Exact Closed Form Characteristic Equations for Transverse Vibration of Timoshenko Beams

Journal of Solid Mechanics

مقاله 5، دوره 15، شماره 3، آذر 2023، صفحه 288-298   

نوع مقاله: Research Paper

شناسه دیجیتال (DOI): 10.22034/jsm.2023.1971470.1757

نویسندگان

Shahriar Hosseini-Hashemi¹؛ K Hosseini-Hashemi²؛ R Nazemnezhad^{* 3}

¹Impact Research Laboratory, Iran University of Science and Technology, Tehran, Iran

²School of Mechanical Engineering, Iran University of Science and Technology, Tehran, Iran

³School of Engineering, Damghan University, Damghan, Iran

چکیده

The dimensionless equations of motion are derived based on the Timoshenko beam theory to study the transverse vibration of beams without further usage of any approximate method. The exact closed form characteristic equations are given within the validity of the Timoshenko beam theory for beams having various boundary conditions. Accurate Eigen frequency parameters are presented for a different length to height ratio for each case. The exact closed form mode shapes related to deflection, slope due to bending and stress resultants are also presented and illustrated for some cases. The modal tests are performed for beams with clamped-Free and Free-Free boundary conditions. Finally, the effect of boundary conditions, length to height ratio on the eigenvalues parameters and vibratory behavior of each distinct case are studied. Validity of the derived closed form characteristic equations are checked through comparison of numerical solutions with the available results. It is believed that in the present work, the exact closed form characteristic equations and their associated Eigen functions, except for the beams with simply supported ends, for the rest of considered cases are obtained for the first time.                 

کلیدواژه‌ها

Bench mark equation؛ Transverse vibration؛ Timoshenko beam؛ Characteristic equation

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