##### From Torsional Vibration of Turbomachinery

## Overview

A *torsional natural frequency* of a mechanical system is a frequency at which the inertia and stiffness torques are completely in balance (see App. C). In the absence of damping in the system, forcing the mechanical system at this frequency would generally result in a theoretical infinite vibration response. An exception to this would be if the modal applied torque (see *shaft response torque* definition in Sec. 2.1) is zero; an example is a stimulus applied at a nodal point for the mode corresponding to the natural frequency.

When a mechanical system is responding purely at one natural frequency in the steady state, its deflection pattern will have a unique shape called the *mode shape* or *eigenvector.* Mode shapes are normalized and frequently to a maximum value of 1, but in reality the maximum value selected is arbitrary. Only the shapes have significance. This is because the system is unforced and so the mode shapes define only the deflection patterns for which the inertia and stiffness forces are completely in balance. For example, for a simple rotor system with three equal point inertias (located at the middle and ends of the rotor, respectively) connected by two springs of equal stiffness, the shapes of its three modes are as shown in Fig. 7.1.

Figure 7.1: Mode shapes for a simple system.

The mode shapes show the relative rotational displacements on the vertical axis (ordinate) with the node number on the horizontal axis (abscissa). The first...

##### Products & Services

##### Topics of Interest

Overview Forced response analysis generally falls into two main areas: steady-state response to sinusoidal stimuli and transient response to any defined applied torque-time history. In general, in...

9.3 Steady-State Forced Response Case Studies 9.3.1 Case study: Mode responsiveness For the simple free-free (unconstrained) torsional mathematical model used at the beginning of Chap. 7, having...

Sometimes design errors occur such that one or more torsional natural frequencies have inadequate separation margins from the main torsional forcing frequencies of concern. As discussed previously,...

9.3.4 Case study: Quantifying accuracy of forced response calculation For a simple cylinder that is built in at one end and has a sinusoidal torque applied at the other end, calculate the forced...

9.3.2 Case study: Effect of applied torque phase angle changes For the same vibration model as in Case Study 9.3.1 and with the same modal damping values ( ?=0.01), examine the effect of varying the...