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lecture110 - ME 563 Mechanical Vibrations Lecture#1...

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ME 563 Mechanical Vibrations Lecture #1 Derivation of equations of motion (Newton-Euler Laws)

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Derivation of Equation of Motion Define the vibrations of interest -Degrees of freedom (translational, rotational, etc.) -Frequency range (<5 Hz, >15 Hz, etc.) -Amplitude range (<2 g, >10 g, linear or nonlinear, etc.) Develop a model representation -Discrete/lumped elements (springs, dampers, etc.) -Continuous elements (beams, rods, membranes, plates, etc.) -Excitation function (ground motion, wind, machinery, etc.) Define motions (kinematics) -u, v, w, θ , etc. -Undeformed or deformed datum, direction w/r/t gravitational field -Constraints on/between the variables and #DOFs (base motion, gears) Derive equations of motion -Newton-Euler laws -Energy/power methods Calculate system parameters -Strength of materials or experimentation -Catalogues from vendors (bushings, mounts, couplings, etc.) Keep track of assumptions 1
Define the vibrations of interest 2

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Derivation of Equation of Motion Define the vibrations of interest - Degrees of freedom (translational, rotational, etc.) -Frequency range (<5 Hz, >15 Hz, etc.) -Amplitude range (<2 g, >10 g, linear or nonlinear, etc.) Develop a model representation -Discrete/lumped elements (springs, dampers, etc.) -Continuous elements (beams, rods, membranes, plates, etc.) -Excitation function (ground motion, wind, machinery, etc.) Define motions (kinematics) -u, v, w, θ , etc. -Undeformed or deformed datum, direction w/r/t gravitational field -Constraints on/between the variables and #DOFs (base motion, gears) Derive equations of motion -Newton-Euler laws -Energy/power methods Calculate system parameters -Strength of materials or experimentation -Catalogues from vendors (bushings, mounts, couplings, etc.) Keep track of assumptions 3
Define the vibrations of interest (Degrees of freedom) Panel rigid body degrees of freedom Panel flexible body degrees of freedom 4

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Derivation of Equation of Motion Define the vibrations of interest -Degrees of freedom (translational, rotational, etc.) - Frequency range (<5 Hz, >15 Hz, etc.) -Amplitude range (<2 g, >10 g, linear or nonlinear, etc.) Develop a model representation -Discrete/lumped elements (springs, dampers, etc.) -Continuous elements (beams, rods, membranes, plates, etc.) -Excitation function (ground motion, wind, machinery, etc.) Define motions (kinematics) -u, v, w, θ , etc. -Undeformed or deformed datum, direction w/r/t gravitational field -Constraints on/between the variables and #DOFs (base motion, gears) Derive equations of motion -Newton-Euler laws -Energy/power methods Calculate system parameters -Strength of materials or experimentation -Catalogues from vendors (bushings, mounts, couplings, etc.) Keep track of assumptions 5
Define the vibrations of interest (Frequency range) Low-frequency (<50 Hz) response High-frequency (>100 Hz) response

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