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PARAMETRIC INVESTIGATION OF THE DYNAMIC AMPLIFICATION FACTOR OF EULER–BERNOULLI BEAMS ON VARIABLE ELASTIC FOUNDATIONS UNDER MOVING DISTRIBUTED LOADS

^1*I.A Idowu,  ²R.A Mustapha, ¹A.A Abdurasid, ¹T.A Abozos, and ¹J.A Ademosu

¹Department of Mathematical Sciences, Lagos State University of Science and Technology, Ikorodu, Lagos

³Department of Mathematics, Lagos State University, Ojo.

E-mail: idlaspotech@yahoo.com,   idowu.ia@lasustech.edu.ng

Abstract: The dynamic behavior of beams subjected to moving loads is an important consideration in the design of transportation and civil engineering structures, including railway tracks, highway bridges, crane girders, and conveyor systems. This study presents a parametric investigation of the dynamic amplification factor (DAF) of an elastically supported Euler–Bernoulli beam resting on a variable elastic foundation under partially distributed moving loads. The beam–foundation interaction is modelled using a spatially varying elastic foundation, while the moving load is represented as a finite-length distributed load travelling at constant velocity. The governing partial differential equation is formulated based on Euler–Bernoulli beam theory and solved using an analytical modal superposition approach complemented by numerical simulations for validation. A comprehensive parametric study is conducted to evaluate the effects of foundation stiffness variation, moving load velocity, load distribution length, beam flexural rigidity, damping ratio, and support stiffness on the dynamic amplification factor and maximum beam deflection. Particular attention is given to identifying critical loading conditions associated with resonance and dynamic instability. The results demonstrate that increasing foundation stiffness and damping significantly reduces the dynamic amplification factor, whereas higher load velocities and longer load distributions may substantially increase the beam response near critical speeds. The findings provide valuable insights into the dynamic behavior of beam–foundation systems and offer practical guidance for the design and optimization of engineering structures subjected to moving distributed loads.

[I.A Idowu,  R.A Mustapha, A.A Abdurasid, T.A Abozos, and J.A Ademosu . PARAMETRIC INVESTIGATION OF THE DYNAMIC AMPLIFICATION FACTOR OF EULER–BERNOULLI BEAMS ON VARIABLE ELASTIC FOUNDATIONS UNDER MOVING DISTRIBUTED LOADS. J Am Sci 2026;22(8):1-15]. ISSN 1545-1003 (print); ISSN 2375-7264 (online). http://www.jofamericanscience.org. 01. doi:10.7537/marsjas220826.01

Keywords: Euler–Bernoulli beam; Dynamic amplification factor (DAF); Variable elastic foundation; Moving distributed load

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ALL IS THE STABLE NUMBER

Chun-Xuan. Jiang

P. O. Box142-206 , Beijing 100854, P. R. China

j555j556@163.com

Abstract: Why we have five fingers. We suggest two principles: (1) the prime principle and (2) the symmetric principle. We prove that 1, 3, 5, 7, 11, 23, 47, and 2, 4, 6, 10, 14, 22, 46, 94 are the most stable numbers, which are the basic building-blocks in clusters and nanostructures. The prime principle is the mathematical foundations for clusters and nanostructures . All is the stable number.

[Chun-Xuan. Jiang. ALL IS THE STABLE NUMBER. J Am Sci 2026;22(8):16-20]. ISSN 1545-1003 (print); ISSN 2375-7264 (online). http://www.jofamericanscience.org. 02. doi:10.7537/marsjas220826.02

Keywords: five fingers; prime principle; symmetric principle; stable numbers; mathematical foundations; clusters and nanostructures

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Tailoring the Interfacial Reinforcement Efficiency of Polyvinyl Alcohol Matrix using Refractory Ceramic Nano-fillers

¹ Dr Jyotsna Chauhan, ²akansha mehto, ³Shaswat Chauhan

¹Professor in RGPV, ²Research scholar ,³ BITS Pilani GOA

ABSTRACT: This   paper explores polymeric nanocomposites based on refractory ceramic oxides with special emphasis on polyvinyl alcohol (PVA) as the host matrix. The aim of the study is to synthesizing nanoparticles and their nanocomposite membranes for improving the structural, optical and morphological characteristics of nanocomposite membrane. This  establishes the foundation by giving an overview of refractory materials and highlighting their important for withstanding high temperatures in a variety of industrial processes along with the literature survey. The area of focus is the incorporation of nanoparticles into a polymer matrix, which provides improved chemical and physical properties. The use of PVA as a host matrix is justified by highlighting its remarkable properties, including mechanical strength, flexibility, and film-forming ability. A thorough explanation of PVA's hydrophilic properties and its wide range of uses from food packaging to sensors, supercapacitors, catalysts, and more is then discussed.

[Dr Jyotsna Chauhan, akansha mehto, Shaswat Chauhan. Tailoring the Interfacial Reinforcement Efficiency of Polyvinyl Alcohol Matrix using Refractory Ceramic Nano-fillers. J Am Sci 2026;22(8):21-30]. ISSN 1545-1003 (print); ISSN 2375-7264 (online). http://www.jofamericanscience.org. 03. doi:10.7537/marsjas220826.03

Keywords: Tailoring; Interfacial Reinforcement Efficiency; Polyvinyl Alcohol; Matrix; Ceramic Nano-fillers

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Markanda River (Tamil Nadu)  and its future

Gangadhara Rao Irlapati

H.No.5-30-4/1, Saibabanagar, Jeedimetla, Hyderabad, India-500055

Email:  gangadhar19582058@gmail.com

Abstract: The Markanda River (Tamil Nadu), belongs to the country of India in the Asian continent.. Here is an important and significant thing that scientists should be grasped and noted by the researchers regarding the changes in climate conditions.. Recently, due to climate changes, water bodies like rivers, lakes, ponds, reservoirs, barrages, dams, and glaciers etc. are drying up or overflowing, causing many catastrophic situations. According to the Indian Monsoon Time Scales, it is come to known that there will be climate changes in the coming years “i.e”  heavy rains and and floods etc. will occur until about 2075, and there will be droughts and famines until about 2150. So, based on the studies of the Indian Monsoon Time Scale, basins and catchment areas of the Markanda River (Tamil Nadu)  will be filled with waters in the coming years. This is just only a scientific observation with a scientific perspective and not that these consequences will occur and in some years it may be fulfilled and in others it may not be fulfilled. In this study, we can take any thing that is useful in scientific research. So scientists, engineers, irrigators etc. can monitor the conditions of the Markanda River (Tamil Nadu) through the establishment and study of the Indian Monsoon Time Scale. Through this research, we can know the future consequences of the above Markanda River (Tamil Nadu) catchment areas and basins. Plans can be made accordingly. So, Indian scientists can establish the Indian Monsoon Time Scale and predict what is going to happen in the above Markanda River (Tamil Nadu) basins and catchment areas in the coming 50 years roughly. Now let us know how to design and establish of Indian Monsoon Time Scale, how to study the climate changes and how to predict the future conditions of the above Markanda River (Tamil Nadu). To predict the future conditions of the Markanda River (Tamil Nadu),  Indian  Monsoon Time Scale is described below for the convenience of Indian scientists to study the precipitation includes drizzle, rain, sleet, snow, ice pellets, graupel, and hail etc. around the catchment areas of the Markanda River (Tamil Nadu). Indian scientists may select and develop a suitable Monsoon Time Scale which is used to estimate the climate conditions in the catchment areas of the Markanda River (Tamil Nadu) as outlined below.

[Gangadhara Rao Irlapati. Markanda River (Tamil Nadu)  and its future. J Am Sci 2026;22(8):31-106]. ISSN 1545-1003 (print); ISSN 2375-7264 (online). http://www.jofamericanscience.org. 04. doi:10.7537/marsjas220826.04

Keywords: Bioforecast (1965-70); A New Hypothetical Model of Cosmology (1970-77) ; Inquisition(1977-79) ; Basics of Geoscope (1980-87) ; Basics of Monsoon Time Scales (1987-91) ; Indian Monsoon Time Scale (1991) ; Researches on Earth and space related issues (1991-2000) ; Numerical Weather Periodic Tables (2000-10) ; Designs of Geoscope projects (2010-20) ; Designs of Global Monsoon Time Scales (2020-)

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