Consider the bending torsion vibrations of a large aspect ratio cantilevered rectangular box beam of

Consider the bending torsion vibrations of
a large aspect ratio cantilevered rectangular box beam of flexural stiffness
EI, length L and mass m. The origin of the coordinate frame is to the left of
the centre of gravity at a distance xcg at a point O. The moment of inertia of
the beam cross-section about the origin is Io, the polar second moment of the
area of cross-section is J and the modulus of rigidity is G. The transverse
displacement is w and the clockwise torsional displacement is θ. The
differential equation of bending-torsion vibration is given by