TY - JOUR
T1 - On the vibration of a Point-Supported linear distributed system
AU - Bergman, L. A.
AU - McFarland, D. Michael
N1 - Copyright:
Copyright 2017 Elsevier B.V., All rights reserved.
PY - 1988/10
Y1 - 1988/10
N2 - The vibration of a constrained dynamical system, consisting of an Euler-Bernoulli beam with homogeneous boundary conditions, supported in its interior by arbitrarily located pin supports and translational and torsional linear springs, is studied. A generalized differential equation is obtained by the method of separation of variables and is solved in terms of the Green’s function and its derivatives of the unconstrained beam. System natural frequencies and modes are obtained, and the orthogonality relation for the natural modes is derived. A general solution for the forced response is given. Finally, two pertinent problems from the literature are examined, and results obtained are compared with those of a small, dedicated finite element formulation to assess the relative accuracy and efficiency of each.
AB - The vibration of a constrained dynamical system, consisting of an Euler-Bernoulli beam with homogeneous boundary conditions, supported in its interior by arbitrarily located pin supports and translational and torsional linear springs, is studied. A generalized differential equation is obtained by the method of separation of variables and is solved in terms of the Green’s function and its derivatives of the unconstrained beam. System natural frequencies and modes are obtained, and the orthogonality relation for the natural modes is derived. A general solution for the forced response is given. Finally, two pertinent problems from the literature are examined, and results obtained are compared with those of a small, dedicated finite element formulation to assess the relative accuracy and efficiency of each.
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U2 - 10.1115/1.3269555
DO - 10.1115/1.3269555
M3 - Article
AN - SCOPUS:0024088862
SN - 1048-9002
VL - 110
SP - 485
EP - 492
JO - Journal of Vibration and Acoustics, Transactions of the ASME
JF - Journal of Vibration and Acoustics, Transactions of the ASME
IS - 4
ER -