Theory of the Dynamic Vibration Neutralizer With Motion-Limiting Stops

1972 ◽  
Vol 39 (2) ◽  
pp. 563-568 ◽  
Author(s):  
S. F. Masri
Keyword(s):  
Exact Solution ◽  
Steady State ◽  
Experimental Studies ◽  
Analog Computer ◽  
Primary System ◽  
Asymptotically Stable ◽  
Mass System ◽  
Dynamic Vibration ◽  
Simulated Motion ◽  
Auxiliary Mass

The exact solution for the steady-state motion of a dynamic vibration neutralizer with motion-limiting stops attached to a sinusoidally excited primary system is derived analytically, and its asymptotically stable regions are determined. Simulated motion on a digital computer and experimental studies with an analog computer corroborate the predictions of the theory. Results of the analysis are applied to modified vibration neutralizers, Lanchester dampers, and impact dampers. It is shown that the incorporation of properly designed motion-limiting stops into the auxiliary mass system will enhance the performance of the foregoing dampers.

Random Excitation of a Nonlinear Vibration Neutralizer

1978 ◽  
Vol 100 (4) ◽  
pp. 681-689 ◽  
Author(s):  
S. F. Masri ◽  
S. J. Stott
Keyword(s):  
Approximate Analytical Solution ◽  
Random Excitation ◽  
Analog Computer ◽  
Primary System ◽  
Experimental Measurements ◽  
Dynamic Vibration ◽  
Power Spectral ◽  
Highly Nonlinear ◽  
Mass Damper ◽  
Auxiliary Mass

An approximate analytical solution is obtained for the stationary response of a highly nonlinear auxiliary mass damper (a dynamic vibration neutralizer with motion-limiting stops) attached to an oscillator that is subjected to random excitation. Experimental measurements with an electronic analog computer and numerically simulated solutions generated by means of a digital computer verify the findings. Results are given for the power spectral density and root-mean-squared level of the response. The effects of various damper parameters on the response of the primary system are determined. The nonlinear damper under consideration is shown to be significantly more effective than the conventional dynamic vibration neutralizer in controlling the response of systems subjected to random excitation.

Response of Pounding Dynamic Vibration Neutralizer Under Harmonic and Random Excitation

2018 ◽  
Vol 86 (2) ◽  
Author(s):  
Sami F. Masri ◽  
John P. Caffrey
Keyword(s):  
Steady State ◽  
Relative Motion ◽  
Closed Form Solution ◽  
Harmonic Excitation ◽  
Random Excitation ◽  
Form Solution ◽  
Primary System ◽  
Tuning Parameters ◽  
Dynamic Vibration ◽  
Highly Nonlinear

Exact steady-state solutions are obtained for the motion of an single-degree-of-freedom (SDOF) system that is provided with a highly nonlinear auxiliary mass damper (AMD), which resembles a conventional dynamic vibration neutralizer (DVN), whose relative motion with respect to the primary system is constrained to remain within a specified gap, thus operating as a “pounding DVN.” This configuration of a conventional DVN with motion-limiting stops could be quite useful when a primary structure with a linear DVN is subjected to transient loads (e.g., earthquakes) that may cause excessive relative motion between the auxiliary and primary systems. Under the assumption that the motion of the nonlinear system under harmonic excitation is undergoing steady-state motion with two impacts per period of the excitation, an exact, closed-form solution is obtained for the system motion. This solution is subsequently used to develop an approximate analytical solution for the stationary response of the pounding DVN when subjected to random excitation with white spectral density and Gaussian probability distribution. Comparison between the analytically estimated rms response of the primary system and its corresponding response obtained via numerical simulation shows that the analytical estimates are quite accurate when the coupling (tuning parameters) between the primary system and the damper are weak, but only moderately accurate when the linear components of the tuning parameters are optimized. It is also shown that under nonstationary, the pounding DVN provides slightly degraded performance compared to the linear one but simultaneously limits the damper-free motion to specified design constraints.

Steady-State Response of a Multidegree System With an Impact Damper

1973 ◽  
Vol 40 (1) ◽  
pp. 127-132 ◽  
Author(s):  
S. F. Masri
Keyword(s):  
Steady State ◽  
Excitation Frequency ◽  
Experimental Studies ◽  
Tall Buildings ◽  
Analog Computer ◽  
Impact Damper ◽  
State Response ◽  
Lumped Parameter ◽  
The Impact ◽  
Story Building

An exact solution is presented for the steady-state motion of a sinusoidally excited n-degree-of-freedom system that is provided with an impact damper. Both the excitation and the damper may be independently applied to any point in the system. Experimental studies with an analog computer and with a mechanical model corroborate the theoretical results. Results of the analysis are applied to the lumped parameter representation of a modern 10 story building, and the effects of various system parameters, including mode shape, excitation frequency, damper location, and force location are determined. It is found that the impact damper is an efficient device for reducing the vibrations of multidegree-of-freedom systems, particularly in structures such as tall buildings.

scholarly journals Magnetoactive elastomers for magnetically tunable vibrating sensor systems

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Tatiana I. Becker ◽  
Yuriy L. Raikher ◽  
Oleg V. Stolbov ◽  
Valter Böhm ◽  
Klaus Zimmermann
Keyword(s):  
Magnetic Field ◽  
Steady State ◽  
Smart Materials ◽  
Excitation Frequency ◽  
Experimental Studies ◽  
Uniform Field ◽  
Sensor Systems ◽  
Ongoing Research ◽  
Amplification Ratio ◽  
Field Distortion

Abstract Magnetoactive elastomers (MAEs) are a special type of smart materials consisting of an elastic matrix with embedded microsized particles that are made of ferromagnetic materials with high or low coercivity. Due to their composition, such elastomers possess unique magnetic field-dependent material properties. The present paper compiles the results of investigations on MAEs towards an approach of their potential application as vibrating sensor elements with adaptable sensitivity. Starting with the model-based and experimental studies of the free vibrational behavior displayed by cantilevers made of MAEs, it is shown that the first bending eigenfrequency of the cantilevers depends strongly on the strength of an applied uniform magnetic field. The investigations of the forced vibration response of MAE beams subjected to in-plane kinematic excitation confirm the possibility of active magnetic control of the amplitude-frequency characteristics. With change of the uniform field strength, the MAE beam reveals different steady-state responses for the same excitation, and the resonance may occur at various ranges of the excitation frequency. Nonlinear dependencies of the amplification ratio on the excitation frequency are obtained for different magnitudes of the applied field. Furthermore, it is shown that the steady-state vibrations of MAE beams can be detected based on the magnetic field distortion. The field difference, which is measured simultaneously on the sides of a vibrating MAE beam, provides a signal with the same frequency as the excitation and an amplitude proportional to the amplitude of resulting vibrations. The presented prototype of the MAE-based vibrating unit with the field-controlled “configuration” can be implemented for realization of acceleration sensor systems with adaptable sensitivity. The ongoing research on MAEs is oriented to the use of other geometrical forms along with beams, e.g. two-dimensional structures such as membranes.

Dynamic Stability of an Impact System Connected With Rock Drilling

1969 ◽  
Vol 36 (4) ◽  
pp. 743-749 ◽  
Author(s):  
C. C. Fu
Keyword(s):  
Computer Simulation ◽  
Exact Solution ◽  
Steady State ◽  
Asymptotic Stability ◽  
Piecewise Linear ◽  
Steady State Solution ◽  
External Excitation ◽  
Rock Drilling ◽  
Impact System ◽  
Number Of Cycles

This paper deals with asymptotic stability of an analytically derived, synchronous as well as nonsynchronous, steady-state solution of an impact system which exhibits piecewise linear characteristics connected with rock drilling. The exact solution, which assumes one impact for a given number of cycles of the external excitation, is derived, its asymptotic stability is examined, and ranges of parameters are determined for which asymptotic stability is assured. The theoretically predicted stability or instability is verified by a digital computer simulation.

scholarly journals Transient Excitation of an Elastic Half Space by a Point Load Traveling on the Surface

1969 ◽  
Vol 36 (3) ◽  
pp. 505-515 ◽  
Author(s):  
D. C. Gakenheimer ◽  
J. Miklowitz
Keyword(s):  
Exact Solution ◽  
Free Surface ◽  
Steady State ◽  
Wave Front ◽  
Half Space ◽  
Displacement Field ◽  
Elastic Half Space ◽  
Point Load ◽  
Limit Case ◽  
Transient Waves

The propagation of transient waves in a homogeneous, isotropic, linearly elastic half space excited by a traveling normal point load is investigated. The load is suddenly applied and then it moves rectilinearly at a constant speed along the free surface. The displacements are derived for the interior of the half space and for all load speeds. Wave-front expansions are obtained from the exact solution, in addition to results pertaining to the steady-state displacement field. The limit case of zero load speed is considered, yielding new results for Lamb’s point load problem.

Beam-Vibration Analysis With the Electric-Analog Computer

1950 ◽  
Vol 17 (1) ◽  
pp. 13-26
Author(s):  
G. D. McCann ◽  
R. H. MacNeal
Keyword(s):  
Steady State ◽  
Vibration Analysis ◽  
Degrees Of Freedom ◽  
Analog Computer ◽  
Accurate Solution ◽  
Rotary Inertia ◽  
Beam Vibration ◽  
Lumped Constant ◽  
Electric Analog

Abstract The authors have developed a true dynamic analogy which has been used with the Cal Tech electric-analog computer for the rapid and accurate solution of both steady-state and transient beam problems. This analogy has been found well suited to the study of beams having several coupled degrees of freedom, including torsion, simple bending, and bending in a plane. Damping and effects such as rotary inertia may be handled readily. The analogy may also be used in the study of systems involving combined beams and “lumped-constant” elements.

Dynamical analysis of a reaction–diffusion SEI epidemic model with nonlinear incidence rate

2021 ◽  
pp. 2150041
Author(s):  
Jianpeng Wang ◽  
Binxiang Dai
Keyword(s):  
Steady State ◽  
Incidence Rate ◽  
Epidemic Model ◽  
Reaction Diffusion ◽  
Dynamical Analysis ◽  
Asymptotically Stable ◽  
Nonlinear Incidence Rate ◽  
Globally Asymptotically Stable ◽  
Nonlinear Incidence ◽  
Positive Steady State

In this paper, a reaction–diffusion SEI epidemic model with nonlinear incidence rate is proposed. The well-posedness of solutions is studied, including the existence of positive and unique classical solution and the existence and the ultimate boundedness of global solutions. The basic reproduction numbers are given in both heterogeneous and homogeneous environments. For spatially heterogeneous environment, by the comparison principle of the diffusion system, the infection-free steady state is proved to be globally asymptotically stable if [Formula: see text] if [Formula: see text], the system will be persistent and admit at least one positive steady state. For spatially homogenous environment, by constructing a Lyapunov function, the infection-free steady state is proved to be globally asymptotically stable if [Formula: see text] and then the unique positive steady state is achieved and is proved to be globally asymptotically stable if [Formula: see text]. Finally, two examples are given via numerical simulations, and then some control strategies are also presented by the sensitive analysis.

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