2. Reference solution#

2.1. Calculation method used for the reference solution#

The reference solution is the one given in sheet SDLL08 /89 of the guide VPCS, which presents the calculation method as follows:

A Rayleigh-Ritz method makes it possible to perform the calculation with two degrees of freedom based on the following symmetric deformation hypotheses:

  • for the abscissa point \(y\) of the side members \(\mathrm{AC}\) and \(\mathrm{DF}\) of length \(\mathrm{L1}\)

_images/Object_4.svg

  • for the abscissa point \(x\) of the crosspiece \(\mathrm{BE}\) of length \(\mathrm{L2}\)

_images/Object_5.svg _images/10002B82000022EF00001089B38A4BC80FC21EA6.svg

2.2. Benchmark results#

The first two natural frequencies and symmetric natural modes (the other natural frequencies of this system are not studied). For the natural modes, we have the following value:

_images/Object_6.svg

In harmonic response we have:

,

at point \(G\).

2.3. Uncertainty about the solution#

Analytical solution.

2.4. Bibliographical references#

  1. J.M. BIGGS. Introduction to Structural Dynamics. New York: McGraw Hill, p.184 (1964).