1. Reference problem

1.1. Geometry

internal radius \(a=0.1m\)

outer radius \(b=0.2m\)

Point coordinates:

	\(A\)	\(B\)	\(C\)		\(D\)	\(E\)	\(F\)
\(x\)	0.100	0.200	\(0.1\mathrm{cos}(22.5)\)		\(0.2\mathrm{cos}(22.5)\)	\(1/\sqrt{2}\)	\(\sqrt{2}\)
\(y\)			\(0.1\mathrm{sin}(22.5)\)	\(0.2\mathrm{sin}(22.5)\)	\(1/\sqrt{2}\)	\(\sqrt{2}\)
\(z\)

1.2. Material properties

\(E=26N/{m}^{2}\)

\(\nu =0.3\)

\(\rho =35\mathrm{Kg}/{m}^{3}\)

There is nothing physical about the very low value of Young’s modulus.

1.3. Boundary conditions and loads

Internal pressure \(P=p{e}^{j\omega t}\)

with \(p=1\mathrm{Mpa}\)

and

\(\omega =0.2\mathrm{rad}/s\)

1.4. Initial conditions

• without initial conditions,

• direct calculation of the harmonic solution.