Analysis on Vibroacoustic Fatigue Life of Empennage in a Hypersonic Vehicle

<table class="table-group" id="tab2"><tr><td><table class="table"><tr><td class="thead-hr" colspan="2"><hr/></td></tr><tr class="thead"><td class="align_left">Modal order</td><td class="align_center">Natural frequency (Hz)</td></tr><tr><td class="thead-hr" colspan="2"><hr/></td></tr><tr><td class="align_left">1</td><td class="align_center">33.5774</td></tr><tr><td class="align_left">2</td><td class="align_center">36.7333</td></tr><tr><td class="align_left">3</td><td class="align_center">153.0123</td></tr><tr><td class="align_left">4</td><td class="align_center">208.4317</td></tr><tr><td class="align_left">5</td><td class="align_center">397.1541</td></tr><tr><td class="align_left"><span style="width: 3.07474ptpx;"><svg height="19.9059pt" id="M26" style="vertical-align:-0.2063999pt" version="1.1" viewbox="-0.0498162 -19.6995 3.07474 19.9059" width="3.07474pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,-10.46)"><path d="M113 -12C146 -12 170 11 170 46C170 78 146 103 114 103S58 78 58 46C58 11 82 -12 113 -12Z"></path></g><g transform="matrix(.013,0,0,-0.013,0,-5.23)"><path d="M113 -12C146 -12 170 11 170 46C170 78 146 103 114 103S58 78 58 46C58 11 82 -12 113 -12Z"></path></g><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M113 -12C146 -12 170 11 170 46C170 78 146 103 114 103S58 78 58 46C58 11 82 -12 113 -12Z"></path></g></svg></span></td><td class="align_center"><span style="width: 3.07474ptpx;"><svg height="19.9059pt" id="M27" style="vertical-align:-0.2063999pt" version="1.1" viewbox="-0.0498162 -19.6995 3.07474 19.9059" width="3.07474pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,-10.46)"><path d="M113 -12C146 -12 170 11 170 46C170 78 146 103 114 103S58 78 58 46C58 11 82 -12 113 -12Z"></path></g><g transform="matrix(.013,0,0,-0.013,0,-5.23)"><path d="M113 -12C146 -12 170 11 170 46C170 78 146 103 114 103S58 78 58 46C58 11 82 -12 113 -12Z"></path></g><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M113 -12C146 -12 170 11 170 46C170 78 146 103 114 103S58 78 58 46C58 11 82 -12 113 -12Z"></path></g></svg></span></td></tr><tr><td class="align_left">31</td><td class="align_center">1012.5375</td></tr><tr><td class="align_left"><span style="width: 3.07474ptpx;"><svg height="19.9059pt" id="M28" style="vertical-align:-0.2063999pt" version="1.1" viewbox="-0.0498162 -19.6995 3.07474 19.9059" width="3.07474pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,-10.46)"><path d="M113 -12C146 -12 170 11 170 46C170 78 146 103 114 103S58 78 58 46C58 11 82 -12 113 -12Z"></path></g><g transform="matrix(.013,0,0,-0.013,0,-5.23)"><path d="M113 -12C146 -12 170 11 170 46C170 78 146 103 114 103S58 78 58 46C58 11 82 -12 113 -12Z"></path></g><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M113 -12C146 -12 170 11 170 46C170 78 146 103 114 103S58 78 58 46C58 11 82 -12 113 -12Z"></path></g></svg></span></td><td class="align_center"><span style="width: 3.07474ptpx;"><svg height="19.9059pt" id="M29" style="vertical-align:-0.2063999pt" version="1.1" viewbox="-0.0498162 -19.6995 3.07474 19.9059" width="3.07474pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,-10.46)"><path d="M113 -12C146 -12 170 11 170 46C170 78 146 103 114 103S58 78 58 46C58 11 82 -12 113 -12Z"></path></g><g transform="matrix(.013,0,0,-0.013,0,-5.23)"><path d="M113 -12C146 -12 170 11 170 46C170 78 146 103 114 103S58 78 58 46C58 11 82 -12 113 -12Z"></path></g><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M113 -12C146 -12 170 11 170 46C170 78 146 103 114 103S58 78 58 46C58 11 82 -12 113 -12Z"></path></g></svg></span></td></tr><tr><td class="align_left">153</td><td class="align_center">2004.5829</td></tr><tr><td class="align_left"><span style="width: 3.07474ptpx;"><svg height="19.9059pt" id="M30" style="vertical-align:-0.2063999pt" version="1.1" viewbox="-0.0498162 -19.6995 3.07474 19.9059" width="3.07474pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,-10.46)"><path d="M113 -12C146 -12 170 11 170 46C170 78 146 103 114 103S58 78 58 46C58 11 82 -12 113 -12Z"></path></g><g transform="matrix(.013,0,0,-0.013,0,-5.23)"><path d="M113 -12C146 -12 170 11 170 46C170 78 146 103 114 103S58 78 58 46C58 11 82 -12 113 -12Z"></path></g><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M113 -12C146 -12 170 11 170 46C170 78 146 103 114 103S58 78 58 46C58 11 82 -12 113 -12Z"></path></g></svg></span></td><td class="align_center"><span style="width: 3.07474ptpx;"><svg height="19.9059pt" id="M31" style="vertical-align:-0.2063999pt" version="1.1" viewbox="-0.0498162 -19.6995 3.07474 19.9059" width="3.07474pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,-10.46)"><path d="M113 -12C146 -12 170 11 170 46C170 78 146 103 114 103S58 78 58 46C58 11 82 -12 113 -12Z"></path></g><g transform="matrix(.013,0,0,-0.013,0,-5.23)"><path d="M113 -12C146 -12 170 11 170 46C170 78 146 103 114 103S58 78 58 46C58 11 82 -12 113 -12Z"></path></g><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M113 -12C146 -12 170 11 170 46C170 78 146 103 114 103S58 78 58 46C58 11 82 -12 113 -12Z"></path></g></svg></span></td></tr><tr><td class="align_left">495</td><td class="align_center">4005.2000</td></tr><tr><td class="align_left"><span style="width: 3.07474ptpx;"><svg height="19.9059pt" id="M32" style="vertical-align:-0.2063999pt" version="1.1" viewbox="-0.0498162 -19.6995 3.07474 19.9059" width="3.07474pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,-10.46)"><path d="M113 -12C146 -12 170 11 170 46C170 78 146 103 114 103S58 78 58 46C58 11 82 -12 113 -12Z"></path></g><g transform="matrix(.013,0,0,-0.013,0,-5.23)"><path d="M113 -12C146 -12 170 11 170 46C170 78 146 103 114 103S58 78 58 46C58 11 82 -12 113 -12Z"></path></g><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M113 -12C146 -12 170 11 170 46C170 78 146 103 114 103S58 78 58 46C58 11 82 -12 113 -12Z"></path></g></svg></span></td><td class="align_center"><span style="width: 3.07474ptpx;"><svg height="19.9059pt" id="M33" style="vertical-align:-0.2063999pt" version="1.1" viewbox="-0.0498162 -19.6995 3.07474 19.9059" width="3.07474pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,-10.46)"><path d="M113 -12C146 -12 170 11 170 46C170 78 146 103 114 103S58 78 58 46C58 11 82 -12 113 -12Z"></path></g><g transform="matrix(.013,0,0,-0.013,0,-5.23)"><path d="M113 -12C146 -12 170 11 170 46C170 78 146 103 114 103S58 78 58 46C58 11 82 -12 113 -12Z"></path></g><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M113 -12C146 -12 170 11 170 46C170 78 146 103 114 103S58 78 58 46C58 11 82 -12 113 -12Z"></path></g></svg></span></td></tr><tr><td class="align_left">900</td><td class="align_center">6000.4287</td></tr><tr class="table-tr"><td colspan="2"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

Mathematical Problems in Engineering

tab2

Table 2

Table 2: Analysis on Vibroacoustic Fatigue Life of Empennage in a Hypersonic Vehicle 