Past researchers suggested that "static instabilities" exist at certain rotational speeds of whirling rods. This paper shows these instabilities are an artefact of the material constitutive laws that are being used well outside their range of applicability. An alternative approach is developed where strains due to rotation are separated from the superimposed vibration. This enables the generally predicted lowering of longitudinal natural frequencies with rotational speed shown to be simply a result of the bulk changes in the geometry of whirling rods. Steady-state equations of whirling rods are formulated in Lagrangian coordinates. Due to the nonlinear nature of the governing equations, an original numerical method is applied to solve the problem. Numerical results are compared with analytical results obtained from the linearized uniaxial model. There is close agreement between these two models at low angular velocities. However, at high angular velocities, discrepancies between them arise, confirming that the nonlinear strain-displacement relationship has significant effect on the results and the inferred "static instabilities." This approach first solves the "static" problem of the deformed geometry of a highly strained whirling rod before longitudinal natural modes are determined by classical methods. Furthermore, conditions for existence and uniqueness of solutions are derived.
In this report, a large eddy simulation (LES) model is used to investigate the conventional types of ventilation system design in the context of a public transport interchange. Various airflow patterns based on two of the most popular ventilation designs (mixing and displacement) are simulated to determine their effect on the fire. The simulation program chosen is the fire dynamics simulator (FDS) published by National Institute of Standards and Technology (NIST). It is found that increased airflow causes the fire temperature to increase by as much as 500 K. Extraction of smoke mixture by fans (exhaust only system) significantly decreases the spread of smoke and fire. Ventilation inlets located at the ground level help to increase the smoke and fire intensity in the occupied zone. Displacement ventilation increases fire intensity and current.
A proposal for a numerical method based on the complete solution collocation method is presented to solve the cable-stayed bridge engineering structural problem. This complete function collocation method is presented from the viewpoint of calculating the pretension forces required for the final completed bridge structure, which is one of the most important and practical considerations in cable-stayed bridge design. The complete function collocation method is used to calculate stay cable forces by solving a set of partial differential equations. The study shows that this mesh-free collocation method can be used to solve practical structural engineering problems and provides an alternative to traditional finite element methods. A simple two-dimensional cable-stayed bridge is presented and is solved to illustrate this numerical method. Governing equations of deformation for a bridge structure are formulated in either Eulerian or Lagrangian coordinate systems according to the situation. Point loads due to stay cables on bridge pylons and bridge deck are modelled by Fourier or Gaussian representations. Transverse natural frequencies of stay cables subject to no body forces and caused by flow-induced vibration due to blowing wind are proposed. The preliminary computational procedure presented in this paper provides the basis for further analysis toward more realistic cable-stayed bridges, which would include nonlinear effects, live loadings and construction stage loadings.
a b s t r a c tLongitudinal vibrations coupled with transverse vibrations of whirling rods are investigated. It is known that longitudinal and transverse vibrations are governed by second and fourth order differential equations, respectively. Due to the Coriolis effect, a system of equations that governs the longitudinal and transverse displacements will be constructed by coupling these two equations together. Solutions of the equations assume small oscillations of vibration being superimposed on the steady state of the whirling rod. Exact and approximate solutions are obtained from the proposed governing equations, where the approximate solutions on displacements and natural frequencies are acquired by neglecting the Coriolis effect. A proposed numerical scheme known as complete function collocation method is implemented to solve the governing equations coupled with longitudinal and transverse displacements. The approximate results on both longitudinal and transverse natural frequencies show that natural frequencies are decreasing while the angular velocity of the rod is increasing. Exact and numerical results on both longitudinal and transverse natural frequencies show that there are no predictable trends whether natural frequencies are increasing or decreasing while the angular velocity of the rod is increasing.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.