Parameters for overhead: Tension,T=15kN Dropper distance,L=7.5m Dropper stiffness, kd=1500N/m Dropper damping coefficient, cd=50Ns/m Linear density of contact wire, =1.07kg/m Parameters for pantograph: lamped parameter model, 3-DOF system Pan-head mass, m1=7.51kg Upper frame mass, m2=5.855kg Lower frame mass, m3=4.645kg Damping coefficients: Pan-head suspension, c1=0Ns/m Upper frame,c2=0Ns/m Lower frame, c3=70Ns/m Stiffness: Pan-head suspension, k1=8380N/m Upper frame,k2=6200N/m Lower frame, k3=80N/m Pantograph speed:v0=70m/s (252km/h) Initial Displacement of pantograph: x0=0m Static value of uplift force:F0=70N Contact between catenary and pan-head is not defined. Positive contact is assumed for all the time.Catenaryismodeledastimevaryingspringsandfirmlyattachedtothepan-headmass m1. Overhead system without considering mass of contact wire: Case 1: Droppers are rigid supports Stiffness variation along a span: Case 2: Droppers are modeled as springs 10 20 30 40 50 60Distancem10000200003000040000Stiffness NmStiffnessvariationalongaspanStiffness variation along a span: Time response at = 13 rad/s: Frequency response: 10 20 30 40 50 60Distancem33003400350036003700StiffnessNmStiffnessvariationalonga spanm1m2m30.2 0.4 0.6 0.8 1.0Time s0.050.050.10Displacement mTimeresponceat 13radsFrequency response at t = 0.5s Case 3: Droppers are modelled as parallel combinations of spring and damper Stiffness and damping coeff. variation along a span at = 10 rad/s m1m2m310 20 30 40 Frequency rads0.020.040.060.08Displacement mFrequencyresponse10 20 30 40 50 60 Length m330034003500360037003800Stiffness NmStiffnessVariation At = 50 rad/s 10 20 30 40 50 60 Length m455055606570DampingCoeff. NsmDampingCoeff.Variation10 20 30 40 50 60 Length m405041004150420042504300Stiffness NmStiffnessVariation10 20 30 40 50 60 Length m35404550556065DampingCoeff. NsmDampingCoeff.VariationAt = 100 rad/s 0 10 20 30 40 50 60 Length m490050005100520053005400Stiffness NmStiffnessVariation0 10 20 30 40 50 60 Length m25303540455055DampingCoeff. NsmDampingCoeff.VariationFrequency response at t=2s Time response at = 10 rad/s m1m2m310 20 30 40 Frequency rads0.010.020.030.040.050.06Displacement mFrequencyresponsem1m2m30.2 0.4 0.6 0.8 1.0Time s0.050.05Displacement mTimeresponseat 10radsTime response at = 50 rad/s Time response at = 100 rad/s m1m2m30.2 0.4 0.6 0.8 1.0Time s0.020.020.040.06Displacement mTimeresponseat 50radsm1m2m30.2 0.4 0.6 0.8 1.0Time s0.020.020.040.06Displacement mTimeresponseat 100rads