Power series expansions of dynamic stiffness matrices for tapered bars and shafts | Zendy

Spyrakos Constantine C. | Zendy; Chen Ching I | Zendy

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Power series expansions of dynamic stiffness matrices for tapered bars and shafts

Author(s) -

Spyrakos Constantine C.,

Chen Ching I

Publication year - 1990

Publication title -

international journal for numerical methods in engineering

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.421

H-Index - 168

eISSN - 1097-0207

pISSN - 0029-5981

DOI - 10.1002/nme.1620300204

Subject(s) - power series , bessel function , stiffness , series (stratigraphy) , laplace transform , convergence (economics) , mathematical analysis , displacement (psychology) , direct stiffness method , series expansion , mathematics , stiffness matrix , tangent stiffness matrix , structural engineering , engineering , geology , economics , psychology , paleontology , economic growth , psychotherapist

Stiffness and consistent mass matrices for tapered bars and shafts are derived with the aid of static displacement functions. Moreover, the corresponding dynamic stiffness matrices are developed in the Laplace transform domain from the exact solutions of axial/torsional governing equations. Power series expansions of the Bessel functions comprising the dynamic stiffness influence coefficients show that the stiffness and consistent mass matrices can be mathematically derived from the dynamic stiffness matrices. A discussion on the convergence of the power series expansions is also presented. The developments provide further insight into the approximations present in conventional consistent mass formulations of frameworks with tapered members.

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