engleski

Vibrational energy flow in spherical shell

Two components of the structural intensity in spherical shell, defined in direction of the usual sphencal coordinates, i. e. the meridional component (in the direction of increasing polar or co-lattitude angle) and peripheral component (in the direction of increasing longitudinal angle), are expressed in terms of displacements of the middle surface. The displacements off the middle surface (the radial dependence) are included in accordance with the Kirchhoff's hypothesis. Only homogeneous and isotropic shell of constant thickness is considered. The components of the structural intensity are integrated across the thickness of the shell's wall to obtain respective components of the unit power flow (the power flow through the section of the shell's wall of unit arc length). Reference to the locally cartesian coordinates (spherical angle multiplied by the radius) at a point on the equator justifies, by analogy to the developable surfaces, an attempt at separation of the term intrinsically dependent on curvature from the "plate-like" terms. (These latter terms for points on the equator correspond to the membrane and flexural terms in flat plates.) Since the expressions for the unit power flow depend only on the instantaneous values of the displacements of the spherical shell, their applicability is limited only by the validity of the Kirchhoff's hypothesis. Description of the free vibrations of the shell is based on a general form of the eqailibrium equations for thin elastic spherical shells which is not limited to the axisymmetrical case. Only the modes of the complete spherical shell are considered. Using this modal decomposition, an analysis is attempted of the influence of the different terms (curvature and plate-like) in their contribution to the total power flow, for the region of frequences admissible by the model approximations.

vibrational energy flow ; spherical shell

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