Rotary inertia

About: Rotary inertia is a research topic. Over the lifetime, 2685 publications have been published within this topic receiving 57922 citations.

Whirling Analysis of Stepped Timoshenko Shaft Carrying Several Rigid Disks

Abstract: Rotor system is the main part of turbomachines. Critical speeds occur when the rotor spin-speed matches with its natural frequencies, and result in great vibration amplitudes often leading to catastrophic failure. Design specifications based on these critical speeds become essential for the engineer. In this paper, whirling vibrations of a spinning, stepped Timoshenko shaft carrying three identical rigid disks are solved using a developed program in Fortran 90 language, based on relationships between the solution coefficient vectors of differential equations of motion. The flexural vibrations are considered in two orthogonal planes. Shear deformation, rotary inertia, and gyroscopic moments are taken into account. This study shows that in the case of the Timoshenko model, the relationship matrix form between the aforementioned vectors presents an advantage, that reduces the number of multiplied matrices when adjacent shaft segments have the same mechanical and geometric properties. The presented approach and Natanson's technique are combined to determine the whirling mode shapes. The accuracy of the presented technique is confirmed by comparing the obtained results with those available in the literature.

Spatial vibrations of eflical heal-exchange pipes excited by internal flow of a heat carrier

Abstract: The principal result of the present work is that on the basis of the variational principle of Hamilton-Ostrogradskii we obtained a complete system of differential equations of the vibrations of helical heat exchange pipes excited by internal flow of the heat carrier, and the analytical formulation of the set of all permissible boundary conditions is provided. It was shown that from the presented system there follow as special cases many results obtained earlier in connection with curved and straight pipes and spatial rods. It was established that depending on the conditions of constraint of the ends of a heat exchange pipe, the system may be conservative or nonconservative. In the former case, loss of stability may be in flexural form when the critical flow rate is exceeded, in the latter case it is the flutter form. We examined actual examples of conservative and nonconservative systems, and we formulated boundary-value problems for them. The suggested equations and dependences may be the basis for further improvement of the theory of vibrations of spatial heat exchange pipes excited by a flow of heat carrier, by taking additionally into account the viscosity of the liquid, the nonsteady state of the flow, the initial stresses in the pipe, the rotary inertia of its sections, damping, and other factors in dependence on the problem under examination and the accuracy required for the actual applications. On the other hand, being very general, the equations and dependences may find applications of their own in practical engineering calculations.

Effects of tip mass and actuator inertia on the behavior of a flexible arm robot

Abstract: There are some important parameters that must be taken into consideration in the design process of the actuator for a flexible single link robot. Among these important factors are the hub inertia and the proper tip mass (including the payload) for optimum performance of the flexible arm system. The main objective of the paper is to study the effect of the actuator inertia as well as the tip mass in the flexible hub torque through the solution of the inverse dynamics problem. For comparison, two reference trajectories; Gaussian velocity, and a polynomial profile are applied. The equations of motion are derived with the help of the extended Hamilton principle using the virtual link coordinate system and the pinned-pinned boundary conditions.

Comparing Exact and Generalized Regression Neural Network Solutions for Free Vibration of Elastically Supported Timoshenko Beams with Attached Masses

Abstract: In this study, as the Artificial Neural Networks (ANN) is becoming increasingly common in the modeling and forecasting in many disciplines of engineering, Generalized Regression Neural Networks (GRNN) model is used to obtain natural frequencies of elastically supported Timoshenko beams with attached masses and the obtained frequencies are compared with the frequencies obtained from the exact solution of the same beam model. The elastically supported cantilever Timoshenko beam carrying multiple attached masses with rotary inertia is chosen as a mathematical model. The concept of fixity factor is used to define the stiffness of the elastic support. The governing equation of the beam elements is solved by applying the separation of variables method in the transfer matrix method (TMM) algorithm that gives the exact solution. The data used in the training, testing and verification phases of GRNN are obtained from TMM. The comparison graphs are presented for training, testing and verification data in numerical analysis to show the effectiveness of the GRNN, and it is resulted that neural network approach gives close results to TMM in training and testing phases.