NONLINEAR-THEORY AND VIBRATION ANALYSIS OF LAMINATED TRUNCATED, THICK, CONICAL SHELLS

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.