chapter_2_mechanicalrev09 [Compatibility Mode]-1

# chapter_2_mechanicalrev09 [Compatibility Mode]-1 - ME 375...

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1 ME 375 System Modeling and Analysis Section 2 – Translating and Rotating Mechanical Systems Spring 2009 School of Mechanical Engineering Douglas E. Adams Associate Professor

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2 Motivational Example Effects of suspension on exhaust system vibration 2.1 In automotive systems, a change to one component can cause noise and vibration problems in other components. - Consumers lose confidence when noises arise and mechanical parts can fail when vibrations are excessive. These problems result in warranty losses, recalls, and significant financial setbacks. Increase in K2 © 2009 D. E. Adams ME 375 – Translating and Rotating Mechanical Systems N&V problem Road
3 Key Points to Remember Three elements and free oscillations 2.2 There are three physical elements in mechanical systems: Inertia - characterized by MASS (M, I) - maintains motion Dissipation characterized by DAMPING (C B We use lumped elements that are ideal We usually deal with equivalent mass, damping and stiffness - characterized by DAMPING (C, B) - eliminates motion Elasticity - characterized by (K) - opposes (or restores) motion Mass and stiffness are easiest to estimate Damping is never correct © 2009 D. E. Adams ME 375 – Translating and Rotating Mechanical Systems Free oscillations only occur when systems contain both mass and stiffness

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4 Mechanical Elements Mass, damping and stiffness characteristics (LINEAR) 2.3 Each lumped (linear) element has its own characteristic: M K f B x Δ x F B F M Also called “C” This is Δ x F K x Note that these are straight lines with constant slopes (also massless!) 1/K is called “flexibility” Newton’s 2 nd Law for a particle © 2009 D. E. Adams ME 375 – Translating and Rotating Mechanical Systems Damper / spring forces are determined by relative motion ( Δ ). Inertia force is determined by absolute acceleration. 1/K is called flexibility
5 Equivalent Mechanical Elements Modeling mechanical elements using first principles 2.4 In most practical situations, we must use models to develop our models Consider the following example P develop our models. Consider the following example: K equiv = E,I 3 3 equiv P LP E ffort Displacment E IK S t i ffness δ == = = © 2009 D. E. Adams ME 375 – Translating and Rotating Mechanical Systems Where did the mass go? Assume: 1) thin beam, 2) low frequency Why? Why?

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6 Mechanical Elements Mass, damping and stiffness characteristics (NONLINEAR) 2.5 Lumped (nonlinear) elements have their own characteristics: M K f B x Δ x F B e.g., Shocks p e.g., Relativity 2 2 1 c v mv p = Δ x F K e.g., Susp. coils Note that these are not straight lines x M © 2009 D. E. Adams ME 375 – Translating and Rotating Mechanical Systems Nonlinear characteristics often provide desirable dynamic characteristics so we use them intentionally.
7 Practical Nonlinear Example - Elastomers 2.6 Linear?

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chapter_2_mechanicalrev09 [Compatibility Mode]-1 - ME 375...

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