Mechanical Vibrations

What you'll learn

• Model machines and structures with appropriate degrees of freedom, convert vibration between displacement, velocity and acceleration in peak, RMS and inch units, and combine springs and phasors correctly.
• Derive equations of motion for undamped single-degree-of-freedom systems and calculate natural frequencies by Newton's law, static deflection, the energy method and Rayleigh's method.
• Determine damping ratios from free decay and half-power bandwidth measurements, distinguish viscous, hysteretic and Coulomb damping, and explain the role of damping in design.
• Calculate the steady-state amplitude and phase of systems under harmonic and rotating-unbalance forces, interpret frequency response functions, and set separation margins from resonance.
• Design vibration isolation for machines and sensitive equipment using transmissibility, static deflection, inertia bases and flexible connections, and identify flanking paths.
• Apply balance quality grades to set unbalance tolerances, and balance rotors in one and two planes by the influence coefficient method.
• Analyze responses to steps, impulses and shock pulses by convolution and numerical integration, and use shock response spectra to assess shipping and handling.
• Find natural frequencies and mode shapes of two-degree-of-freedom systems and design tuned vibration absorbers, including damped absorbers with optimum tuning.
• Solve multi-degree-of-freedom eigenvalue problems numerically, use orthogonality and modal coordinates, and analyze torsional vibration of drive trains.
• Calculate natural frequencies of strings, bars, shafts and beams with various boundary conditions, including cantilevers with tip masses, and apply the Rayleigh-Ritz method.
• Estimate critical speeds of rotors, explain Jeffcott rotor behavior, wet and dry critical speeds and oil whirl, and evaluate separation margins against industry practice.
• Select and use vibration transducers and FFT analysis, calculate bearing defect frequencies, apply ISO 20816 severity zones, and diagnose and correct faults in a pump installation.