TY - JOUR
T1 - Graphical representation of Timoshenko beam modes for clamped-clamped boundary conditions at high frequency
T2 - Beyond transverse deflection
AU - Smith, Robert W.M.
N1 - Funding Information:
The author thanks Thomas B. Gabrielson and Steven L. Garrett for useful discussions leading to this work. Support for this work was provided in part by the Applied Research Laboratory of the Pennsylvania State University.
PY - 2008/6
Y1 - 2008/6
N2 - Transverse deflection and bending-slope mode shapes for a clamped-clamped Timoshenko beam are presented in combined form and compared with finite element (FE) results. The linkage between the cut-on frequency for multiple phase velocities, and noteworthy change in the character of the mode shapes predicted by Timoshenko beam theory (TBT), observed in recent paper by van Rensburg and van der Merwe, is illustrated. While previous work in bounded systems has employed comparisons of TBT and FE obtained resonance frequencies to demonstrate the limits of validity of TBT, direct comparison of the mode shapes predicted by TBT and FE provides an alternative means of comparison, and unambiguously indicates TBT is not valid above the cut-on frequency for the case considered. Typographical errors in Huang's analysis are also noted.
AB - Transverse deflection and bending-slope mode shapes for a clamped-clamped Timoshenko beam are presented in combined form and compared with finite element (FE) results. The linkage between the cut-on frequency for multiple phase velocities, and noteworthy change in the character of the mode shapes predicted by Timoshenko beam theory (TBT), observed in recent paper by van Rensburg and van der Merwe, is illustrated. While previous work in bounded systems has employed comparisons of TBT and FE obtained resonance frequencies to demonstrate the limits of validity of TBT, direct comparison of the mode shapes predicted by TBT and FE provides an alternative means of comparison, and unambiguously indicates TBT is not valid above the cut-on frequency for the case considered. Typographical errors in Huang's analysis are also noted.
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U2 - 10.1016/j.wavemoti.2008.01.002
DO - 10.1016/j.wavemoti.2008.01.002
M3 - Article
AN - SCOPUS:44549085428
SN - 0165-2125
VL - 45
SP - 785
EP - 794
JO - Wave Motion
JF - Wave Motion
IS - 6
ER -