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To acquire exact solutions of double-functionally graded Timoshenko beam system on Winkler-Pasternk elastic foundation, which are benchmarks of double-beam systems in the field of engineering, motion differential equations of double-beam system are derived using Hamilton’s principle. In this paper, the exact dynamic stiffness matrix of double-functionally graded Timoshenko beam system on Winkler-Pasternak...
In this paper, the motion differential equations of the bi-directional functionally graded Timoshenko beam are established using Hamilton’s principle. The material properties of the beam change exponentially in both axial and thickness directions. Using the variable substitution method, state space differential equations of the structure are established. First, the dynamic stiffness matrix is formed...
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