The Influence of Imperfect Contact Conditions between Layers of a Hollow Sandwich Sphere on its Natural Frequencies
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THE INFLUENCE OF IMPERFECT CONTACT CONDITIONS BETWEEN LAYERS OF A HOLLOW SANDWICH SPHERE ON ITS NATURAL FREQUENCIES
Y. M. Sevdimaliyev,1* S. D. Akbarov,2,3 and N. Yahnioglu2
Keywords: natural frequencies, hollow sandwich sphere, imperfect contact condition, spheroidal vibration, torsional vibration The influence of imperfect contact conditions between layers of a hollow sandwich sphere on its natural frequencies is studied. It is assumed that the materials of face layers are the same, but different from the core layer material. Each layer is made of a homogeneous isotropic material and has a constant thickness. Investigations are performed using a piecewise homogeneous body model with the use of exact three-dimensional equations and relations of elastodynamics. The solution of the corresponding equations of motion of the hollow sandwich sphere is presented through the Helmholtz potentials in spherical coordinates. Numerical results for the influence of imperfect contact conditions between layers on the natural frequencies of the sphere are presented and discussed. It is established that an imperfect contact between sphere layers can decrease its natural frequencies significantly.
Introduction For engineering applications of structural elements, it is necessary to study problems of their vibration at different external loadings and actions and to determine the dynamic characteristics of structures. One of the most important dynamic characteristics of the elements is their eigenfrequencies. If the frequency of an external force is equal to the eigenfrequency of a structural element, resonance arises, which is most dangerous from the viewpoint of technics, causing the destruction of Baku State University, Azerbaijan Yildiz Technical University, Istanbul 3 Academy of Sciences of Azerbaijan, Baku * Corresponding author; e-mail: [email protected] 1 2
Translated from Mekhanika Kompozitnykh Materialov, Vol. 56, No. 4, pp. 791-812, July-August, 2020. Original article submitted October 22, 2019; revision submitted May 15, 2020. 0191-5665/20/5604-0541 © 2020 Springer Science+Business Media, LLC
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structural members of buildings, plants, flying devices, etc. Moreover, for the occurrence of resonance, it is not necessary that the amplitude of the external load be high. In connection with the wide application of layered composite materials in different leading branches of modern industry, there arises an imperative need for studying eigenfrequencies of structural elements made from these materials and subjected to dynamic actions. Investigations in this area have been carried out mainly for prismatic and cylindrical elements [1-3]. Depending on technological achievements, various are becoming not only materials, but also the forms of structural elements. One of them are spheroidal layered ones to whose eigenfrequencies is devoted the present work. Let us consider some earlier studies. In [4], a mathematical model of the stress-strain state of a three-layer metal composite system of bearing assemblies at grinding is devel
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