Foundation Isolation - 53296 Mode shapes (stiffness of a structure in each axis) identify the physical direction of each frequency mode and any deformations, such as bending or twisting. In general, a structure's modes indicate the relative degree of structural stiffness among various points on that structure (Figure 4).Examining mode shapes in a vibrating structure is avaluable step in adjusting vibration amplitudes at critical points by varying the stiffness, mass and damping in a structure.Forces imposed by the supported machine caninduce a high enough vibration amplitude at the natural frequency (or one of the response modes) of the foundation to cause resonance or amplification of the vibration. The single most important factor in any successful design where machine induced vibra- tion is involved (source) is to avoid resonance between the machine and the foundation. Data on forces, such as axial, shear, torques andmoments for maximum loading at each support or attachment location of the machine are necessary to predict the load conditions on the foundation. These loads are used to determine the longitudinal and/or transverse (width) reinforcement and concrete strength required, which relates directly to any deflection. The modulus of elasticity is a key design factor inthe strength of concrete. (See Figure 6.) Limits on the differential deflection allowed from one point to another on a foundation are set to avoid possible damage or misalignment of conduit and other con- nections. The depth of a foundation is determined by the bearing strength of the soil, the machine sup- port requirements (structural stiffness) and in critical designs, the dynamic stiffness, which includes the foundation's natural frequency and bending modes.Geometry and mass are important considerations inthe dynamic design of foundations. However, the foundation-to-equipment mass ratios that are some- times recommended, do little in preventing founda- tion vibration unless the dynamic response of the foundation is known.A finite element analysis will define and model themode shapes and response frequencies of the foun- dation, as well as the response of the isolation sys- tem and foundation to machine induced inputs and/or environmental inputs (Figure 5).