Free vibration analysis of circular thin plates with stepped thickness by the DSC element method |
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| Affiliation: | 1. State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, No. 29 Yudao Street, Nanjing 210016, China;2. School of Civil Engineering and Architecture, Nantong University, Nantong 224019, China;1. Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan, Kashan, 87317-51167, Islamic Republic of Iran;2. Department of Innovation Engineering, Università del Salento, 73100, Lecce, Italy;3. DICAM, Department School of Engineering and Architecture, University of Bologna, Italy;1. Department of Civil Engineering, Faculty of Engineering, Hakim Sabzevari University, Sabzevar, Iran;2. Department of Mechanical Engineering, Faculty of Engineering, Hakim Sabzevari University, Sabzevar, Iran;1. Military Technical Academy, Bucharest, Romania;2. Military Technical Academy, Bucharest, Romania;1. Department of Mechanics, Tianjin University, Tianjin, 300072, China;2. Tianjin Key Laboratory of Nonlinear Dynamics and Control, Tianjin, 300072, China |
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| Abstract: | Novel formulation is presented by using the discrete singular convolution (DSC) for free vibration analysis of circular thin plates with uniform and stepped thickness. Different from the commonly used ones in literature, regularity conditions are not needed at the circular plate center point to avoid singularity. DSC circular and annular thin plate elements are established. For the DSC circular plate element with radius of R1, the stiffness equation is first formulated in region [−R1, R1] with even number of nodes and then reduced to region [0, R1] by using either symmetric or anti-symmetric conditions. The proposed DSC circular and annular plate elements are used for obtaining frequencies of uniform/stepped circular thin plates or annular thin plates with different boundary conditions. Comparison of the present DSC results to existing analytic and numerical solutions verifies the proposed formulations. The present research extends the DSC method to free vibration of circular thin plates with stepped thicknesses. |
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| Keywords: | Novel formulations Discrete singular convolution element method Free vibration Circular thin plate Stepped thickness |
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