Free vibrations of an orthotropic thin cylindrical shell on a Pasternak foundation

The basic objective of the present study is to investigate the influences o f foundation parameters, orthotropy of materials represented by elastic mod uli ratio, axial wave parameter, and circumferential wave number on three e igenfrequencies. Dynamic equilibrium equations and frequency equation are d eveloped, and the eigenfrequencies are calculated. It is found that the fou ndation modulus primarily affects the radial mode eigenfrequency and has no effect on torsional and longitudinal modes, whereas the shear modulus does have influence on radial as well as tangential modes of vibration, though the effect on radial mode frequency is more dominating. The elastic moduli ratio chiefly affects the radial mode in a manner similar to that of a foun dation modulus. When the shell rests on a Pasternak foundation, the lowest eigenfrequency vs circumferential wave-number characteristics do not have t he well-known dip, and the minimum frequency occurs when the circumferentia l wave number is zero for all values of axial wave parameter.