Superelement approximation

In this case, the Euler-Bernoulli beam has been modeled using a number of superelements. Each superelement consists of a series of three rigid bodies connected by springs Cz\ and Cz3 as depicted in Fig. C.2. Again, the beam is built in at the base. The torsional spring constants for each superelement are determined as follows:

Lse with E the modulus of elasticity, Iz the area moment of inertia, and Lse the length of the superelement which is, in turn, defined as

Lse = We with L the length of the Euler-Bernoulli beam and Nse the number of superelements the beam is subdivided in (see Fig 3.15 on page 72). The most important difference with the lumped-mass method is that rigid bodies within a superelement are not of equal length.

Figure C.2: Fixed-free Euler-Bernoulli beam discretized with one superelement, with o: 1 degree of freedom rotational joints.

The first four eigenfrequencies of the superelement approximation as function of the number of elements are listed in Table C.4. The pattern is clear: dividing the beam into more superelements produces more eigenfrequencies (of which only the first four are shown), and improves the accuracy. The limiting case being an infinite number of superelements of which the eigenfrequencies equal to those of the exact solution. In addition, the mode shapes become better defined with an increasing number of superelements, since information on more locations along the beam is available (see Fig. 4.4 on page 119).

Renewable Energy 101

Renewable Energy 101

Renewable energy is energy that is generated from sunlight, rain, tides, geothermal heat and wind. These sources are naturally and constantly replenished, which is why they are deemed as renewable. The usage of renewable energy sources is very important when considering the sustainability of the existing energy usage of the world. While there is currently an abundance of non-renewable energy sources, such as nuclear fuels, these energy sources are depleting. In addition to being a non-renewable supply, the non-renewable energy sources release emissions into the air, which has an adverse effect on the environment.

Get My Free Ebook


Post a comment