The natural frequencies of a thermally loaded fixed-fixed beam (Figure P1.37) are a function of the material
Question:
The natural frequencies of a thermally loaded fixed-fixed beam (Figure P1.37) are a function of the material properties of the beam, including:
\(E\), the elastic modulus of the beam
\(ho\), the mass density of the beam
\(\alpha\), the coefficient of thermal expansion The geometric properties of the beam are
\(A\), its cross-sectional area
\(I\), its cross section moment of inertia
\(L\), its length Also,
\(\Delta T\), the temperature difference between the installation and loading
Present different problems that are to be formulated in nondimensional form. For each problem answer the following.
(a) What are the dimensions involved in each of the parameters?
(b) How many dimensionless parameters does the Buckingham Pi theorem predict are in the non-dimensional formulation of the relation between the natural frequencies and the other parameters?
(c) Develop a set of dimensionless parameters.
Step by Step Answer:
