Free Vibration Characteristics of Isotropic and Laminated Orthotropic Spherical Caps

Free Vibration of Layered Piezoelectric Spherical Caps

“…In this section, we study the free vibration response of layered elastic caps using the "rst order shear deformation theory and compare these results with those of a Ritz discrete layer method [19] and those reported by others [16,18]. Axisymmetric and asymmetric frequencies for an isotropic shell are computed "rst and are compared with results from other studies to check the accuracy of these two methods.…”

“…The axisymmetric frequencies of a clamped isotropic hemispherical shell with h/a"0)1 are calculated using "rst order shear deformation theory and the Ritz discrete layer method [19], and compared with the results of references [16,18]. Mild steel is considered for the example of an isotropic shell.…”

“…Substituting these relations into Hamilton's principle yields the corresponding weak form. These resulting terms have been integrated through the thickness to eliminate the dependence on r using a shear correction factor of 5/6 [18]. Substituting the approximate displacements and their variations into the weak forms and collecting terms allows for writing the "nal equation for periodic harmonic motions in terms of the periodic frequency in matrix form as…”

“…Axisymmetric free vibration of moderately thick polar orthotropic hemispherical shells were studied by Chao et al [17] under various boundary conditions with sliding, guided pin, clamped and hinged edges. Gautham and Ganesan [18] studied free vibration characteristics of isotropic and laminated orthotropic spherical caps.…”

Supersonic Flutter of a Spherical Shell Partially Filled with Fluid

“…For cases both with and without these effects, he determined the natural frequencies for the shell motion that was independent of θ for circumferential mode number 0 n = . Tessler and Spiridigliozzi [31], Gautham and Ganesan [34] analyzed the case of clamped hemispherical shell. Ventsel et al [35] studied the case of simply supported spherical shell using the boundary elements method for various circumferential mode numbers ( )…”