Three-dimensional vibrations of solid cones with and without an axial circular cylindrical hole

Kang, Jae-Hoon; Leissa, A. W.

doi:10.1016/j.ijsolstr.2004.02.017

Cited by 11 publications

(2 citation statements)

References 6 publications

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“…Pol. Architectura, 16 (4), 5-14. doi: 10.22630/ASPA.2017.16.4.01. Papers concerning hollow truncated cones -solids of revolution with recti-or curvilinear generatrices (Kang & Leissa, 2004;Wu & Chiang, 2004) are rare and their authors deal only with selected, special geometrical cases of hollow bars.…”

Section: Introductionmentioning

confidence: 99%

Analysis of free vibrations of cantilever bars with parabolically variable cross-sections using the Rayleigh’s method

Szlachetka

Jaworski

Chalecki

2018

ACTA SCIENTIARUM POLONORUM - Architectura Budownictwo

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The Rayleigh's method can be used to determine the first natural frequency of bars (beams or posts) with non-uniform cross-section. The authors have analysed slender bars made of an elastic material and having the shape of a solid of revolution: a curvilinear truncated cone and curvilinear conical pipe. It has been assumed that the bar axis deflected during vibrations has a shape of a beam deflected by a static constant continuous load. The Rayleigh's method has been applied in the paper in aim to determine the first frequency of free (transverse) vibrations of posts formed as a cantilever bars having the shape of solid and hollow curvilinear truncated cone with the generatrix being a parabola which is convex in relation to the cone axis. The results of calculations are very close to those obtained with finite element method (FEM).

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Section: Introductionmentioning

confidence: 99%

Analysis of free vibrations of cantilever bars with parabolically variable cross-sections using the Rayleigh’s method

Szlachetka

Jaworski

Chalecki

2018

ACTA SCIENTIARUM POLONORUM - Architectura Budownictwo

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“…Since then, many scholars have used this method to analyze different objects' vibration characteristics, including uniform and nonuniform beams, rectangular plates, and thin plates, according to one-dimensional or two-dimensional theory [27][28][29][30]. Then, Leissa and Kang used the Ritz method with an admissible function composed of algebraic polynomial multiplying boundary functions based on three-dimensional elasticity theory to analyze the vibration characteristic of thick, linearly tapered, annular plates [31,32]. This method can be used to analyze the vibration characteristics of plates with arbitrary thickness.…”

Section: Introductionmentioning

confidence: 99%

Three-Dimensional Free Vibration Analysis of Gears with Variable Thickness Using the Chebyshev–Ritz Method

Liu

Wang

et al. 2018

Mathematical Problems in Engineering

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To reflect vibration more comprehensively and to satisfy the machining demand for high-order frequencies, we presented a three-dimensional free vibration analysis of gears with variable thickness using the Chebyshev–Ritz method based on three-dimensional elasticity theory. We derived the eigenvalue equations. We divided the gear model into three annular parts along the locations of the step variations, and the admissible function was a Ritz series that consisted of a Chebyshev polynomial multiplying boundary function. The convergence study demonstrated the high accuracy of the present method. We used a hammering method for a modal experiment to test two annular plates and one gear’s eigenfrequencies in a completely free condition. We also applied the finite element method to solve the eigenfrequencies. Through a comparative analysis of the frequencies obtained by these three methods, we found that the results achieved by the Chebyshev–Ritz method were close to those obtained from the experiment and finite element method. The relative errors of four sets of data were greater than 4%, and the errors of the other 48 sets were less than 4%. Thus, it was feasible to use the Chebyshev–Ritz method to solve the eigenfrequencies of gears with variable thickness.

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Free Vibration of Cantilever Bars Having a Shape of Solid and Hollow Curvilinear Truncated Cone

Szlachetka

Jaworski

Chalecki

2018

Springer Proceedings in Mathematics &Amp; Statistics

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Three-dimensional vibrations of solid cones with and without an axial circular cylindrical hole

Cited by 11 publications

References 6 publications

Analysis of free vibrations of cantilever bars with parabolically variable cross-sections using the Rayleigh’s method

Analysis of free vibrations of cantilever bars with parabolically variable cross-sections using the Rayleigh’s method

Three-Dimensional Free Vibration Analysis of Gears with Variable Thickness Using the Chebyshev–Ritz Method

Free Vibration of Cantilever Bars Having a Shape of Solid and Hollow Curvilinear Truncated Cone

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