Asymptotic solutions of non-classical boundary-value problems of the natural vibrations of orthotropic shells |
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| Institution: | 1. Institute of Applied Dynamics, Department of Mechanical Engineering, Technical University of Darmstadt, Otto-Berndt-Str. 2, 64287 Darmstadt, Germany;2. Rotordynamics & Preventive Acoustics, Global Engineering Core Science, BorgWarner Turbo Systems Engineering, DE-67292 Kirchheimbolanden, Germany;1. School of Materials, The University of Manchester, Manchester, M13 9PL, England, UK;2. Oxford Instruments NanoAnalysis, HP12 2SE, High Wycombe, UK;1. Advanced Structural Integrity and Vibration Research (ASIVR), Faculty of Mechanical Engineering, Universiti Malaysia Pahang (UMP), 26600, Pekan, Pahang, Malaysia;2. Photonics Research Centre, Faculty of Science, University of Malaya, 50603, Kuala Lumpur, Malaysia |
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| Abstract: | The natural vibrations of orthotropic shells are considered in a three-dimensional formulation for different versions of the boundary conditions on the faces: rigid clamping rigid clamping, rigid clamping free surface, and mixed conditions. Asymptotic solutions of the corresponding dynamic equations of the three-dimensional problem of the theory of elasticity are obtained. The principal values of the frequencies of natural vibrations are determined. It is shown that three types of natural vibrations occur in the shell: two shear vibrations and a longitudinal vibration, which are due solely to the boundary conditions on the faces. It is proved that each boundary layer has its own natural frequency. The boundary-layer functions are determined and the rates at which they decrease with distance from the faces inside the shell are established. |
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