In-plane vibrations of a circumferential arch elastically restrained against rotation at one end and with an intermediate support

1987 ◽  
Vol 22 (4) ◽  
pp. 261-270 ◽  
Author(s):  
C.P. Filipich ◽  
R. Carnicer ◽  
V.H. Cortínez ◽  
P.A.A. Laura
Keyword(s):  
Intermediate Support ◽  
Elastically Restrained

Optimal Design of an Intermediate Support for a Beam With Elastically Restrained Boundaries

2011 ◽  
Vol 133 (3) ◽  
Author(s):  
D. Wang
Keyword(s):  
Optimal Design ◽  
Optimality Criterion ◽  
Closed Form Solution ◽  
Frequency Equation ◽  
Form Solution ◽  
Support Design ◽  
Intermediate Support ◽  
Optimum Position ◽  
Classical Boundary ◽  
Elastically Restrained

A straight, slender beam with elastically restrained boundaries is investigated for optimal design of an intermediate elastic support with the minimum stiffness for the purpose of raising the fundamental frequency of the beam to a given value or to its upper bound. Based on the optimality criterion of the support design, the characteristic frequency equation can readily be formulated. Then, a closed-form solution is presented for estimating the minimum stiffness and optimum position of the intermediate support such that the analysis of the various classical boundary conditions is only a degenerate case of the present problem. With the procedure developed, the effects of the general cases of the beam restraint boundaries on the optimal design of the intermediate support are studied in detail. Numerical results show that the optimum position will move gradually apart from the end with the degree increment of the boundary restraints. Moreover, it is also observed that the rotational restraint affects the optimal design of the support more remarkably than the translational one at the lower values of the restraint constants, but becomes less effective at the higher constants.

Vibration of Beam with Elastically Restrained Ends and Rotational Spring-Lumped Rotary Inertia System at Mid-Span

2015 ◽  
Vol 15 (02) ◽  
pp. 1450040 ◽  
Author(s):  
Seyed Mojtaba Hozhabrossadati ◽  
Ahmad Aftabi Sani ◽  
Masood Mofid
Keyword(s):  
Technical Note ◽  
Rotary Inertia ◽  
Mode Shapes ◽  
Bernoulli Beam ◽  
Mass System ◽  
Rotational Spring ◽  
Beam System ◽  
Sample Frequency ◽  
Elastically Restrained ◽  
Euler Bernoulli Beam

This technical note addresses the free vibration problem of an elastically restrained Euler–Bernoulli beam with rotational spring-lumped rotary inertia system at its mid-span hinge. The governing differential equations and the boundary conditions of the beam are presented. Special attention is directed toward the conditions of the intermediate spring-mass system which plays a key role in the solution. Sample frequency parameters of the beam system are solved and tabulated. Mode shapes of the beam are also plotted for some spring stiffnesses.

Discussion of “Buckling of Elastically Restrained Columns”

1966 ◽  
Vol 92 (4) ◽  
pp. 92-98
Author(s):  
Sahib Zaki Al-Sarraf ◽  
Anatol A. Eremin
Keyword(s):  
Elastically Restrained
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