Cs. Xu et al., NONLINEAR-THEORY AND VIBRATION ANALYSIS OF LAMINATED TRUNCATED, THICK, CONICAL SHELLS, International journal of non-linear mechanics, 31(2), 1996, pp. 139-154
Non-linear equations of transverse motion for a generally laminated, t
runcated, conical shell are derived by use of the dynamic virtual work
principle. The effects of transverse shear deformation, rotatory iner
tia and geometric initial imperfection are taken into account. A solut
ion for non-linear free vibrations of a symmetrically laminated, cross
-ply, geometrically perfect, thick, conical shell with its two ends bo
th clamped and both simply supported is expressed in the form of gener
alized double Fourier series with time-dependent coefficients. The Gal
erkin procedure furnishes a system of equations for time functions whi
ch are solved by the method of harmonic balance. Non-linear vibrations
of circular cylindrical shells and annular plates are treated as spec
ial cases. Numerical results in non-linear vibrations of symmetric cro
ss-ply conical laminates are presented graphically for different param
eters. Present results are also compared with available data for speci
al cases.