Free Vibration Analysis of Fiber Metal Laminate Annular Plate by State-Space Based Differential Quadrature Method

<table>Variation of the first mode natural frequency with the radius of the plate for different layups and clamped-clamped boundary condition (<svg height="12.4375" id="M95" style="vertical-align:-0.1638pt" version="1.1" viewbox="0 0 55.875 12.4375" width="55.875" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,12.162)"><path d="M452 333q0 -82 -46 -164t-116 -128q-81 -53 -158 -53q-26 0 -51 13t-37 32q-26 41 -6 134l91 431q7 40 2.5 47t-34.5 7h-33l2 25q36 4 72.5 13t58.5 15.5t28 6.5q10 0 4 -29l-91 -391h2q65 77 130 116.5t105 39.5q36 0 56.5 -32t20.5 -83zM365 316q0 76 -35 76
q-31 0 -93.5 -49t-107.5 -110q-12 -37 -17 -70q-9 -65 12 -96.5t59 -31.5q31 0 56 14q53 29 89.5 105t36.5 162z" id="x1D44F"></path></g><g transform="matrix(.017,-0,0,-.017,12.744,12.162)"><path d="M535 323h-483v50h483v-50zM535 138h-483v50h483v-50z" id="x3D"></path></g><g transform="matrix(.017,-0,0,-.017,27.447,12.162)"><path d="M241 635q53 0 94 -28.5t63.5 -76t33.5 -102.5t11 -116q0 -58 -11 -112.5t-34 -103.5t-63.5 -78.5t-94.5 -29.5t-95 28t-64.5 75t-34.5 102.5t-11 118.5q0 58 11.5 112.5t34.5 103t64.5 78t95.5 29.5zM238 602q-32 0 -55.5 -25t-35.5 -68t-17.5 -91t-5.5 -105
q0 -76 10 -138.5t37 -107.5t69 -45q32 0 55.5 25t35.5 68.5t17.5 91.5t5.5 105t-5.5 105.5t-18 92t-36 68t-56.5 24.5z" id="x30"></path></g><g transform="matrix(.017,-0,0,-.017,35.607,12.162)"><path d="M113 -12q-24 0 -39.5 16t-15.5 42q0 24 16 40.5t40 16.5t40 -16.5t16 -40.5q0 -26 -16 -42t-41 -16z" id="x2E"></path></g><g transform="matrix(.017,-0,0,-.017,39.483,12.162)"><path d="M241 635q53 0 94 -28.5t63.5 -76t33.5 -102.5t11 -116q0 -58 -11 -112.5t-34 -103.5t-63.5 -78.5t-94.5 -29.5t-95 28t-64.5 75t-34.5 102.5t-11 118.5q0 58 11.5 112.5t34.5 103t64.5 78t95.5 29.5zM238 602q-32 0 -55.5 -25t-35.5 -68t-17.5 -91t-5.5 -105
q0 -76 10 -138.5t37 -107.5t69 -45q32 0 55.5 25t35.5 68.5t17.5 91.5t5.5 105t-5.5 105.5t-18 92t-36 68t-56.5 24.5z" id="x30"></path></g><g transform="matrix(.017,-0,0,-.017,47.642,12.162)"><path d="M153 550l-26 -186q79 31 111 31q90 0 141.5 -51t51.5 -119q0 -93 -89 -166q-85 -69 -173 -71q-32 0 -61.5 11.5t-41.5 23.5q-18 17 -17 34q2 16 22 33q14 9 26 -1q61 -50 124 -50q60 0 93 43.5t33 104.5q0 69 -41.5 110t-121.5 41q-53 0 -102 -20l38 305h286l6 -8
l-26 -65h-233z" id="x35"></path></g>
</svg> m, <svg height="16.450001" id="M96" style="vertical-align:-3.39066pt" version="1.1" viewbox="0 0 70.287498 16.450001" width="70.287498" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,12.162)"><path d="M499 88q-41 -46 -83.5 -73t-68.5 -27q-41 0 -19 98l52 225q10 43 8 59.5t-16 16.5q-37 0 -112 -65t-117 -135q-14 -42 -38 -179q-36 -7 -75 -20l-7 8l127 594q8 40 2.5 49t-35.5 9h-35l5 25q36 3 71.5 13t56.5 18t25 8q11 0 3 -38l-88 -417h2q77 102 195 167q44 24 79 24
q61 0 30 -130l-52 -220q-8 -33 4 -33q8 0 31 14.5t43 33.5z" id="x210E"></path></g>
<g transform="matrix(.012,-0,0,-.012,8.837,16.25)"><path d="M383 397q0 -32 -35 -49q-12 -6 -23 8q-37 45 -84 45t-90 -71q-40 -65 -40 -167q0 -57 22 -86t59 -29q38 0 81.5 24.5t69.5 51.5l16 -21q-44 -53 -104 -84t-109 -31q-56 0 -89.5 41t-33.5 117q0 61 30 124t79 105q33 28 81 50.5t86 22.5q34 0 59 -15.5t25 -35.5z" id="x1D450"></path></g>
<g transform="matrix(.017,-0,0,-.017,19.013,12.162)"><path d="M535 323h-483v50h483v-50zM535 138h-483v50h483v-50z" id="x3D"></path></g><g transform="matrix(.017,-0,0,-.017,33.699,12.162)"><path d="M241 635q53 0 94 -28.5t63.5 -76t33.5 -102.5t11 -116q0 -58 -11 -112.5t-34 -103.5t-63.5 -78.5t-94.5 -29.5t-95 28t-64.5 75t-34.5 102.5t-11 118.5q0 58 11.5 112.5t34.5 103t64.5 78t95.5 29.5zM238 602q-32 0 -55.5 -25t-35.5 -68t-17.5 -91t-5.5 -105
q0 -76 10 -138.5t37 -107.5t69 -45q32 0 55.5 25t35.5 68.5t17.5 91.5t5.5 105t-5.5 105.5t-18 92t-36 68t-56.5 24.5z" id="x30"></path></g><g transform="matrix(.017,-0,0,-.017,41.859,12.162)"><path d="M113 -12q-24 0 -39.5 16t-15.5 42q0 24 16 40.5t40 16.5t40 -16.5t16 -40.5q0 -26 -16 -42t-41 -16z" id="x2E"></path></g><g transform="matrix(.017,-0,0,-.017,45.735,12.162)"><path d="M241 635q53 0 94 -28.5t63.5 -76t33.5 -102.5t11 -116q0 -58 -11 -112.5t-34 -103.5t-63.5 -78.5t-94.5 -29.5t-95 28t-64.5 75t-34.5 102.5t-11 118.5q0 58 11.5 112.5t34.5 103t64.5 78t95.5 29.5zM238 602q-32 0 -55.5 -25t-35.5 -68t-17.5 -91t-5.5 -105
q0 -76 10 -138.5t37 -107.5t69 -45q32 0 55.5 25t35.5 68.5t17.5 91.5t5.5 105t-5.5 105.5t-18 92t-36 68t-56.5 24.5z" id="x30"></path></g><g transform="matrix(.017,-0,0,-.017,53.894,12.162)"><path d="M241 635q53 0 94 -28.5t63.5 -76t33.5 -102.5t11 -116q0 -58 -11 -112.5t-34 -103.5t-63.5 -78.5t-94.5 -29.5t-95 28t-64.5 75t-34.5 102.5t-11 118.5q0 58 11.5 112.5t34.5 103t64.5 78t95.5 29.5zM238 602q-32 0 -55.5 -25t-35.5 -68t-17.5 -91t-5.5 -105
q0 -76 10 -138.5t37 -107.5t69 -45q32 0 55.5 25t35.5 68.5t17.5 91.5t5.5 105t-5.5 105.5t-18 92t-36 68t-56.5 24.5z" id="x30"></path></g><g transform="matrix(.017,-0,0,-.017,62.053,12.162)"><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>
</svg> m).</table>

Advances in Materials Science and Engineering

fig8

Figure 8

Figure 8: Free Vibration Analysis of Fiber Metal Laminate Annular Plate by State-Space Based Differential Quadrature Method 