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Dynamic Analysis of Timoshenko Beam with Nonuniform Cross Section and Kirchhoff Plate with Nonuniform Thickness Under Moving Mass

Roshandel, Davood | 2010

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 41025 (09)
  4. University: Sharif University of Technology
  5. Department: Civil Engineering
  6. Advisor(s): Mofid, Massoud
  7. Abstract:
  8. In this study dynamic response of Timoshenko beam and rectangular Kirchhoff plate under moving mass are investigated. Applying Hamilton’s principle, governing differential equations of beam and plate are derived considering the effect of moving mass. Afterward, a numerical-analytical solution based on eigen function expansion method for analyzing nonuniform beams and plates by means of beams’ and plates’ free vibration modes is presented and convergence of the solution is proved by proving that the governing differential equations of Timoshenko beam and Kirchhoff plates are self adjoint. Modal orthogonality circumstances are discussed due to their important role in eigen function expansion method which leads to a method for analyzing Timoshenko beam with various boundary conditions and Kirchhoff plate with rotational inertia. Next various numerical examples are solved using eigen function expansion method. Several cases such as Timoshenko beam with various boundary conditions, Timoshenko beam with nonuniform cross section, rectangular Kirchhoff plate considering rotational inertia, rectangular Kirchhoff plate with nonuniform thickness and effect of multi traveling masses on beams and plates are analyzed. With respect to variety of plate’s boundary conditions, in this study numerical examples are only presented for two boundary conditions: simple-free-simple-free and four simple edges
  9. Keywords:
  10. Traveling Mass ; Kirchhoff Rectangular Plate ; Non-Uniform Cross-Section Beam ; Selfadjoint ; Timoshenko Beams ; Boundary Conditions ; Eigen Function Expansion

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