Transverse Vibrations of an Orthotropic Plate with a Collection of Inclusions of Any Configuration with Different Types
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TRANSVERSE VIBRATIONS OF AN ORTHOTROPIC PLATE WITH A COLLECTION OF INCLUSIONS OF ANY CONFIGURATION WITH DIFFERENT TYPES OF CONNECTIONS WITH THE MATRIX T. V. Shopa
UDC 539.3
Within the framework of an improved theory that takes into account transverse shear strains and inertial components, we construct the solution of the problem of stationary flexural vibration of an orthotropic plate containing a collection of arbitrarily located curvilinear inclusions. We analyze various types of connections of these inclusions with the plate. The outer boundary of the plate has an arbitrary geometric configuration. In this boundary, we impose mixed boundary conditions harmonic in time. The solution is constructed by using the indirect method of boundary element. We used the sequential approach to the representation of Green functions. Keywords: vibration, orthotropic plate, holes, indirect method of boundary elements.
Introduction In the literature, one can find mainly the investigations of the vibration of plates with concentrated or attached masses. However, the problem of through inclusions of certain sizes and shapes is not well investigated. In [1], the solution of the problem of transverse vibration of a rectangular orthotropic hingedly supported plate containing an arbitrarily located absolutely rigid inclusion of any geometric shape was constructed within the framework of a simplified Timoshenko model by using the indirect method of boundary elements and the indirect approach to finding Green's functions. The inclusion is rigidly fastened to the plate. The authors investigated the influence of its mass on the frequencies of natural vibrations of the plate in the presence of central circular inclusion. The influence of preliminary tension on the forced vibration of a hingedly supported plate with two circular inclusions under the action of harmonic (in time) flexural forces on the upper face was analyzed in [2]. The boundary-value problem was formulated on the basis of the three-dimensional linearized theory of elastic waves in prestressed bodies and solved by the finite-element method. The dynamic stress concentration around inclusions was analyzed. In what follows, we construct the solution of the problem of stationary vibration of an orthotropic plate with an arbitrary number of inclusions of any shapes, orientations, and locations, different types of connections with the plate, and arbitrary mixed harmonic (in time) boundary conditions on the outer boundary of the plate of any shape by the indirect boundary-element method within the framework of an improved theory that takes into account the presence of transverse shears and inertial components, including the rotary inertia. Pidstryhach Institute for Applied Problems in Mechanics and Mathematics, Ukrainian National Academy of Sciences, Lviv, Ukraine; e-mail: [email protected]. Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 55, No. 1, pp. 89–97, January–February, 2019. Original article submitted March 16, 2018. 94
1068-820X/19/5501–0094
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