Premium
The damped transient behaviour of finite beams and plates
Author(s) -
Koenig Herbert A.,
Davids Norman
Publication year - 1969
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.1620010203
Subject(s) - cantilever , transient (computer programming) , beam (structure) , finite element method , enhanced data rates for gsm evolution , rotary inertia , transient response , shear (geology) , mechanics , moment of inertia , structural engineering , physics , inertia , materials science , classical mechanics , engineering , computer science , composite material , telecommunications , electrical engineering , operating system
The direct Finite Element Analysis which was successfully employed in the solution of dynamic flexural traveling wave problems is extended herein to provide the transient behaviour of finite beams and plates in which shear deformation and rotatory inertia are considered. The particle and angular velocities are exponentially damped so that the static solutions for these problems are obtained with the same analysis which provided the dynamic and transient cases. Three special cases are chosen as examples. In the first, a sinusoidally varying shear force is applied at the tip of a cantilever beam. The resonant characteristics of this beam for both the undamped and damped cases are studied. In the second, a step shear loading is applied to a cantilever beam and its damped dynamic history is studied. Finally, a circular plate whose outer edge is simply supported is impacted at its inner edge by a step moment and its damped transient behaviour is determined. The idea of the methods is potentially applicable to dynamic problems in general.