Riassunto Mechanical Vibrations

Introduction 1 Chapter to why vibrations study etc

Vibrations sound are earthquake everywhere of vibration atoms noise temperature be Vibrations diseases systems catastrophic can collapses dangerous very failure fatigue electronic deices malfunctioning.

NUN ViboN of the declination Vit Acoustics is automotive The NUH and harshness vibration noise Any irritating noise an means acronym annoying for It's of of the to of is NUH and vehicle vibration a a Study object important passenger the of that the the Nut individual terms make understand up acronym meaning the.

Vibration is through senses as a occur a on can shaking perception perceived trembling of and sight objects tough a watching touching vibrating the with to Noise sand abnormal normal i is as unpleasant an perceived respect of vehicle the operation It lo the to to vehicle refers.

Harshness motion refers in specifically simply roughness it to also the sand to refers definitions and some quality perception according for the with of vibrations effect associated sensation rigid physical example suspension.

Degree one systems freedom 2 Chapter or free oscillator

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Free damped oscillator

FREE DAMPED oscillator l'invii Let's the consider dampen viscous reaction dissipata an energy the Face relative depends velocity µ on c F ciF ri e FeM The of motion equation is thxmi ciEon oa T e elastic meta viscous.

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Damping ratio

Damping Ratio 3 We hae solutions can 445c's di3 1 him1 andar rests and are negative AperiodicE motion Aperiodic damping tt BeatX Ae critical km di3 1 Aaa2 rest and c and coincidenti CriticalX E Aperiodic subcritical h'tttt X A Bf damping f eec'e km di3 1e3 da and andare complex conjugate Sibaritici E Beat dediti BeateditAX4 Santos IN toconte.

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Harmonically forced oscillator

Harmonically forced oscillator so of the motion contrasnae is Eon in Focittà MI cite cosµ rejma.no fithe ed we prefer in space making Complex etat LiMI Eon Foci in M complexion ed domain indeed FG cinte FoF ti j smart cosa the is Fully problem equivalent.

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Vibration isolation

Vibration isolation da Isolation NN Fare excited trasmissibility as support the tichere to able is so a we wanna being point suspension design this hae the trasmits if and to oscillata Force evolsivate base m the.

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Vibration From excitation the transmitted sismico support etat YoY ithe wem Iz CatK maiGrc Gesùii e ii f that.

Example corrugated roads

EXAMPLE io ROADS OF CORRUGATED Washboarding 2Ti wavelength FASTER state ris IF GO YOU slow too I That's result the H working region.

Periodic forcing Fourier series

Periodic Fourier forcing series to SUPERPosition principle Xo Consider the o system halt Fitf ci Where µ e Ìoo if F Fe tbh t with t costt ba a e the then Solution is b XLt X fa t tlinea This if True it said the system a is principle is is superposition ad.

Fourier Series Flt of Fourier be the Function Any can period periodic a expressed through series The of il the function function series suitably is periodic trigonometric Series convengasmooth Consider function harmonic Cootsinan Note the snoot txtcio 2Tsn period a the consider time dimensionless we 7 Got2ft e the become precedent son sn Etait of of without loss the so consider function can 2Tperiod we generality a Fran T to period HE busin rear rta Zenithcosn period E 2 t.

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Dirichlet conditions

Dirichlet conditions Xconditions The Dirichlet the iff Fourier and Ltof exists Function only certain series can genta is satisfied conditions are F the I of Finite it within discontinuities t castra number is on present a period Flt and has of I within Fornite the number max non period a ÌlfI Idt the t'At io is absolutely on period integrable In the such Fourier of the condition period series in point any converge.

Response forcing of an oscillator periodic

0 ResPonce Forcina OF an a oscillator periodic to Let's costola faµ ao Horin tf rootdi sncos va the From the of the and oscillates analyse we can spaposition Following principle response solution the superimpose cio the forced Kochmio dat tt e statically system the sduttopatata is I24.

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We 1 that condition is a can see resonance damping of to excitation infinite number rise conditions periodic resonances n gives.

Example square wave

EXAMPLE SQUAREWAVE Ten of of the One terms terns the hundred Series Series effect Gibbs fitthe of Gibbs whit doesn't the effect the the ogni series discontinuity in proximity the that's not the Function Function deemed because ogni in discontinuity is Check fa29 of notes lecture meapag.

Arbitrary excitation time domain approach

ARBITRARY Excitation time i Domain approach THE da THE di Impulse Rac Function Unit EÈ Let's the F EdtI Face within of tormentarsi consider a a o impulse o face Fare if and very short time intensi that Fase the E consider we impulsive now acting impulse conrspond.mg 1folli IF F a 1I e because o Dirac this the Delta of Fare kind be by unitary con symbolically impulse represented a special S fa t.frt z oa S E dt 1t o trafa5 T t.tot not deemed.

Dirac function recall

Dirac function X DIRAC Function recall X SHS the mathematics tetto Dmc oII de a see the let's delta often Function why deemed see unitary is impulse as SE t Let called ti define EoEmotion discontinuous Fornite ous a impulse se lei telo E The DiscAnatra of Innit the Finite the is impulse I Iim Scelti8 t Function not is s o.

Response to an impulse

Response An an impulse to oscillator of unitary AF in un We the have situation SCHmi cittalet's Innit the the to and now integrale Impact dimi tcitkddt.jp E sahit tE the terms and three consider separately In Otmiimi unIo a Free damped oscillation Eo solmcIozfcidE oÈ.io E soo stHoltIo 5Wh144 Udte sn the miti mud applying conditions t soetico Ièo where a a 11 3codm un.

The convolution integral

The convolution integral Flt Consider oscillata harmonic excitation ansn aarbitrary non aol.mg FAMilt thxtcx.lt t Initial the rest conditions oscillata in is are homogeneous t.roupto This indeed of doesn't generality non implies loosing assumption throated be initial by conditions taking can homogeneous from the advantage principle superposition FG of by be described can a series mathematically each impulse forces acts infinite.