia of cross sections, predicts an unphysical and unbounded initial rotation at the point of application. A finite length Euler–Bernoulli beam, when modeled using finite elements, predicts a mesh-dependent response that shows fast large-amplitude oscillations setting in very quickly. The simplest introduction of rotary inertia yields the Rayleigh beam model, which has more reasonable behavior including a finite wave speed at all frequencies. If a Rayleigh beam is given an impulsive moment at a location away from its boundaries, then the predicted behavior has an instantaneous finite jump in local slope or rotation, followed by smooth evolution of the slope for a finite time interval until reflections arrive from the boundary, causing subsequent slope discontinuities in time. We present a detailed study of the angular impulse response of a simply supported Rayleigh beam, starting with dimensional analysis, followed by modal expansion including all natural frequencies, culminating with an asymptotic formula for the short-time response. The asymptotic formula is obtained by breaking the series solution into two parts to be treated independently term by term, and leads to a polynomial in time. The polynomial matches the response from refined finite element (FE) simulations.</p>","PeriodicalId":50204,"journal":{"name":"Journal of Engineering Mathematics","volume":"13 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2023-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138529992","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Wave scattering by Pi-type breakwater floating in deep water 深水漂浮pi型防波堤对波浪的散射

IF 1.3 4区工程技术

Journal of Engineering Mathematics Pub Date : 2023-11-21 DOI: 10.1007/s10665-023-10301-7

R. B. Kaligatla, S. Singh, B. N. Mandal

{"title":"Wave scattering by Pi-type breakwater floating in deep water","authors":"R. B. Kaligatla, S. Singh, B. N. Mandal","doi":"10.1007/s10665-023-10301-7","DOIUrl":"https://doi.org/10.1007/s10665-023-10301-7","url":null,"abstract":"<p>This article presents a study on surface gravity wave scattering by a rectangular (box-type) breakwater with thin side plates in the situation of oblique incident waves in deep water. Applying the continuity of fluid pressure and velocity to Havelock’s expansion of velocity potentials, the problem is converted to an integral equation of the Fredholm type, whose solution is the horizontal component of fluid velocity. The integral equation is solved by employing Galerkin’s approximation with polynomials as basis functions multiplied by suitable weight functions. The wave reflection and transmission coefficients are calculated numerically to find the breakwater’s performance on wave scattering. The accuracy of the results is verified through numerical convergence and checking of the energy balance equation. The rectangular breakwater reflects long waves to some extent in water of infinite depth, in contrast to a thin breakwater. The thin plates attached to the rectangular breakwater show a reduction in wave transmission. Furthermore, the attachment of thin plates leads to an increment in horizontal force and a reduction in vertical force.</p>","PeriodicalId":50204,"journal":{"name":"Journal of Engineering Mathematics","volume":"45 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2023-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138530001","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A nature-inspired meta-heuristic knowledge-based algorithm for solving multiobjective optimization problems 一种基于自然启发的元启发式知识算法，用于求解多目标优化问题

4区工程技术

Journal of Engineering Mathematics Pub Date : 2023-11-10 DOI: 10.1007/s10665-023-10304-4

Muskan Kapoor, Bhupendra Kumar Pathak, Rajiv Kumar

引用次数: 0

Damping matrix of a lightly damped dynamic system 轻阻尼动力系统的阻尼矩阵

4区工程技术

Journal of Engineering Mathematics Pub Date : 2023-10-28 DOI: 10.1007/s10665-023-10300-8

Rui Wang, Wei-Chau Xie, Binh-Le Ly

引用次数: 0

Extended finite similitude and dimensional analysis for scaling 尺度的扩展有限相似和量纲分析

4区工程技术

Journal of Engineering Mathematics Pub Date : 2023-10-25 DOI: 10.1007/s10665-023-10296-1

Keith Davey, Raul Ochoa-Cabrero

{"title":"Extended finite similitude and dimensional analysis for scaling","authors":"Keith Davey, Raul Ochoa-Cabrero","doi":"10.1007/s10665-023-10296-1","DOIUrl":"https://doi.org/10.1007/s10665-023-10296-1","url":null,"abstract":"Abstract The theory of scaling called finite similitude does not involve dimensional analysis and is founded on a transport-equation approach that is applicable to all of classical physics. It features a countable infinite number of similitude rules and has recently been extended to other types of governing equations (e.g., differential, variational) by the introduction of a scaling space $$Omega _{beta }$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msub> <mml:mi>Ω</mml:mi> <mml:mi>β</mml:mi> </mml:msub> </mml:math> , within which all physical quantities are deemed dependent on a single dimensional parameter $$beta $$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>β</mml:mi> </mml:math> . The theory is presently limited to physical applications but the focus of this paper is its extension to other quantitative-based theories such as finance. This is achieved by connecting it to an extended form of dimensional analysis, where changes in any quantity can be associated with curves projected onto a dimensional Lie group. It is shown in the paper how differential similitude identities arising out of the finite similitude theory are universal in the sense they can be formed and applied to any quantitative-based theory. In order to illustrate its applicability outside physics the Black-Scholes equation for option valuation in finance is considered since this equation is recognised to be similar in form to an equation from thermal physics. It is demonstrated that the theory of finite similitude can be applied to the Black-Scholes equation and more widely can be used to assess observed size effects in portfolio performance.","PeriodicalId":50204,"journal":{"name":"Journal of Engineering Mathematics","volume":"CE-33 4","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135218789","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Gravity waves generated by an oscillatory surface pressure in a two-layer fluid with a porous bottom 在底部多孔的两层流体中，由振荡表面压力产生的重力波

4区工程技术

Journal of Engineering Mathematics Pub Date : 2023-10-19 DOI: 10.1007/s10665-023-10298-z

Selina Hossain, Arijit Das, Soumen De, B. N. Mandal

引用次数: 0

Dynamic stress response analysis of inhomogeneous medium containing inhomogeneous inclusions under action of SH waves 含非均匀夹杂体的非均匀介质在SH波作用下的动应力响应分析

4区工程技术

Journal of Engineering Mathematics Pub Date : 2023-10-17 DOI: 10.1007/s10665-023-10297-0

Yun Zhu, Zai-lin Yang, Jian Zhao, Yi-cun Chen, Yong-tao Mi

引用次数: 0

Mathematical modelling of laser-instigated magneto-thermo-mechanical interactions inside half-space 半空间内激光激发磁-热-机械相互作用的数学模型

4区工程技术

Journal of Engineering Mathematics Pub Date : 2023-10-01 DOI: 10.1007/s10665-023-10292-5

Rakhi Tiwari

引用次数: 0

The second law of thermodynamics for open systems 开放系统的热力学第二定律

4区工程技术

Journal of Engineering Mathematics Pub Date : 2023-09-27 DOI: 10.1007/s10665-023-10294-3

Pulat A. Tadjibaev, Orifjon M. Tojiboev

引用次数: 0

The effects of heterogeneity on solute transport in porous media: anomalous dispersion 非均质性对多孔介质中溶质输运的影响:反常色散

4区工程技术

Journal of Engineering Mathematics Pub Date : 2023-09-27 DOI: 10.1007/s10665-023-10293-4

Adam J. Butler, Chunendra K. Sahu, Michael J. Bickle, Jerome A. Neufeld

{"title":"The effects of heterogeneity on solute transport in porous media: anomalous dispersion","authors":"Adam J. Butler, Chunendra K. Sahu, Michael J. Bickle, Jerome A. Neufeld","doi":"10.1007/s10665-023-10293-4","DOIUrl":"https://doi.org/10.1007/s10665-023-10293-4","url":null,"abstract":"Abstract Mixing of solute in sub-surface flows, for example in the leakage of contaminants into groundwater, is quantified by a dispersion coefficient that depends on the dispersivity of the medium and the transport velocity. Many previous models of solute transport data have assumed Fickian behaviour with constant dispersivity, but found that the inferred dispersivity increases with the distance from the point of injection. This approach assumes that the dispersion on either side of the advective front is symmetric and that the concentration there is close to half of the injected value. However, field data show consistent asymmetry about the advective front. Here, motivated by experimental data and a fractal interpretation of porous media, we consider a simplified heterogeneous medium described by a dispersivity with a power-law dependence on the downstream distance from the source and explore the nature of the asymmetry obtained in the solute transport. In a heterogeneous medium of this type, we show that asymmetry in solute transport gradually increases with the increase in heterogeneity or fractal dimension, and the concentration at the advective front becomes increasingly different from 50% of that at the inlet. In particular, for a sufficiently heterogeneous medium, the concentration profiles at late-time approach a non-trivial steady solution and, as a result, the concentration at a downstream location will never reach that at the inlet. By fitting the Fickian solution to our results, we are able to connect the parameters from our model to those found from experimental data, providing a more physically grounded approach for interpreting them.","PeriodicalId":50204,"journal":{"name":"Journal of Engineering Mathematics","volume":"50 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135537531","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0