ABSTRACT
This chapter discusses free vibrations of shells, which occur in the absence of applied loads but are initiated by some initial conditions imposed on the shell, and forced vibrations of shells, which result from the application of time-dependent loads. The equation of axisymmetrical free vibrations can be obtained from the governing differential equation of the axisymmetrically loaded circular cylindrical shell. The governing equations of free vibrations of conical shells can be derived from equations of the general linear shell theory by introducing the curvilinear coordinates. According to the Rayleigh-Ritz method, natural frequencies of free vibrations of shallow shells are determined from the condition of a minimum of the sum of the potential and kinetic energies of the shell. The natural frequencies of free vibrations depend on the character and value of applied static loading, such as the normal surface pressure, axial force, torque, etc.
