Structural Engineering and Mechanics

  • 제9권3호
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  • Pages.269-288
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  • 2000
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  • 1225-4568(pISSN)
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  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

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Exact solutions for free vibration of multi-step orthotropic shear plates

  • Li, Q.S. (Structural Dynamics Research Centre, Department of Building and Construction, City University of Hong Kong)
  • 발행 : 2000.03.25
⟨ 이전 논문 다음 논문 ⟩

초록

The governing differential equations for free vibration of multi-step orthotropic shear plates with variably distributed mass, stiffness and viscous damping are established. It is shown that a shear plate can be divided into two independent shear bars to determine the natural frequencies and mode shapes of the plate. The jk-th natural frequency of a shear plate is equal to the square root of the square sum of the j-th natural frequency of a shear bar and the k-th natural frequency of another shear bar. The jk-th mode shape of the shear plate is the product of the j-th mode shape of a shear bar and the k-th mode shape of another shear bar. The general solutions of the governing equations of the orthotropic shear plates with various boundary conditions are derived by selecting suitable expressions, such as power functions and exponential functions, for the distributions of stiffness and mass along the height of the plates. A numerical example demonstrates that the present methods are easy to implement and efficient. It is also shown through the numerical example that the selected expressions are suitable for describing the distributions of stiffness and mass of typical multi-storey buildings.

키워드

참고문헌

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피인용 문헌

  1. Vibratory characteristics of multistep nonuniform orthotropic shear plates with line spring supports and line masses vol.110, pp.3, 2001, https://doi.org/10.1121/1.1387995
  2. Bending and vibration characteristics of a strengthened plate under various boundary conditions vol.25, pp.9, 2003, https://doi.org/10.1016/S0141-0296(03)00063-4
  3. Time-dependent interfacial sliding in fiber composites under longitudinal shear vol.61, pp.4, 2001, https://doi.org/10.1016/S0266-3538(00)00237-2
  4. Stability of multi-step flexural-shear plates with varying cross-section vol.16, pp.5, 2003, https://doi.org/10.12989/sem.2003.16.5.597