About a sequential method for non destructive testing of structures by mechanical vibrations

The presence and growth of cracks voids or fields of pores under applied forces or environmental actions can produce a meaningful lowering in the proper frequencies of normal modes of mechanical vibration in structures.A quite general expression for the square of modes proper frequency as a functional of displacement field,density field and elastic moduli fields is used as a starting point.The effect of defects on frequency are modeled as equivalent changes in density and elastic moduli fields,introducing the concept of region of influence of each defect.An approximate expression is obtained which relates the relative lowering in the square of modes proper frequency with position,size,shape and orientation of defects in mode displacement field.Some simple examples of structural elements with cracks or fields of pores are considered.the connection with linear elastic fracture mechanics is briefly exemplified.A sequential method is proposed for non-destructive testing of structures using mechanical vibrations combined with properly chosen local nondestructive testing methods