Arabian Journal for Science and Engineering https://doi.org/10.1007/s13369-018-3577-4 RESEARCH ARTICLE - CIVIL ENGINEERING Analytical Study on Dynamic Response Due to a Moving Load on Distinctly Characterized Orthotropic Half-Spaces Under Different Physical Conditions with Comparative Approach A. K. Singh 1 · M. K. Pal 1 · A. Negi 1 · K. Ch. Mistri 1 Received: 18 June 2017 / Accepted: 26 September 2018 © King Fahd University of Petroleum & Minerals 2018 Abstract The present article analyzes the induced compressive, shear and tensile stresses due to a moving load on three distinctly char- acterized irregular orthotropic half-spaces, viz. functionally graded orthotropic viscoelastic half-space (Case-I), functionally graded initially stressed orthotropic elastic half-space (Case-II) and orthotropic magnetoelastic half-space (Case-III) under hydrostatic initial stress. The expressions for said induced stresses are deduced in closed form using analytical approach. The influences of various physical parameters, viz. maximum depth of irregularity, functionally gradedness, irregularity factor, initial stress, magnetoelastic coupling parameter, hydrostatic initial stress and frictional coefficient on induced stresses for concerned cases, have been investigated with a comparative analysis. To depict the outcomes numerically, the half-spaces comprised of Carbon fiber, Prepreg and T300/5208/graphite/epoxy material have been taken into account and the observations are highlighted. Moreover, some notable characteristics have been outlined and delineated through graphs. Keywords Moving load · Induced stress · Orthotropic–viscoelastic · Orthotropic–magnetoelastic · Functionally graded 1 Introduction Investigation on response of medium subjected to static or moving load has drawn considerable attention of many researchers and engineers for the past few decades [1]. The dynamic problems subjected to moving loads are common in real-world scenario. In daily life, the different types of structures used in conveyance, viz. bridges, guideways, over- head cranes, cableways, runways, roadways, are subjected to moving load. Due to variation in position, the moving load differs from other dynamic loads [2]. Furthermore, due to increase in high-speed train networks, the elevation of vibration level due to high-speed trains is a challeng- ing problem for engineers and researchers. Generally, the movement of dynamic load (viz. movement of high-speed trains over a structure) excites the structure which may result into elevation of vibration levels. Due to this, railway tracks may get significantly influenced which may further cause accident and affect passenger safety [3]. Therefore, B M. K. Pal mkpal.mathematics@gmail.com 1 Indian Institute of Technology (Indian School of Mines) Dhanbad, Dhanbad, Jharkhand, India the investigation of stresses induced due to a moving load becomes imperative for many researchers because it may be used to examine the dynamic strength of the structure. The anisotropic materials have been extensively used in engineering applications for the past few years. The struc- tures corresponding to orthotropic symmetry have significant applications to mechanical and civil engineering because of different material properties in two mutually perpendicular directions. The dynamic response of an orthotropic medium subjected to a moving load plays a vital role in the design of bridge [4]. Many engineering materials such as laminated composite, fibrous composite, rolled sheets can be regarded as orthotropic materials. Most bridge decks used in highway bridges are orthotropic in nature [4,5]. Orthotropic materi- als (e.g., graphite/epoxy) have been also used in the design of aircraft structures because of high specific strength and stiffness, resistance to cracking by fatigue loading and their immunity to corrosion [6]. In the present scenario, function- ally graded materials (FGMs) have received considerable attention because of its possible applications in astronautic and aeronautic engineering. The inhomogeneous composites defined by gradual variations in both compositional charac- teristics and material properties are classified as functionally graded materials. These types of materials are broadly used 123