ABSTRACT
The basic dynamic equilibrium state of a deformable spring-mass system is established in Section 10.1 based on Newton’s second law of motion. The free-vibration response of the single-degree-of-freedom (SDOF) spring-mass system, induced by an initial perturbation to the static rest state, is analyzed in Section 10.2 – eventually leading to the important fundamental relationship among stiffness, mass, and vibration frequency properties of the system. Section 10.3 is devoted to the analytical descriptions of forced vibration response and resonance behavior of SDOF linear elastic system. The use of frequency separation concept, to define targets for subsystem designs, is discussed with reference to a hypothetical automotive system example in Section 10.4. Analytical techniques to estimate the vibration frequency and mode shapes of relatively more complex systems, having uniformly distributed system and mass properties, are developed in Section 10.5. The basic definitions of SDOF vibration characteristics are extended to multi-degree-of-freedom (MDOF) system property definitions in Section 10.6 – developing the analytical formulations to calculate the vibration frequencies from stiffness and mass property matrices of MDOF systems. Mass matrix calculation of finite elements, not discussed in earlier chapters, is discussed in Section 10.7. Numerical techniques for the calculations of MDOF mode shapes and frequencies, as implemented in finite element software packages, are reviewed in Section 10.8. Relative efficiencies of different numerical techniques, for the analysis of large MDOF systems, are also discussed in that section. Software-based analysis of modal frequencies and mode shapes of finite element models is discussed with ABAQUS-specific options in Section 10.9. Finally, practice problems for modal frequency analysis of MDOF finite element models are presented in Section 10.10.
