IMPACT FORCE & INDUCED VIBRATION

Engineering Fundamentals

INTRODUCTION

Bodies collide e.g. when play is present in the design. This collision comprises elastical or plastical deformations to the colliding bodies and it induces vibrations to the system.

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Equations

collision stiffness (if both are ‘rigid’ take the local Hertzian stiffness)
C=\frac{C_1C_2}{C_1+C_2}

relative velocity
v=v_1-v_2

impact (collision) force
F_{impact}=v\sqrt {mC}

approach of bodies
u=\frac{F_{impact}}{C}=v\sqrt{\frac {m}{C}}

deceleration to v=0
a=-\frac{v}{2\sqrt{\frac {m}{C}}}

deceleration time
t=\sqrt{\frac{2u}{a}}=\sqrt{\frac{4m}{c}}

induced resonance frequency
\omega =\frac {v}{u}, f=\frac{\omega }{2\pi }

Impact force and induced vibration

Collision of 2 bodies, inducing vibrations.

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