On the Mechanism of Energy Loss During Wave Propagation in an Elastic Medium Containing a Small Volume Fraction of Spherical Inclusions

On the Mechanism of Energy Loss During Wave Propagation in an Elastic Medium Containing a Small Volume Fraction of Spherical Inclusions | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article On the Mechanism of Energy Loss During Wave Propagation in an Elastic Medium Containing a Small Volume Fraction of Spherical Inclusions Safarov Ismoil, Teshaev Muhsin, Usmonov Botir, Saipnazarov Jonibek This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7582182/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Problems related to the identification of inhomogeneities, as well as the determination of their sizes and physical properties, are considered highly important and relevant in geophysics. This study investigates the influence of spherical wave curvature on the dynamic stresses in viscoelastic spherical bodies and the surrounding deformable medium. Based on the study of spherical compression wave scattering on a spherical body embedded in a viscoelastic medium, the dynamic stresses in both the body and the surrounding medium are determined. The aim of this study is to investigate the dynamic stress-strain state of spherical bodies under the action of spherical longitudinal or transverse harmonic waves, and to analyze the effect of spherical wave curvature on the dynamic stresses in viscoelastic spherical bodies. Methods. The equations of motion for spherical bodies are described by integro-differential equations derived based on the assumptions of viscoelasticity theory. The problem of diffraction of harmonic spherical waves in a spherical body is solved using displacement potentials. The displacement potentials are determined from the solutions of the Helmholtz equations. The arbitrary constants are found from boundary conditions imposed between the bodies. As a result, the formulated problem is reduced to a system of inhomogeneous algebraic equations with complex coefficients. Based on the methods of Muller, Gauss, and Laplace, a solution methodology and algorithm have been developed. Results In the course of the solution, it was found that at certain values of the viscoelastic and density parameters of the inclusion, low-frequency natural oscillations arise in the unbounded medium. These oscillations are essentially aperiodic motions, since the imaginary part of the natural frequency is large. viscoelastic body longitudinal and transverse oscillations dynamic deformation spherical wave displacement amplitude Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-7582182","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":515669507,"identity":"84e569f1-1c31-4d04-a256-ce9cb8b158e0","order_by":0,"name":"Safarov Ismoil","email":"","orcid":"","institution":"Tashkent Chemical-Technological Institute","correspondingAuthor":false,"prefix":"","firstName":"Safarov","middleName":"","lastName":"Ismoil","suffix":""},{"id":515669508,"identity":"4859b267-c19a-4ce8-a9a3-d85990b6e910","order_by":1,"name":"Teshaev Muhsin","email":"","orcid":"","institution":"Academy of Sciences of Uzbekistan named after V.I. 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This study investigates the influence of spherical wave curvature on the dynamic stresses in viscoelastic spherical bodies and the surrounding deformable medium. Based on the study of spherical compression wave scattering on a spherical body embedded in a viscoelastic medium, the dynamic stresses in both the body and the surrounding medium are determined. The aim of this study is to investigate the dynamic stress-strain state of spherical bodies under the action of spherical longitudinal or transverse harmonic waves, and to analyze the effect of spherical wave curvature on the dynamic stresses in viscoelastic spherical bodies.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eMethods.\u003c/strong\u003e The equations of motion for spherical bodies are described by integro-differential equations derived based on the assumptions of viscoelasticity theory. The problem of diffraction of harmonic spherical waves in a spherical body is solved using displacement potentials. The displacement potentials are determined from the solutions of the Helmholtz equations. The arbitrary constants are found from boundary conditions imposed between the bodies. As a result, the formulated problem is reduced to a system of inhomogeneous algebraic equations with complex coefficients. Based on the methods of Muller, Gauss, and Laplace, a solution methodology and algorithm have been developed.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eResults\u003c/strong\u003e In the course of the solution, it was found that at certain values of the viscoelastic and density parameters of the inclusion, low-frequency natural oscillations arise in the unbounded medium. 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