New Damped-Jerk trajectory for vibration reduction

This paper derives a jerk-shaped profile to address the vibration reduction of underdamped flexible dynamics of motion system. The jerk-limited profile is a widespread smooth command pattern used by modern motion systems. The ability of the jerk-limited profile to cancel the residual vibration of an undamped flexible mode is clearly explained using an equivalent continuous filter representation and the input shaping formalism. This motivates the design of a new jerk-shaped profile, named Damped-Jerk profile, to extend the previous result to the more common case of underdamped systems. Both simulations and experimental results demonstrate the effectiveness of the proposed Damped-Jerk profile to reduce damped vibration

Changing the eigenfrequency spectrum using passive vibration absorbers

Using a substructure coupling technique the problem of assigning anti resonances is reformulated as a pole placement problem which can be analyzed in a more general framework. A possible approach to create these points of zero vibration is by attaching passive undamped vibration absorbers. As this approach is sensitive to changes in the excitation frequency, a robustness measure is proposed. Based on this measure, a better understanding is provided regarding the attachment location of the absorber and the absorber mass

Dynamic response of a viscously damped two adjacent degree of freedom system linked by inerter subjected to base harmonic excitation

The study investigates the dynamic response of a viscously damped two adjacent single degree-of-freedom (2-ASDOF) system coupled by a connection that includes an inerter element. The dynamical model of a pair of simple oscillators coupled with various connection elements is synthetic but also representative to describe different classes of structures (i.e. contiguous buildings, adjacent walls and frames and so on). The specific kind of connection fundamentally alters the dynamic behavior of the entire system. Coupling elements typically studied are springs, dampers, linear or non-linear, passive, semi-active or active, e.g. [1,2]. The inerter is a novel device able to generate a resisting force, proportional to the relative acceleration of its terminals, equivalent to a force produced with an apparent (inertial) mass two orders of magnitude greater than its own physical (gravitational) mass [3]. In this study, a non-conservative connection, realized with a spring-inerter-viscous damper elements, adjusted in parallel, is considered as linking scheme for the 2-ASDOF system. In order to perform modal analysis, the first order state-space representation is adopted and the modal equations for the viscously damped system are derived. By solving the eigenvalue problem, the attention is focused on how modal parameters, i.e. the natural frequencies, the modal damping ratios and modes are affected by the connection. The system is then subject to harmonic base excitation and frequency response functions are depicted showing the influence of the link (through spring stiffness, inertance and damping coefficient) on the dynamic response. From the analysis with the different linking schemes, it emerges that the specific kind of connection influences the system dynamic characteristics

Feasibility of nonlinear absorbers for transient vibration reduction

Torsional vibrations are a cause of severe damage to flexible couplings and gearboxes of a dredger drive line. In this paper the feasibility of three different vibration absorbers is discussed when reducing transient vibrations originating from sudden load changes. The classical linear absorber is compared to two nonlinear ones, one with a cubic spring (known as the nonlinear energy sink or NES) and one with a combination of a linear and a cubic spring (a Duffing type absorber). Both nonlinear absorbers succeed in achieving a multimodal vibration reduction, whereas the linear absorber can only mitigate a single vibration mode. The most important reduction is however obtained in the initial phase where the energy of one vibration mode is decreased through a beating phenomenon. A much slower energy reduction of the remaining vibration modes takes place after this initial phase. As a result, both the NES and the Duffing type absorber still need to be tuned to the most important mode, despite their ability to mitigate multiple modes

Self frequency-locking of a chain of oscillators

The paper studies the vibrational modes of a slightly damped uniform chain, with n masses coupled by elastic forces. It will be shown that, for certain lengths of the chain, that is for certain values of n, the damping of one of the masses at a specific position in the chain is able to constrain the vibration of the system to oscillate at a specific frequency. The damped mass turns out to be a node of the chain, subdividing it in two parts. This node can be considered as the synchronization element of the two subchains. As a consequence the oscillating system of n-masses is self-locking to the synchronized frequency of its subchains

Bernoulli's Transformation of the Response of an Elastic Body and Damping

Bernoulli's transformation and the related separation of variables method or modal analysis as classically applied to the partial differential equation of motion of an elastic continuum will always conclude an undamped response. However, this conclusion lacks reliability, since the underlying analysis assumes either integrandwise differentiability (i.e. differentiation and integration signs are interchangeable) or termwise differentiability (i.e. the derivative of an infinite series of terms equals the sum of the derivatives of the terms) for Bernoulli's transformation, which not only is responsible for the undamped response but also is arbitrary. This paper using Bernoulli's transformation examines an elastic uniform column ruled by the generalized Hooke’s law and subjected to axial surface tractions at its free end or a free axial vibration, and shows that the above differentiability assumptions underlying classical analysis are equivalent and actually constitute a limitation to the class of the response functions. Only on this limitation, damping appears to be inconsistent with the elastic column response. Removing the limitation through nontermwise differentiability of Bernoulli’s transformation results in a damped response of the elastic column, which indicates that damping actually complies with the generalized Hooke’s law as applied to elastic continua

In-house experiments in large space structures at the Air Force Wright Aeronautical Laboratories Flight Dynamics Laboratory

The Flight Dynamics Laboratory is committed to an in-house, experimental investigation of several technical areas critical to the dynamic performance of future Air Force large space structures. The advanced beam experiment was successfully completed and provided much experience in the implementation of active control approaches on real hardware. A series of experiments is under way in evaluating ground test methods on the 12 meter trusses with significant passive damping. Ground simulated zero-g response data from the undamped truss will be compared directly with true zero-g flight test data. The performance of several leading active control approaches will be measured and compared on one of the trusses in the presence of significant passive damping. In the future, the PACOSS dynamic test article will be set up as a test bed for the evaluation of system identification and control techniques on a complex, representative structure with high modal density and significant passive damping

Self frequency-locking of a chain of oscillators

arXiv:1006.1722, Classical Physics, Cornell University Librar

Experimental evaluation of a tuned electromagnetic damper for vibration control of cryogenic turbopump rotors

Experiments were performed on a passive tuned electromagnetic damper that could be used for damping rotor vibrations in cryogenic turbopumps for rocket engines. The tests were performed in a rig that used liquid nitrogen to produce cryogenic turbopump temperatures. This damper is most effective at cryogenic temperatures and is not a viable damper at room temperature. The unbalanced amplitude response of the rotor shaft was measured for undamped (baseline) and damped conditions at the critical speeds of the rotor (approx. 5900 to 6400 rpm) and the data were compared. The tests were performed for a speed range between 900 and 10 000 rpm. The tests revealed that the damper is very effective for damping single-mode narrow bandwidth amplitude response but is less effective in damping broadband response or multimode amplitude response

Fourier Spectra and Shock Spectra for Simple Undamped Systems - A Generalized Approach

Fourier spectra and shock spectra for transient excitation