Difference-frequency Forces Research Articles

Parametric study of pounding tuned mass damper for subsea jumpers

In previous study, a pounding tuned mass damper (PTMD) was proposed to reduce the undesired vibration of a subsea jumper. Both experimental and numerical results verified the effectiveness of the PTMD. This paper aims to enhance the understanding of the PTMD through a parametric study. The jumper is subjected to sinusoidal forces of different frequencies. The reduction ratio is defined for evaluation of the mitigation performance. Three parameters are considered in this study: the pounding stiffness, the gap between the delimiter and the mass block, and the mass ratio. The parametric studies show that the PTMD system is not so sensitive to the small variations of the pounding stiffness and the gap. The reduction ratio is significantly increased with the mass ratio increased up to 2%. Afterwards, it is not so economic or practically feasible to enlarge the mass ratio.

Acoustic characteristics inside cylindrical structure with end plates excited at different frequencies

In order to study coupling between vibration of a structure and a sound field in contact with the structure, a cavity surrounded by a rigid cylinder having thin elastic plates at both ends is adopted as an analytical model. When excitation forces of different frequencies are applied to the respective plates, the plate vibrations and the sound field inside the cavity become aperiodic, because of the coupling between the systems. In the present investigation, distribution of the sound pressure level inside the cavity is studied in detail in order to clarify the coupling behavior. The results show that when the respective plates vibrate at the same circumferential order, the vibration modes of the plates, which effect the coupling of the plate vibrations and the sound field, cause the aperiodic nature of each system to develop. In this case, since the dominant mode exists in formation of the sound field, it significantly influences the aperiodic nature of the coupling systems. In the case of vibration modes where the plates vibrate at different circumferential orders, the behaviors of the three systems, whose coupling has been restrained, approximate a steady state. Consequently, the dominant mode does not appear in the sound field.

Nonlinear Hydrodynamic Forces on Flexible Structures: A Combined-Force Model

A new combined-force method is suggested to approximate the second-order difference frequency forces from diffraction theory (Φ2 theory) with less computational effort. The new method is formulated by combining two limiting cases of the Φ2 theory; i.e., Newman’s approximation and the slender Φ2 theory. Numerical results show that the new method reproduces the individual nonlinear effects of the Φ2 theory better than the existing approximations. Results of this work also show the limitations of Morison’s equation as the slender-body counterpart of the diffraction theory for nonlinear problems.

Chaos in a double driven dissipative nonlinear oscillator.

We propose an anharmonic oscillator driven by two periodic forces of different frequencies as a time-dependent model for investigating quantum dissipative chaos. Our analysis is done in the framework of the statistical ensemble of quantum trajectories in a quantum state diffusion approach. The quantum dynamical manifestations of chaotic behavior, including the emergence of chaos, properties of strange attractors, and quantum entanglement, are studied by numerical simulation of the ensemble averaged Wigner function and von Neumann entropy.

Vibration absorber for helicopter

A vibration absorber for a helicopter rotor includes a hub portion, a mass portion encircling the hub portion and a plurality of resilient arms extending in a spaced-apart spiral pattern between the hub and the mass. In operation, the hub portion of the vibration absorber is mounted on a helicopter rotor so as to be rotated with the rotor about an axis of rotation of the rotor, the resilient arms ensuring that the mass is capable of equal resilient deflection in any direction within its plane of rotation whereby the vibration absorber simultaneously reduces in-plane vibration forces of different frequencies.

Combination tones of summed type in a non-linear damped vibratory system with two degrees of freedom

The combination tones of summed type are studied in a non-linear damped vibratory system with two degrees of freedom, excited by two external harmonic forces of different frequencies. Equations are given for the response curves, the phase angles and the back bones of the summation tones. The stability of the summation tones is investigated by the method of varying amplitudes and phases. Numerical results and effects of the parameters are explained.

Recherche numérique d'oscillations composées du type additif dans un système oscillant non-linéaire amorti à deux degrés de liberté

The combination tones of summed type are studied in a non-linear damped vibratory system of two degrees of freedom with spring characteristics of second and third order and excited by two external harmonic forces of different frequencies. A modified Galerkin method is presented, based on the replacement of some integrals by their Simpson approximations instead of using the formulae given by M. Urabe. For some systems this modified method has the advantage to ameliorate the precision of the Galerkin approximations and to diminish considerably the error of these approximations. The existence and stability of an exact periodic solution is discussed and the error bound of the Galerkin approxi¬ mations is given. The modified Galerkin method is compared to other approximation methods for two numerical examples.

On Multiple Excitation of an Elastic System

The possibility of excitation of nonlinear elastic system by the combination frequencies produced when two forces of different frequencies act on the system is investigated, using the approximate method of Rayleigh. Experimental evidence is cited to support the results of the calculations, namely, that the combination frequencies need not be considered as potential sources of excitation.