Another aspect of interest is the difference between SDOF and MDOF
damage responses using solely averaged power spectra.
systems have more complicated FRFs that contain multiple resonant frequencies or modes of vibration, one for each degree of freedom.
The equipment used to simultaneously excite MDOF
can be separated into two generic types--orthogonal and hexapod.
The overall system response for MDOF
systems, using matrix notation, is given by the motion equation for MDOF
damped systems  as
Gasparini, "Response of MDOF
systems to vector random excitation," Journal of the Engineering Mechanics Division, vol.
The size of all matrices is N x N where N is the number of degree of freedom of the MDOF
Smallwood proposed control algorithms for MDOF
random vibration as far back as the late 1970s, MDOF
vibration was not formally recognized in the MIL-STD-810 until the 2008 release of MIL-STD-810G.
Let us now consider a SISO linear dynamic system with Multiple Degrees Of Freedom (MDOF
), such as a vibrating mechanical structure stressed by a force F (applied at a fixed point along a fixed direction) and oscillating with vibration u (at a given inspection point and along a given direction).
By solving such example, it is illustrated that the present techniques are not an adhoc approach; it can be generalized to investigate more complicated nonlinear multi-degree-of-freedom (MDOF
) dynamical systems.
The frames are modeled as complex multi-degree of freedoms (MDOF
) systems in this study.
For that purpose, a Multi-Degree-Of-Freedom (MDOF
) system is adopted and described in subsequent sections.
This paper focuses on the energy harvesting performance of our analog vibration suppression system for a multiple degree of freedom (MDOF
) structure under various excitations.