Towards the Design of an Optimal Energetic Sink in a Strongly Inhomogeneous Two-Degree-of-Freedom System

2006 ◽  
Vol 74 (6) ◽  
pp. 1078-1086 ◽  
Author(s):  
L. I. Manevitch ◽  
E. Gourdon ◽  
C. H. Lamarque
Keyword(s):  
Computer Simulation ◽  
Energy Transfer ◽  
Comparative Analysis ◽  
Analytical Solution ◽  
Experimental Verification ◽  
Degree Of Freedom ◽  
Analytical Prediction ◽  
Energy Pumping ◽  
Strong Energy ◽  
Two Degree Of Freedom

Analytical, numerical, and experimental results of energy pumping in a strongly inhomogeneous two-degree-of-freedom system are to be presented in this study. The latter is based both on efficient analytical solution and comparative analysis for various types of energetic sinks. Considering the efficient pumping process as damped beating with strong energy transfer, it is shown that we can design the sinks with amplitude-phase variables which provide the most efficient result. In this study, the main types of energetic sinks are to be compared. Computer simulation has confirmed the analytical predictions which had been obtained. Experimental verification of the analytical prediction is considered for a particular type of sink.

A comparative analysis of modal motions for the gyroscopic and non-gyroscopic two degree-of-freedom conservative systems

2016 ◽  
Vol 385 ◽  
pp. 300-309 ◽  
Author(s):  
Xiao-Dong Yang ◽  
Hua-Zhen An ◽  
Ying-Jing Qian ◽  
Wei Zhang ◽  
Roderick V.N. Melnik
Keyword(s):  
Comparative Analysis ◽  
Degree Of Freedom ◽  
Conservative Systems ◽  
Two Degree Of Freedom

A Wave-Based Analytical Solution to Free Vibrations in a Combined Euler–Bernoulli Beam/Frame and a Two-Degree-of-Freedom Spring–Mass System

2018 ◽  
Vol 140 (6) ◽  
Author(s):  
C. Mei
Keyword(s):  
Analytical Solution ◽  
Coupling Effect ◽  
Free Vibrations ◽  
Degree Of Freedom ◽  
Transverse Motion ◽  
Bernoulli Beam ◽  
Combined System ◽  
Mass System ◽  
Euler Bernoulli Beam ◽  
Two Degree Of Freedom

In this paper, natural frequencies and modeshapes of a transversely vibrating Euler–Bernoulli beam carrying a discrete two-degree-of-freedom (2DOF) spring–mass system are obtained from a wave vibration point of view in which vibrations are described as waves that propagate along uniform structural elements and are reflected and transmitted at structural discontinuities. From the wave vibration standpoint, external forces applied to a structure have the effect of injecting vibration waves to the structure. In the combined beam and 2DOF spring–mass system, the vibrating discrete spring–mass system injects waves into the distributed beam through the spring forces at the two spring attached points. Assembling these wave relations in the beam provides an analytical solution to vibrations of the combined system. Accuracy of the proposed wave analysis approach is validated through comparisons to available results. This wave-based approach is further extended to analyze vibrations in a planar portal frame that carries a discrete 2DOF spring–mass system, where in addition to the transverse motion, the axial motion must be included due to the coupling effect at the angled joint of the frame. The wave vibration approach is seen to provide a systematic and concise technique for solving vibration problems in combined distributed and discrete systems.

scholarly journals Competitive energy transfer between a two degree-of-freedom dynamic system and an absorber with essential nonlinearity

2010 ◽  
Vol 62 (3) ◽  
pp. 573-592 ◽  
Author(s):  
Thanh Tung Pham ◽  
Stéphane Pernot ◽  
Claude Henri Lamarque
Keyword(s):  
Energy Transfer ◽  
Dynamic System ◽  
Degree Of Freedom ◽  
Two Degree Of Freedom

Analytical Prediction of Periodic Motions in a Machine Tool With Loss of Effective Chip Contact

2008 ◽  
Author(s):  
Brandon C. Gegg ◽  
Steven C. S. Suh ◽  
Albert C. J. Luo
Keyword(s):  
Machine Tool ◽  
Closed Form ◽  
Systems Theory ◽  
Phase Trajectory ◽  
Degree Of Freedom ◽  
Analytical Prediction ◽  
Periodic Motions ◽  
Discontinuous Systems ◽  
Closed Form Solutions ◽  
Two Degree Of Freedom

This study applies a discontinuous systems theory by Luo (2005) to an approximate machine-tool model. The machine-tool is modeled by a two-degree of freedom forced switching oscillator. The switching of the model emulates the various types of dynamics in a machine-tool system. The main focus of this study is the loss of effective chip contact and boundaries of this motion. The periodic motions will be studied through the mappings developed for this machine-tool. The periodic motions will be numerically and analytically predicted via closed form solutions. The phase trajectory, velocity, and force responses are presented.

Analytical Prediction of Chatter Stability in Milling—Part II: Application of the General Formulation to Common Milling Systems

1998 ◽  
Vol 120 (1) ◽  
pp. 31-36 ◽  
Author(s):  
E. Budak ◽  
Y. Altintas¸
Keyword(s):  
Numerical Solutions ◽  
Degree Of Freedom ◽  
Analytical Prediction ◽  
Chatter Stability ◽  
Peripheral Milling ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Chatter Prediction ◽  
Milling Chatter ◽  
Two Degree Of Freedom

The general formulation for the milling chatter prediction developed in Part I of the paper is applied to common milling systems. Three cases are considered: a workpiece with single-degree-of-freedom, a face milling cutter with two-degree-of-freedom, and peripheral milling of a cantilevered thin web. The general milling stability formulation is further simplified for the less complicated models. For each case, an analytical expression which explicitly relate the chatter limit to the milling conditions and tool-workpiece dynamics are derived. The analytical predictions are compared with numerical and time domain solutions proposed by previous research. It is shown that the proposed method can accurately predict the chatter limits in milling and thus eliminates the time consuming numerical solutions.

Enhanced Targeted Energy Transfer by Vibro Impact Cubic Nonlinear Energy Sink

2018 ◽  
Vol 10 (06) ◽  
pp. 1850061 ◽  
Author(s):  
Y. M. Wei ◽  
X. J. Dong ◽  
P. F. Guo ◽  
Z. K. Peng ◽  
W. M. Zhang
Keyword(s):  
Energy Transfer ◽  
Energy Absorption ◽  
Nonlinear Energy Sink ◽  
Targeted Energy Transfer ◽  
Analytical Treatment ◽  
Efficient Manner ◽  
Energy Pumping ◽  
Energy Sink ◽  
Two Degree Of Freedom ◽  
Nonlinear Energy

Passive targeted energy transfer (TET) that describes a highly efficient manner of energy absorption is considerably enhanced by a new form of absorber proposed in this paper. The absorber is attached to the primary linear oscillator (LO) through cubic stiffness and bilateral barriers that set to induce vibro-impact (VI). Both essential nonlinearity and non-smooth nonlinearity are considered. Energy pumping phenomenon is found, and complexification averaging method is used to give an analytical treatment for the essential stiffness nonlinearity. At a low level of impulse excitation where energy pumping of nonlinear energy sink (NES) does not occur, by introducing VI energy pumping is brought up. At the optimal TET state, the vibro-impact cubic (VIC) absorber improves the efficiency of cubic NES on energy reduction to a certain degree. For a two-degree-of-freedom LO, the new absorber can absorb most energy of the broadband excitation which is a novel improvement compared with normal NES. Broadband excitations like input with sufficient bandwidth and random signals are found to be absorbed extensively by the VIC NES, meaning that the VIC NES as a nonlinear passive vibration absorber can be very efficient on broadband vibration energy absorption.

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