Influence of Non-Structural Localized Inertia on Free Vibration Response of Thin-Walled Structures by Variable Kinematic Beam Formulations

<table class="table-group" width="800px"><tr class="fig-image" id="a"><td><img alt="141982.fig.0019a" src="https://static.hindawi.com/articles/sv/volume-2014/141982/figures/141982.fig.0019a.jpg"/></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(a) </b>Mode 2, <svg height="11.225" id="M251" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 16.4375 11.225" width="16.4375" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,10.963)"><path d="M384 0h-275v27q67 5 81.5 18.5t14.5 68.5v385q0 38 -7.5 47.5t-40.5 10.5l-48 2v24q85 15 178 52v-521q0 -55 14.5 -68.5t82.5 -18.5v-27z" id="x31"></path></g><g transform="matrix(.017,-0,0,-.017,8.222,10.963)"><path d="M137 343l67 33q37 17 63 17q79 0 129.5 -53t50.5 -131q0 -92 -58 -156.5t-147 -64.5t-147 68t-58 182q0 63 17 119t43 95.5t61.5 72t69 52t67.5 31.5q62 22 128 33l6 -32q-56 -11 -108 -35q-149 -71 -184 -231zM227 337q-47 0 -95 -27q-6 -23 -6 -70q0 -93 36 -155.5
t96 -62.5q53 0 78 45.5t25 105.5q0 68 -35 116t-99 48z" id="x36"></path></g>
</svg> L9 LE model (57.023 Hz)</td></tr></table></td></tr><tr class="fig-image" id="b"><td><img alt="141982.fig.0019b" src="https://static.hindawi.com/articles/sv/volume-2014/141982/figures/141982.fig.0019b.jpg"/></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(b) </b>Mode 2, FEM-3D model (54.551 Hz)</td></tr></table></td></tr><tr class="fig-image" id="c"><td><img alt="141982.fig.0019c" src="https://static.hindawi.com/articles/sv/volume-2014/141982/figures/141982.fig.0019c.jpg"/></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(c) </b>Mode 10, <svg height="11.225" id="M252" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 16.4375 11.225" width="16.4375" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,10.963)"><path d="M384 0h-275v27q67 5 81.5 18.5t14.5 68.5v385q0 38 -7.5 47.5t-40.5 10.5l-48 2v24q85 15 178 52v-521q0 -55 14.5 -68.5t82.5 -18.5v-27z" id="x31"></path></g><g transform="matrix(.017,-0,0,-.017,8.222,10.963)"><path d="M137 343l67 33q37 17 63 17q79 0 129.5 -53t50.5 -131q0 -92 -58 -156.5t-147 -64.5t-147 68t-58 182q0 63 17 119t43 95.5t61.5 72t69 52t67.5 31.5q62 22 128 33l6 -32q-56 -11 -108 -35q-149 -71 -184 -231zM227 337q-47 0 -95 -27q-6 -23 -6 -70q0 -93 36 -155.5
t96 -62.5q53 0 78 45.5t25 105.5q0 68 -35 116t-99 48z" id="x36"></path></g>
</svg> L9 LE model (109.87 Hz)</td></tr></table></td></tr><tr class="fig-image" id="d"><td><img alt="141982.fig.0019d" src="https://static.hindawi.com/articles/sv/volume-2014/141982/figures/141982.fig.0019d.jpg"/></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(d) </b>Mode 10, FEM-3D model (101.58 Hz)</td></tr></table></td></tr></table>

<table>Modal shapes of the hollow-rectangular box beam.</table>

Shock and Vibration

fig19

Figure 19

Figure 19: Influence of Non-Structural Localized Inertia on Free Vibration Response of Thin-Walled Structures by Variable Kinematic Beam Formulations 

Figure 19 | Influence of Non-Structural Localized Inertia on Free Vibration Response of Thin-Walled Structures by Variable Kinematic Beam Formulations 