Calculation of exact vibration modes for plane grillages by the dynamic stiffness methodA dynamic stiffness method is developed for the calculation of the exact modal parameters for plane grillages which consist of straight and uniform beams with coincident elastic and inertial axes. Elementary bending-torsion beam theory is utilized, and bending translation is restricted to one direction. The exact bending-torsion dynamic stiffness matrix is obtained for a straight and uniform beam element with coincident elastic and inertial axes. The element stiffness matrices are assembled using the standard procedure of the static stiffness method to form the dynamic stiffness matrix of the complete grillage. The exact natural frequencies, mode shapes, and generalized masses of the grillage are then calculated by solving a nonlinear eigenvalue problem based on the dynamic stiffness matrix. The exact modal solutions for an example grillage are calculated and compared with the approximate solutions obtained by using the finite element method.
Document ID
19830039855
Acquisition Source
Legacy CDMS
Document Type
Conference Paper
Authors
Hallauer, W. L., Jr. (Virginia Polytechnic Inst. and State Univ. Blacksburg, VA, United States)
Liu, R. Y. L. (Virginia Polytechnic Institute and State University Blacksburg, VA, United States)