This analysis extends similar results previously obtained in a paper by Den Hartog and Li, where the remainder torque is calculated at one end of a homogeneous system. Comparative computations made there with complex Holzer tables show excellent agreement with results obtained from the theory of distributed systems. The general boundary-value problem, including the response to an externally applied torque at any section, is solved in this paper. The special case of a homogeneous engine system with a flywheel at one end is analyzed in detail. The theory is illustrated with comparative computations using complex Holzer tables for such a system with external torque applied at a section remote from the ends. Again, numerical results obtained by both methods are in excellent agreement.

Energy dissipation in flexural vibrations is considered by introducing into the Timoshenko beam equation viscous-damping terms proportional to the time rate of extensional strain. Two modes of wave transmission arise from the roots of a quartic equation. On the lower mode, a solution is indicated in terms of characteristic functions which represent the damped natural vibrations. For a specified range of values of damping, the amplitudes of natural vibrations are governed by characteristic damping factors which exhibit a maximum in the region of frequencies where wave velocities are dispersed. There can be no frequency cut-offs. In the higher mode of wave motion, the characteristic damping factors exhibit a monotone increase toward short wave-length limits analogous to those obtained in the Bernoulli-Euler-Sezawa equation.

A solution is obtained for forced oscillations with nonlinear second-order terms. The stability of this solution is given by its variational equation. The boundary of stability is analyzed by both the perturbation and continued fraction methods. The amplitude of osclllation with damping terms is also determined by the iteration procedure.

A rough analysis of the effect of an annular ring on the sloshing oscillations of liquid in a cylindrical tank is carried out. The damping per cycle (logarithmic decrement) for moderate amplitudes is predicted as proportional to the square root of the amplitude and the three-halves power of the ring area. The corresponding force on the ring also is calculated.

Presented herein is a report on a wire-damping device which has shown considerable damping ability when placed in a hollow rotor blade. A series of tests is reported which have all shown the damping ability of this device at nonrotating and rotating conditions. Two theories are postulated and expressions derived to explain the mechanism of damping by the wires for nonrotating-type damping and rotating-type damping. The postulated mechanism for damping in the nonrotating rotor blade considers that the wires absorb energy by rubbing around one another as a result of the motion imparted by the vibratory motion of the blade. The postulated mechanism for damping in the rotating rotor blade considers that a component of centrifugal force holds the wires against the side of the blade and the vibratory bending motion of the blade causes relative motion between the blade wall and the adjacent wires to absorb energy. Criteria are set forth for determining which mechanism is operative. Good correlation was obtained between test and theory.

Orthogonality relations between the eigenvectors of damped linear dynamic systems with lumped parameters are derived; and from these relations co-ordinates are found in terms of which uncoupled equations of motion can be written. Methods are developed for determining transient stresses in terms of these co-ordinates. The present treatment is extended to systems involving transient damping and to continuous systems.

The response of nonlinear, second-order systems is examined from a new point of view which greatly simplifies presentation of the usual frequency-response diagrams. The use of “natural” forcing functions results in a general equation relating the maximum amplitude of the applied force to the maximum amplitude of the restoring force. The relationship is found to be a function of the ratio of the period of free oscillation to the period of the forcing function. The results apply for any second-order system without damping and with a nonlinear (or linear) restoring force. The special cases of a linear system and of Duffing’s equation are considered to illustrate similarities as well as differences between treatment of linear and nonlinear frequency-response problems.

The purpose of this study is to find a significant accelerometer accuracy criterion for measuring transients, and to apply it to the investigation of optimum damping and the range of frequency response required. It is proposed that the effect of instrument distortions on the response spectrum of a transient be used to evaluate the acceptability of the measurement. The application of this response-spectrum criterion to some selected acceleration pulses indicates that the optimum instrument damping for a transient measurement is essentially the same as for the measurement of periodic motions and that the accelerometer period should be less than 0.4 of the pulse duration for 5 per cent accuracy. A reasonable generalization of the results to more complex transients is made.

A method is presented for calculating the optimum concentrated damping for the vibration of continuous systems. It is applied to ( a ) a string damped near one end, ( b ) a cantilever beam driven at the center and damped at the free end, ( c ) a uniform blade with dovetail damping, and ( d ) the damped dynamic absorber. Aside from the specific results which are shown in the examples, there are some general conclusions. The vibration velocity and vibratory force are not necessarily in phase at maximum amplitude for optimum damping. The decay rate at optimum damping is not necessarily related to amplification at resonance, i.e. δ ≠ π / Q

Propane-air mixtures were burned in an effectively open-ended tube containing a screen flameholder. Two types of instability were observed. Of these, one is described in some detail. A driving mechanism is proposed and examined in the light of Rayleigh’s criterion. Finally, a linear, one-dimensional theory is presented, taking into account both the driving and damping effects in the system. The predictions of this theory are shown to be in good agreement with the experimental results.