Relationship between Static Stiffness and Modal Stiffness of Structures

Abstract

See, stats, and : https : / / www . researchgate . net / publication / 259342742 Relationship Modal Article DOI : 10 . 12962 / j20882033 . v21i2 . 36 CITATIONS 4 READS 724 2 : Some : Elasticity , semi - analytical Corrosion Endah Institut 38 SEE Tianjian The 69 SEE All . The . Abstract   This paper derives the relationship between the static stiffness and modal stiffness of a structure . The static stiffness and modal stiffness are two important concepts in both structural statics and dynamics . Although both stiffnesses indicate the capacity of the structure to resist deformation , they are obtained using different methods . The former is calculated by solving the equations of equilibrium and the latter can be obtained by solving an eigenvalue problem . A mathematical relationship between the two stiffnesses was derived based on the definitions of two stiffnesses . This relationship was applicable to a linear system and the derivation of relationships does not reveal any other limitations . Verification of the relationship was given by using several examples . The relationship between the two stiffnesses demonstrated that the modal stiffness of the fundamental mode was always larger than the static stiffness of a structure if the critical point and the maxi - mum mode value are at the same node , i . e . for simply supported beam and seven storeys building are 1 . 5% and 15% respectively . The relationship could be applied into real structures , where the greater the number of modes being considered , the smaller the difference between the modal stiffness and the static stiffness of a structure .