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Proceedings of the Estonian Academy of Sciences

ISSN 1736-7530 (electronic)   ISSN 1736-6046 (print)
Formerly: Proceedings of the Estonian Academy of Sciences, series Physics & Mathematics and  Chemistry
Published since 1952

Proceedings of the Estonian Academy of Sciences

ISSN 1736-7530 (electronic)   ISSN 1736-6046 (print)
Formerly: Proceedings of the Estonian Academy of Sciences, series Physics & Mathematics and  Chemistry
Published since 1952
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An exact solution of truss vibration problems; pp. 244–263

(Full article in PDF format) https://doi.org/10.3176/proc.2019.3.04


Authors

Andres Lahe, Andres Braunbrück, Aleksander Klauson

Abstract

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.

Keywords

truss bar vibration, transfer equations, essential boundary conditions at joints, natural boundary conditions at joints, master–slave connectivity, transverse inertial forces.

References

 

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Current Issue: Vol. 68, Issue 3, 2019




Publishing schedule:
No. 1: 20 March
No. 2: 20 June
No. 3: 20 September
No. 4: 20 December