Research Article
Effect of Parabolically Varying Non-homogeneity on Thermally Induced Vibration of Orthotropic Trapezoidal Plate with Thickness Varies Parabolically in Both Directions
Issue:
Volume 1, Issue 1, March 2026
Pages:
1-11
Received:
26 August 2025
Accepted:
23 January 2026
Published:
6 February 2026
Abstract: The aim of present paper is to find the frequencies using the mathematical model: Effect of parabolically varying non-homogeneity on thermally induced vibration of orthotropic trapezoidal plate with thickness varies parabolically in both directions. In the above model both thickness and density varies parabolically. Rayleigh-Ritz method is used to solve the governing differential equation for maximum strain energy and maximum kinetic energy for orthotropic trapezoidal plate. Two term deflection function corresponding to clamped-simply supported clamped-simply supported (C-S-C-S) boundary condition is defined by the product of the equation of the prescribed continuous piecewise boundary shape. The effect of frequencies for first and second mode investigated with the variations in structural parameters such as taper constant, non-homogeneity constant, aspect ratio and thermal gradient respectively. Differential equations for maximum strain energy and maximum kinetic energy for orthotropic trapezoidal plate are solved using the mathematica software. All the results are calculated with great accuracy and are displayed graphically. To validate the model all the results are also compared with the preexisting literature and fit well. So by developing such type of model we increase sustainability and also reduce the environmental hazards.
Abstract: The aim of present paper is to find the frequencies using the mathematical model: Effect of parabolically varying non-homogeneity on thermally induced vibration of orthotropic trapezoidal plate with thickness varies parabolically in both directions. In the above model both thickness and density varies parabolically. Rayleigh-Ritz method is used to ...
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Research Article
Modification of Automobile Shock Absorbers Thickness and Weight Parameters for Adaptation on Poorly Maintained Roads via Mathematical Modelling
Benard Ouma Owino*,
Cleophas M. Kweyu,
Titus Chebion Rotich
Issue:
Volume 1, Issue 1, March 2026
Pages:
12-18
Received:
27 August 2025
Accepted:
8 September 2025
Published:
14 February 2026
Abstract: Uneven oscillatory forces applied to an object cause vibration, which can lead to noise, discomfort, and mechanical wear. The optimization of shock absorber thickness and weight is critical for enhancing vehicle performance on poorly maintained roads. In automobiles, vibrations due to irregular road surfaces have been mitigated using shock absorbers to enhance performance, comfort, and control. The main aim of this study was to determine the effect of automotive weights and shock absorber thickness on automobile vibrations. The objectives of this study were; to formulate a mathematical model describing the effect of automobile weight on unsteady vibrations; to generate numerical solutions of the mathematical model equations for the shock absorber modified to reduce vibrations at the mounting points; and to analyze from the numerical solution the effects of increase in velocity and weight on the automobile unsteady spring vibration. A mathematical model was developed, utilizing the central difference scheme for discretization and solved using the Jacobian iterative method, with stability conditions implemented. Through computational simulations, various thickness and weight configurations were tested under diverse road conditions. The results indicate a significant improvement in shock absorber performance, with optimized configurations that increasing shock absorber thickness reduced vibration amplitude by approximately 35%, while increased vehicle weight amplified vibrations by 20%, necessitating thicker shock absorbers for stability. Higher speeds above 80 km/h intensified unsteady vibrations on poorly maintained roads. The study concludes that modifying shock absorber thickness and optimizing weight distribution can effectively minimize automobile vibrations.
Abstract: Uneven oscillatory forces applied to an object cause vibration, which can lead to noise, discomfort, and mechanical wear. The optimization of shock absorber thickness and weight is critical for enhancing vehicle performance on poorly maintained roads. In automobiles, vibrations due to irregular road surfaces have been mitigated using shock absorber...
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Research Article
The Effect of Combining Two Models on Mathematical Achievement and the Development of Procedural Fluency Among Fifth-Grade Science Students in Mathematics
Ammar Awad Saleh*
Issue:
Volume 1, Issue 1, March 2026
Pages:
19-33
Received:
12 December 2025
Accepted:
25 December 2025
Published:
14 February 2026
Abstract: This research aims to study the effect of integrating two models on mathematical achievement and the development of procedural fluency among fifth-grade science students in mathematics. The research sample consisted of two groups: an experimental group of (31) students who studied according to the strategies of binary analysis, synthesis, and fragmented knowledge integration, and a control group of (33) students who studied according to the traditional method. The researcher prepared an achievement test tool consisting of multiple-choice objective items and a procedural fluency scale. After conducting the necessary statistical analyses, it was administered to students in both research groups. The results showed statistically significant differences in mathematical achievement and the development of procedural fluency among students, in favor of the experimental group Based on the research results, the researcher recommends the following. 1) Focus on the use of modern teaching strategies, including the analysis and synthesis strategies and the fragmented knowledge integration strategies, in teaching mathematics. 2) Integrate the analysis and synthesis strategies and the fragmented knowledge integration strategies into the curriculum and teaching methods curriculum in colleges of education. The researcher proposed several suggestions, including: 1) Studying the impact of other types of strategies, such as analysis and synthesis and the integration of fragmented knowledge, on various dependent variables, such as attitude, information retention, cognitive preference, concept acquisition, and others. 2) Comparing the impact of analysis and synthesis and the integration of fragmented knowledge with other effective teaching strategies, such as mental description, constructivist learning, and multiple intelligences..
Abstract: This research aims to study the effect of integrating two models on mathematical achievement and the development of procedural fluency among fifth-grade science students in mathematics. The research sample consisted of two groups: an experimental group of (31) students who studied according to the strategies of binary analysis, synthesis, and fragm...
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