mobility analogy mobility analogy called analogy analogy method representing mechanical system analogous electrical system advantage large body theory analysis techniques concerning complex electrical systems especially field filters converting electrical representation tools electrical domain directly applied mechanical system modification advantage occurs systems converting mechanical system electrical domain allows entire system analysed unified mathematical behaviour simulated electrical system identical mathematical behaviour represented mechanical system element electrical domain corresponding element mechanical domain analogous equation laws circuit analysis laws apply electrical domain apply mechanical mobility analogy mobility analogy main mechanical electrical representing mechanical systems electrical domain analogy roles voltage current reversed methods electrical representations produced dual circuits mobility analogy preserves mechanical system transferred electrical domain analogy hand analogy preserves analogy electrical mechanical mobility analogy applications mobility analogy widely model behaviour mechanical filters filters intended use electronic circuit work entirely mechanical waves provided input output filter convert electrical mechanical domains common use field audio equipment consist mechanical moving parts acoustic waves waves mechanical motion air molecules fluid medium elements electrical analogy developed mechanical system described abstract mechanical network mechanical system broken number ideal elements paired electrical symbols mechanical elements network shown following sections individual element mechanical electrical elements elements assumed mechanical component possessing element small time taken mechanical waves end component neglected developed distributed elements transmission lines greatest benefits element circuits mechanical required passive electrical elements resistance determined mechanical property chosen represent voltage property chosen represent current mobility analogy voltage velocity current force mechanical defined ratio force velocity analogous electrical electrical mechanical commonly called mobility analogy resistance mechanical analogy electrical resistance loss energy moving system processes friction mechanical component analogous shock property analogous resistance electrical analogy mechanical governed equation law formula analogous equation mechanical domain formula resistance voltage current mechanical resistance force velocity induced force electrical represents real electrical likewise mechanical resistance real mechanical mechanical analogy mobility analogy compliance common mechanics discuss compliance mechanical component analogous spring governed equation formula analogous equation mechanical domain form law formula time mechanical compliance purely imaginary given formula analogous mechanical given formula electrical imaginary unit angular frequency mechanical mechanical analogy mobility analogy mass mechanical component analogous large rigid weight governed equation formula analogous equation mechanical domain newton second law motion formula mass purely imaginary given formula analogous mechanical given formula curious difficulty arises mass analogy electrical element connected fact mechanical systems velocity mass importantly acceleration measured fixed reference frame usually earth considered terminal system element mass terminal velocity analogous electric potential terminal zero velocity analogous electric ground potential mass led university_of_cambridge define new energy storing element mechanical networks called component possesses called unlike mass allowed different arbitrary equation given formula equal opposite force applied respectively units mass kilograms system indicates relationship smith define network element suggested construction real mechanical component small prototype smith consists able slide cylinder connected rack gear drives inside cylinder counter rotating order prevent developing energy provided pushing returned moves opposite direction device stores energy like block mass actual mass small ideal mass points cylinder case independently connected parts mechanical system necessarily connected ground smith found application formula racing known alternative banned tuned mass forms vehicle suspension secretly following collaboration smith teams believed smaller tuned mass contact patch load variations tyres smith suggests reduce machine vibration difficulty mass mechanical limited mobility analogy corresponding problem occurs analogy case represented standard elements mechanical consists mass element compliance element mechanical analogous electrical circuits consisting real mechanical components mass compliance practical proposition single component fact difficult pure mass pure compliance single component spring certain compliance mass mass compliance eliminated altogether mechanical key component mechanical filters generators exist active electrical elements voltage source current source generators mechanical mobility analogy constant current generator constant force generator mechanical constant voltage generator constant velocity generator example constant force generator constant force spring example practical constant velocity generator lightly loaded powerful machine motor driving belt analogous real voltage source battery remains near constant voltage load provided load resistance higher battery internal resistance systems require convert electrical mechanical domains analogous port networks like described pair simultaneous arbitrary parameters numerous possible representations form applicable mobility analogy arbitrary parameters units matrix form electrical taken port representation formula element formula short circuit mechanical presented mechanical zero voltage short circuit applied electrical element formula conversely electrical presented electrical mechanical driving load zero force remaining elements formula formula describe forward reverse transfer functions respectively analogous transfer hybrid electrical mechanical quantity mechanical analogy simple machine force applied load greater input force depending mechanical advantage machine greater unity respectively mechanical advantage analogous turns ratio mobility analogy mechanical advantage unity analogous step greater unity analogous step power energy examples simple circuit figure shows mechanical arrangement platform mass suspended substrate spring resistance mobility analogy equivalent circuit shown right arrangement consists parallel circuit system frequency natural frequency heavily advantages principal advantage mobility analogy alternative analogy preserves mechanical system elements series mechanical system series electrical equivalent circuit elements parallel mechanical system remain parallel electrical equivalent principal disadvantage mobility analogy maintain analogy electrical mechanical mechanical represented electrical mechanical resistance represented electrical electrical equivalent circuit force analogous voltage generator called force analogous current history historically analogy use long mobility analogy mechanical associated mobility analogy introduced overcome issue preserving independently idea germany developed treatment general mathematical theory perspective introduced new analogy
Mobility analogy