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Natural frequencies of a toroidal shells of revolution with hollow elliptical cross-section are determined by the Ritz method from a three-dimensional (3-D) theory while traditional shell theories are mathematically two-dimensional (2-D). The Legendre polynomials, which are mathematically orthonomal, are used instead of ordinary algebraic polynomials as admissible functions. The present analysis is...
Based on the modified strain gradient theory (MSGT) in conjunction with the Timoshenko beam theory, the vibrational behavior under thermal environment of variable section functionally graded (FG) microbeams carrying microparticles is studied. The eigenfrequency equations are derived using the Chebyshev–Ritz method. The effects of temperature dependence of material properties and the initial thermal...
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