An exact solution of truss vibration problems

• Main Authors: Andres Lahe, Andres Braunbrück, Aleksander Klauson
• Format: Article
• Language: English
• Published: Estonian Academy Publishers 2019-05-01
• Series: Proceedings of the Estonian Academy of Sciences
• Subjects: truss bar vibration; transfer equations; essential boundary conditions at joints; natural boundary conditions at joints; master–slave connectivity; transverse inertial forces.
• Online Access: http://www.kirj.ee/public/proceedings_pdf/2019/issue_3/proc-2019-3-244-263.pdf

The Elements by a System of Transfer equations (EST) method offers exact solutions to various vibration problems of trusses, beams, and frames. The method can be regarded as an improved or modified transfer matrix method. Using the EST method, the roundoff errors generated by multiplying transfer arrays are avoided. It is assumed that the bars of trusses are connected by frictionless joints. Longitudinal vibration of a truss bar is described by a differential equation. In a direction perpendicular to the longitudinal axis, no bending can occur. In a transverse direction the rigid bar displacements vary linearly. The rigid bar rotational moment of inertia is taken into account. The transfer equations for the truss bar are presented. The transverse displacements at the joint (node) of an elastic and a rigid bar are equal. The essential boundary conditions at joints for the differential equation are the compatibility conditions of the displacements of truss elements. The natural boundary conditions at joints are the equilibrium equations of longitudinal elastic forces and transverse inertial forces of rigid bars.