Forced Harmonic Response of a Continuous System Displaying Eigenvalue Veering Phenomena

1995 ◽  
Vol 117 (4) ◽  
pp. 439-444 ◽  
Author(s):  
J. H. Ginsberg ◽  
Hoang Pham
Keyword(s):  
Natural Frequencies ◽  
Continuous System ◽  
Harmonic Excitation ◽  
Force Response ◽  
Concentrated Force ◽  
Peak Displacement ◽  
Harmonic Response ◽  
State Response ◽  
Exact Eigenvalue ◽  
Hysteretic Loss

Prior studies of self-adjoint linear vibratory systems have extensively explored the free vibration phenomena associated with veering of eigenvalue loci that depict the dependence of natural frequencies on a system parameter. The present work is an exploration of the effect of such phenomena on the response of a nearly-periodic continuum to harmonic excitation. The focus of the analysis is the prototypical system of a two-span beam with a strong torsional spring at the intermediate pin support. The results of an exact eigenvalue analysis, not previously disclosed, are used to perform a modal analysis of the steady-state response to a harmonic concentrated force applied to the middle of one span. The modal equations are used to identify situations in which the force response is localized to one span, as well as the degree to which the location and magnitude of the peak displacement display parameter sensitivity. The effect of hysteretic loss on forced localization is discussed.

Forced Harmonic Response of a Continuous System Displaying Eigenvalue Veering Phenomena

1993 ◽  
Author(s):  
Jerry H. Ginsberg ◽  
Hoang Pham
Keyword(s):  
Natural Frequencies ◽  
Continuous System ◽  
Harmonic Excitation ◽  
Forced Response ◽  
Steady State Response ◽  
Concentrated Force ◽  
Peak Displacement ◽  
Harmonic Response ◽  
State Response ◽  
Exact Eigenvalue

Abstract Prior studies of self-adjoint linear vibratory systems have extensively explored the phenomenon of veering of eigenvalue loci that depict the dependence of natural frequencies on a system parameter. The present work is an exploration of the effect of such phenomena on the response of a continuum to harmonic excitation. The focus of the analysis is the prototypical system of a two-span beam with a strong torsional spring at the intermediate pin support. The results of an exact eigenvalue analysis, not previously disclosed, are used to perform a modal analysis of the steady-state response of the beam to a harmonic concentrated force applied to the middle of one span. The analysis is used to identify situations in which the forced response is localized to one span, as well as the degree to which the location and magnitude of the peak displacement displays parameter sensitivity.

scholarly journals Vibration Equation of Fractional Order Describing Viscoelasticity and Viscous Inertia

Open Physics ◽  
2019 ◽  
Vol 17 (1) ◽  
pp. 850-856 ◽  
Author(s):  
Jun-Sheng Duan ◽  
Yun-Yun Xu
Keyword(s):  
Fractional Derivative ◽  
Fractional Order ◽  
Fractional Derivatives ◽  
Harmonic Excitation ◽  
Steady State Response ◽  
Vibration System ◽  
Derivative Operator ◽  
Vibration Equation ◽  
State Response ◽  
Frequency Relation

Abstract The steady state response of a fractional order vibration system subject to harmonic excitation was studied by using the fractional derivative operator ${}_{-\infty} D_t^\beta,$where the order β is a real number satisfying 0 ≤ β ≤ 2. We derived that the fractional derivative contributes to the viscoelasticity if 0 < β < 1, while it contributes to the viscous inertia if 1 < β < 2. Thus the fractional derivative can represent the “spring-pot” element and also the “inerterpot” element proposed in the present article. The viscosity contribution coefficient, elasticity contribution coefficient, inertia contribution coefficient, amplitude-frequency relation, phase-frequency relation, and influence of the order are discussed in detail. The results show that fractional derivatives are applicable for characterizing the viscoelasticity and viscous inertia of materials.

Reduction of Harmonic Response of Cylindrical Shells

1975 ◽  
Vol 97 (4) ◽  
pp. 1371-1377 ◽  
Author(s):  
G. B. Warburton
Keyword(s):  
Cantilever Beams ◽  
Steady State Response ◽  
Optimum Conditions ◽  
Harmonic Force ◽  
Shell Surface ◽  
Single Degree Of Freedom ◽  
Harmonic Response ◽  
State Response ◽  
Single Degree ◽  
Mode Method

The normal mode method is used to investigate the reduction in the steady-state response of a simply supported cylindrical shell when conventional absorbers are attached to the shell. Two types of excitation are considered: (a) a single radial harmonic force, and (b) a harmonic pressure distributed over the shell surface. The effect upon response of varying the absorber parameters is studied. Optimum conditions for specific cases are obtained and compared with those required to minimize response when absorbers are added to cantilever beams and to the classical single degree of freedom system.

Analytical evaluation of track response in the vertical direction due to a moving load

2016 ◽  
Vol 23 (18) ◽  
pp. 2989-3006 ◽  
Author(s):  
Wlodzimierz Czyczula ◽  
Piotr Koziol ◽  
Dariusz Kudla ◽  
Sergiusz Lisowski
Keyword(s):  
Steady State ◽  
Moving Load ◽  
Vertical Direction ◽  
Vertical Displacement ◽  
Steady State Response ◽  
Concentrated Force ◽  
State Response ◽  
Weakly Coupled ◽  
Wide Range ◽  
Rail Deflection

In the literature, typical analytical track response models are composed of beams (which represent the rail) on viscoelastic or elastic foundations. The load is usually considered as a single concentrated force (constant or varying in time) moving with constant speed. Concentrated or distributed loads or multilayer track models have rarely been considered. One can find some interesting results concerning analysis of distributed loads and multilayer track structures that include both analytical and numerical approaches. However, there is a noticeable lack of sufficient comparison between track responses under concentrated or distributed load and between one and multilayer track models. One of the unique features of the present paper is a comparison of data obtained for a series of concentrated and distributed loads, which takes into account a wide range of track parameters and train speeds. One of the fundamental questions associated with the multilayer track model is the level of coupling between the rail and the vibrations of the sleepers. In this paper, it is proved that sleepers are weakly coupled with the rail if the track is without significant imperfections, and the steady-state response is analyzed for this case. In other words, sleeper vibrations do not influence the rail vibrations significantly. Therefore the track is analyzed by means of a two-stage model. The first step of this model determines rail vibration under a moving load, and then the sleeper vibration is calculated from previously obtained kinematic excitation. The model is verified by comparison of the obtained results with experimental data. Techniques based on Fourier series are applied to the solution of the steady-state track response. Another important problem associated with track response under moving loads arises from the analysis of the effect of longitudinal forces in rails on vertical displacement. It is shown that, in the case of the steady-state response, longitudinal forces do not influence rail displacements significantly and this observation remains correct for a wide range of track parameters and train speeds. The paper also analyzes the legitimacy of the statement that additional rail deflection between sleepers, compared to the continuous rail support, can be considered as a track imperfection.

Forced Harmonic Response of Grouped Blade Systems: Part II—Application

1996 ◽  
Vol 118 (1) ◽  
pp. 137-145 ◽  
Author(s):  
L. F. Wagner ◽  
J. H. Griffin
Keyword(s):  
Numerical Model ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Turbine Blades ◽  
Modal Identification ◽  
Harmonic Response ◽  
Model Based ◽  
Grouped Blades ◽  
Flexible Disk ◽  
Symmetric Structures

The vibration of grouped blades on a flexible disk should, for purposes of economy and clarity of modal identification, be analyzed using procedures developed for cyclically symmetric structures. In this paper, a numerical model, based on the theory of cyclically symmetric structures, is applied to the vibration analysis, and in particular, the harmonic response, of a flexible disk supporting a number of groups, or packets, of turbine blades. Results are presented to show variations in the modal participation factors as a function of such parameters as disk flexibility, blade density, and the total number of assembled groups. It is also shown that many characteristics of the system spectra of natural frequencies are strongly dependent on the number of blade groups.

scholarly journals Optimal switch timing for piezoelectric-based semi-active vibration reduction techniques

2017 ◽  
Vol 28 (16) ◽  
pp. 2275-2285 ◽  
Author(s):  
Christopher R Kelley ◽  
Jeffrey L Kauffman
Keyword(s):  
Vibration Reduction ◽  
Harmonic Excitation ◽  
Peak Displacement ◽  
Reduction Techniques ◽  
At Resonance ◽  
Near Resonance ◽  
Switch Time ◽  
Vibration Sensing ◽  
Dimensional Parameters ◽  
Active Vibration

Piezoelectric-based semi-active vibration reduction techniques typically rely on rapid changes in the electrical boundary conditions or corresponding stiffness state. Approaches such as state switching and synchronized switch damping on a resistor or an inductor require four switching events per vibration cycle, with switch timing associated with displacement extrema. Any deviation from this switch timing affects the performance of these techniques. Typical harmonic forcing analyses focus on the energy dissipation and only evaluate the performance at resonance. This study evaluates displacement reduction for harmonic excitation, both at resonance and for frequencies near resonance. Furthermore, it examines the effect of sub-optimal switch timings. Numerical simulations of a non-dimensional model are performed, and an analytical solution is derived for any switch time. This analysis shows that the optimal switch timing depends on the forcing frequency relative to the natural frequency of the structure. Thus, the classical switch time at peak displacement is only optimal when the excitation is exactly at resonance. Even when the optimal switch timing is known, uncertainties in vibration sensing cannot guarantee that switches will occur at the desired moment. Therefore, this work characterizes the degradation in vibration reduction performance when switching away from the optimal switch time based on global, non-dimensional parameters.

Dynamic structure-soil-structure interaction

1973 ◽  
Vol 63 (4) ◽  
pp. 1289-1303
Author(s):  
J. Enrique Luco ◽  
Luis Contesse
Keyword(s):  
Soil Structure ◽  
Natural Frequencies ◽  
Shear Walls ◽  
Dynamic Structure ◽  
Soil Structure Interaction ◽  
Sh Wave ◽  
Low Frequencies ◽  
High Frequencies ◽  
State Response ◽  
Fixed Base

abstract A study is made of the dynamic interaction, through the soil, between two parallel infinite shear walls placed on rigid foundations. The steady-state response of both structures for a vertically incident SH wave is obtained and compared with the corresponding values resulting from consideration of only one structure. It is found that the additional interaction effects caused by the presence of a second structure are especially important at low frequencies and in the neighborhood of the fixed-base natural frequencies of the second structure. For high frequencies it is sufficient to consider the interaction between each structure and the soil, ignoring the presence of other structures.

Nonlinear Harmonic Vibration Analysis of a Fully Clamped Micro-Beam

2015 ◽  
Author(s):  
Mehran Sadri ◽  
Davood Younesian ◽  
Ebrahim Esmailzadeh
Keyword(s):  
Vibration Analysis ◽  
Multiple Scales ◽  
Special Kind ◽  
Equation Of Motion ◽  
Harmonic Excitation ◽  
Harmonic Vibration ◽  
Potential Wells ◽  
State Response ◽  
Nonlinear Forced Vibration ◽  
First Time

Nonlinear harmonic vibration analysis of a clamped-clamped micro-beam is studied in this paper. Nonlinear forced vibration of a special kind of micro-actuators is examined for the first time. Galerkin method is employed to derive the equation of motion of the micro-beam with two symmetric potential wells. An electric force composed of DC and AC components is applied to the structure. Multiple Scales method (MSM) is used to solve the nonlinear equation of motion. Primary and secondary resonances are taken into account and steady-state response of the microbeam is obtained. A parametric study is then carried out to investigate the effects of different parameters on the amplitude-frequency curves. Finally, phase plot and Poincare map have been taken into consideration to investigate the influence of the amplitude of the harmonic excitation on stability of the microelectromechanical system.

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