The Effect of High-Frequency Parametric Excitation on a Stochastically Driven Pantograph-Catenary System

<table>The amplitude <svg height="11.6375" id="M133" style="vertical-align:-0.1638pt" version="1.1" viewbox="0 0 19.625 11.6375" width="19.625" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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<g transform="matrix(.012,-0,0,-.012,7.238,14.938)"><path d="M352 391q0 -31 -27 -44q-14 -7 -24 6q-39 48 -84 48q-23 0 -39.5 -15t-16.5 -40q0 -43 73 -90q49 -32 70 -58t21 -57q0 -58 -62 -105.5t-129 -47.5q-40 0 -75.5 25t-35.5 52q0 28 32 46q7 4 15 3t11 -6q19 -31 48.5 -50.5t54.5 -19.5q34 0 54 19.5t20 42.5q0 43 -65 81
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</svg> and the width of the resonant region <svg height="11.425" id="M135" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 23.887501 11.425" width="23.887501" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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</svg> as functions of the fast excitation parameter <svg height="18.362499" id="M136" style="vertical-align:-5.76988pt" version="1.1" viewbox="0 0 49.775002 18.362499" width="49.775002" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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<g transform="matrix(.012,-0,0,-.012,41.45,15.188)"><path d="M619 670q0 -13 -9 -26t-18 -19q-13 -10 -25 2q-36 38 -66 38q-31 0 -54.5 -50t-45.5 -185h120l-20 -31l-107 -12q-23 -138 -57 -293q-27 -122 -55 -184.5t-75 -109.5q-60 -61 -114 -61q-25 0 -47.5 15t-22.5 31q0 17 31 44q11 8 20 -1q10 -11 31 -19t35 -8q26 0 47 19
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</svg>.</table>

Shock and Vibration

fig5

Figure 5

Figure 5: The Effect of High-Frequency Parametric Excitation on a Stochastically Driven Pantograph-Catenary System 