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- W619707460 abstract "The primary goal of this investigation was to deter mine the effects of concentrated external viscous damping proportional to transverse velocity on the free and forced vibration of beams. The model used to represent this problem was the elementary Bernoulli-Euler differential equation for flexural vibration, which was modified by add ing terms representing the type of damping under considera tion. Starting from this modified equation, general solu tions were derived in terms of both exact and approximate representations of the normal modes of free damped vibra tion. Galerkin's method was used to construct the approxi mate solution, which may be applied to a wide variety of beam configurations for which an exact solution is either impossible or prohibitively difficult. Both general solu tions are presented in a form applicable to any beam configuration' with homogeneous boundary conditions, either distributed or concentrated damping, and arbitrary forcing input and initial conditions. Numerical results for a specific example were cal culated from both solutions. The example chosen was a uniform simply supported beam with a dashpot attached at viii ix the center of its span. Normal mode functions and charac teristic frequencies were calculated for a range of dashpot strength by both methods; comparison showed very good agreement between exact and approximate values. Forced vibration due to sinusoidal motion of the beam supports was considered, and the steady state strain energy and power dissipated by damping were computed using the approximate solution. Results for the example showed that the influence of concentrated damping may be interpreted in terms of its effects on the normal modes of vibration. These effects were found to differ both qualitatively and quantitatively for the various modes. The relationship between the normal modes of damped vibration and their more familiar undamped counter parts was examined, and a physically meaningful descrip tion of the nature of these modes was offered. Comments on the utility of the normal mode solutions and suggestions for further investigation are included." @default.
- W619707460 created "2016-06-24" @default.
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- W619707460 date "1968-01-01" @default.
- W619707460 modified "2023-09-24" @default.
- W619707460 title "FLEXURAL VIBRATION OF BEAMS WITH EXTERNAL VISCOUS DAMPING" @default.
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- W619707460 hasPublicationYear "1968" @default.
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