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- W3148492037 abstract "Abstract. The work is devoted to the study of free vibrations taking into account the self-weight of vertical rod structures, which in the design scheme are reduced to a clamped-pinned rod. The research used the author's method, which is based on the exact solution of the corresponding partial differential equation of vibration with variable coefficients. For the given boundary conditions the frequency equation is written in dimensionless form and the method of finding its roots is determined. Determining the frequencies of natural vibration is reduced to finding the corresponding dimensionless coefficients from the frequency equations. Representing the vibration coefficient as a variable function of the dimensionless parameter that characterizes the mechanical system, and calculating the data set on the allowable range of parameter values, the vibration coefficient was approximated by a polynomial. As a result, the final formulas for calculating the vibration coefficient and, consequently, the natural frequency for a rod with any physical and mechanical characteristics are obtained. The calculation of the natural frequency of the steel catenary riser (SCR) reduced to a given design scheme is performed. When designing risers, among other things, the characteristics of the internal fluid flow, vibration of the equipment are taken into account. However, it is mandatory in the practice of dynamic calculations of structures to study the frequency spectrum of their nature vibrations. Because these constructions, as a rule, have quite large height, the question of the account of self-weight at their designing is rather important aspect. An example in which the author's method calculates the first three oscillation frequencies is considered. Comparing them with the known formulas for weightless rods, it was found that taking into account the self-weight decrease the value of the corresponding frequencies. The error of values for the first frequency is the largest and is 15%. The greatest difference between the corresponding natural frequencies, taking into account the self-weight, is achieved at the critical value of the longitudinal load, in terms of stability." @default.
- W3148492037 created "2021-04-13" @default.
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- W3148492037 date "2021-03-04" @default.
- W3148492037 modified "2023-09-24" @default.
- W3148492037 title "METHOD OF ROD STRUCTURES’ CALCULATION FOR VIBRATIONS TAKING INTO ACCOUNT SELF-WEIGHT" @default.
- W3148492037 doi "https://doi.org/10.31650/2415-377x-2021-82-37-46" @default.
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