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Tuesday, July 9 • 15:30 - 15:50

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With the continuous development of industry, variable section beams including high speed moving loads with large mass are widely used. Thus, it is of great significance to study the vibration response of variable-section beam considering inertia effect. Most past research focuses on the vibration response of uniform beams considering inertial effects, but there is little research on the vibration response of variable section beam with moving loads considering the inertia effect. In this paper, a variable section beam is simplified as a multi-stage ladder beam. Based on the Timoshenko beam model, the lateral vibration differential equation of the Timoshenko beam is expressed as the form of the transfer matrix. Then the specific boundary conditions are substituted to solve the natural frequency and mode shape of the system. The Newmark method is used to solve the forced vibration response of the ladder beam with a moving load considering inertial effect. Following this step, the vibration response considering the influence of the inertia effect is studied and compared with the situation that does not consider the influence of inertia effect. In addition, the calculation results are compared with Euler beam model. The results show that the mass, velocity, and acceleration of moving loads influence the response of the variable section beam considering inertia effect. Mass is the main factor which affects the results. The inertia effect caused by the acceleration and velocity can be ignored when the mass of moving load is small. At high-order natural frequency, the natural frequency of the Timoshenko beam is lower than the natural frequency of the Euler beam; At low-order natural frequency, the difference between the two is small.The results have good engineering applicability.

avatar for Simon Jones

Simon Jones

Associate Professor, Rose-Hulman Institute of Technology
Professional interests include undergraduate engineering education, finite element modeling, ground-borne vibrations, vibrations of musical instruments, and dynamics of toys.

Guilhem Michon



Tuesday July 9, 2019 15:30 - 15:50 EDT
St-Laurent 7
  T07 Struct. dyn. & nonlin. vib., RS03 Struct ac & vibr

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