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Monday, July 8 • 11:20 - 11:40
VIBRATION OF LAYERED CONICAL SHELLS USING COLLOCATION WITH CHEBYSHEV POLYNOMIAL

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Vibrational characteristics of layered truncated conical shells are studied. The method of collo-cation with Chebyshev polynomial approximation is applied for solving the problem. The for-mulation of the problem is based on an extension of Love's first approximation theory. The governing equations of motion are obtained in terms of the reference surface displacements. The equations are coupled in the longitudinal, circumferential and transverse displacement functions. Assumption of the solution in separable form leads to the ordinary differential equa-tions in the assumed displacement functions, which are functions of only a meridional coordi-nate. These equations are still coupled and have to be solved only numerically, in their general form. The displacements are assumed in series of Chebyshev polynomials. Collocation leads to a set of homogeneous equations in the unknown coefficients in the series assumed and become as a generalised eigenvalue problem solving which the frequency parameter values and the cor-responding mode shapes of vibration are obtained. Parametric studies are made to find the in-fluence of the many geometric and material parameters available on the frequencies. The effect of layering and that of neglecting the coupling between extensional and flexural displacements are studied, in particular. The results are presented in terms of graphs and are discussed

Moderators
avatar for Simon Jones

Simon Jones

Associate Professor, Rose-Hulman Institute of Technology
Professional interests include undergraduate engineering education, finite element modeling, ground-borne vibrations, vibrations of musical instruments, and dynamics of toys.
GM

Guilhem Michon

Professor, ISAE-SUPAERO

Authors

Monday July 8, 2019 11:20 - 11:40 EDT
St-Laurent 7
  T07 Struct. dyn. & nonlin. vib., RS03 Struct ac & vibr

Attendees (8)