TY - CHAP
T1 - Harmonic Forcing of a Two-Segment Timoshenko Beam
AU - Mazzei, Arnaldo J.
AU - Scott, Richard A.
PY - 2018/5/31
Y1 - 2018/5/31
N2 - This work treats the lateral harmonic forcing, with spatial dependencies, of a two-segment beam. The segments are compact so Timoshenko theory is employed. Initially the external transverse load is assumed to be spatially constant. The goal is the determination of frequency response functions. A novel approach is used, in which material and geometric discontinuities are modeled by continuously varying functions. Here logistic functions are used so potential problems with slope discontinuities are avoided. The approach results in a single set of ordinary differential equations with variable coefficients, which is solved numerically, for specific parameter values, using MAPLE®. Accuracy of the approach is assessed using analytic and assumed mode Rayleigh-Ritz type solutions. Free-fixed and fixed-fixed boundary conditions are treated and good agreement is found. Finally, a spatially varying load is examined. Analytic solutions may not be readily available for these cases thus the new method is used in the investigation.
AB - This work treats the lateral harmonic forcing, with spatial dependencies, of a two-segment beam. The segments are compact so Timoshenko theory is employed. Initially the external transverse load is assumed to be spatially constant. The goal is the determination of frequency response functions. A novel approach is used, in which material and geometric discontinuities are modeled by continuously varying functions. Here logistic functions are used so potential problems with slope discontinuities are avoided. The approach results in a single set of ordinary differential equations with variable coefficients, which is solved numerically, for specific parameter values, using MAPLE®. Accuracy of the approach is assessed using analytic and assumed mode Rayleigh-Ritz type solutions. Free-fixed and fixed-fixed boundary conditions are treated and good agreement is found. Finally, a spatially varying load is examined. Analytic solutions may not be readily available for these cases thus the new method is used in the investigation.
UR - https://digitalcommons.kettering.edu/mech_eng_facultypubs/187
UR - https://doi.org/10.1007/978-3-319-75390-4_1
U2 - 10.1007/978-3-319-75390-4_1
DO - 10.1007/978-3-319-75390-4_1
M3 - Chapter
BT - Special Topics in Structural Dynamics
ER -