Download - SODF Vibrations Review
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MECH 515 Midterm Review
Discrete systems: systems composed of an assembly of multiple parts, in which thesystems response is dependent on the combination of each individual components
behavior.
Componentso Springs
Proportional to displacement(linear range) store/release potentialenergy.
Assumed massless Spring force is conservative: independent of path Predicted behavior
o Viscous Damper Proportional to velocity (linear range) dissipate energy, Assumed massless Damper force is non-conservative
o Masses Proportional to acceleration store/release kinetic energy
1st Order Systems: no mass, so 2nd Order Systems: Equilibrium: point where the net forces equal zero. Stability
Asymptotically Stable Stable Unstable
Natural Frequency: frequency at which the system will resonate under free vibration.
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Damped 2nd Order Systemso Overdamped ( : two
different real roots, takes longer
to converge than critically
damped without oscillating.
o Critically damped ( : theimaginary part goes to 0, so there
is a double real root. Converges
to zero as fast as possible without oscillating.
o Underdamped ( 1): complex roots, oscillates at the damped naturalfrequency (), takes longer to converge.
Harmonic Excitationo Excitation frequency: frequency at which the force is exiting the systemo Frequency response (): measure of the system response to a harmonic
excitation of frequency (); usually complex.
o Magnification factor (||): the amplitude of forced vibration motion withrespect to the magnification of the static deflection as a function of the frequency
ratio (/ )
o Resonance condition: violent vibration when the excitation frequency equals tothe natural frequency ( )
o Harmonic balance: balances the response to ensure is steady state, by equatingeach coefficient creating 2 equations, which have to be satisfied.
Periodic Excitationo Periodic functions can be expressed as linear combinations of harmonic functions
by Fourier series.
o Superposition can be used to combine individual responses for each individualexcitation.
o The series can be either in exponential (complex form) or trigonometric (realform) functions.
o Fundam. frequency ( ): called 1st harmonic, wh. is the p harmonic.o For periodic function even with time, the Fourier series reduces to a cosine terms.o For periodic function oddwith time, the Fourier series reduces to asine terms.o Frequency ratio: determines the systems performance