The Optimization of Damping of Four Configurations of a Vibrating Uniform Beam

1963 ◽  
Vol 85 (3) ◽  
pp. 259-264 ◽  
Author(s):  
Alex Henney ◽  
J. P. Raney
Keyword(s):  
Digital Computer ◽  
Empirical Formula ◽  
Response Curves ◽  
Maximum Displacement ◽  
Single Degree Of Freedom ◽  
Displacement Response ◽  
Single Degree ◽  
Uniform Beam ◽  
Computer Response ◽  
Analytical Expressions

Approximate analytical expressions for optimum damping for four configurations of forcing and damping a uniform beam were evaluated and the displacement responses for optimum damping values obtained from these expressions were calculated by a digital computer. It was found that the responses were accurately optimized. The sensitivity of maximum displacement response to deviation from optimum damping was investigated, but no analytical expressions relating change to deviation were obtained. An empirical formula, based upon consideration of the response of the beam as a single-degree-of-freedom system, was shown to be a good approximation of results obtained from the computer response curves. The four configurations investigated were relatively insensitive to changes in damping from optimum.

Exact determination of critical damping in multiple exponential kernel-based viscoelastic single-degree-of-freedom systems

2019 ◽  
Vol 24 (12) ◽  
pp. 3843-3861 ◽  
Author(s):  
Mario Lázaro
Keyword(s):  
Past History ◽  
Degree Of Freedom ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Critical Curves ◽  
History Of ◽  
Definition Of ◽  
Analytical Expressions ◽  
Critical Damping

In this paper, exact closed forms of critical damping manifolds for multiple-kernel-based nonviscous single-degree-of-freedom oscillators are derived. The dissipative forces are assumed to depend on the past history of the velocity response via hereditary exponential kernels. The damping model depends on several parameters, considered variables in the context of this paper. Those parameter combinations which establish thresholds between induced overdamped and underdamped motion are called critical damping manifolds. If such manifolds are represented on a coordinate plane of two damping parameters, then they are named critical curves, so that overdamped regions are bounded by them. Analytical expressions of critical curves are deduced in parametric form, considering certain local nondimensional parameters based on the Laplace variable in the frequency domain. The definition of the new parameter (called the critical parameter) is supported by several theoretical results. The proposed expressions are validated through numerical examples showing perfect fitting of the determined critical curves and overdamped regions.

Localization Phenomena of Nonlinear Vibrations in Three-Blade Wind Turbines

2013 ◽  
Author(s):  
Takashi Ikeda ◽  
Yuji Harata ◽  
Hisashi Takahashi ◽  
Yukio Ishida
Keyword(s):  
Wind Turbines ◽  
Degrees Of Freedom ◽  
Nonlinear Vibrations ◽  
Coupled System ◽  
Wind Pressure ◽  
Response Curves ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Frequency Responses ◽  
Time Histories

Vibration characteristics of three-blade wind turbines are investigated. The system is modeled by a coupled system of the flexible tower with two degrees of freedom and each blade with a single degree of freedom, and these blades are subjected to wind pressure which varies depending on the height from the ground. The vibrations of the three-blade wind turbines are theoretically analyzed to determine the natural frequency diagrams, frequency responses, stationary time histories and their FFT results. It is found that several peaks appear at the specific range of the rotational speed ω in the response curves because of both the wind pressure and the parametric excitation terms. In three-blade wind turbines, vibrations including predominant components of 3ω and its higher harmonics appear near these peaks. The response curves near the highest peak exhibit soft spring types due to the nonlinearities of the restoring moments of the blades. In the numerical simulations, “localization phenomena” in the blades, which vibrate at different amplitudes, are observed. The influence of an imperfection of the three blades is also examined.

Quasiperiodic galloping of a wind-excited tower near secondary resonances of order 2

2016 ◽  
Vol 23 (4) ◽  
pp. 574-586
Author(s):  
Ilham Kirrou ◽  
Lahcen Mokni ◽  
Mohamed Belhaq
Keyword(s):  
Harmonic Component ◽  
Multiple Scale ◽  
Degree Of Freedom ◽  
Quasiperiodic Solution ◽  
Single Degree Of Freedom ◽  
Superharmonic Resonance ◽  
Single Degree ◽  
Secondary Resonances ◽  
Analytical Expressions

Quasiperiodic galloping of a wind-excited tower under unsteady wind is investigated analytically near secondary (sub/superharmonic) resonances of order 2 considering a single degree-of-freedom model. The case where the unsteady wind develops multiharmonic excitations consisting of the two first harmonic terms is examined. We perform two successive multiple scale methods to obtain analytical expressions of a quasiperiodic solution and its modulation envelope near the secondary resonances. The influence of unsteady wind on the quasiperiodic galloping and on the frequency of its modulation is examined for different cases of wind excitation. The results show that the quasiperiodic galloping onset and its modulation envelope can be influenced, depending on the activated resonance and the harmonic component induced by the unsteady wind. It is also shown that the frequency of the quasiperiodic galloping is higher near the 2-superharmonic resonance in all cases of wind excitation.

scholarly journals Sliding-vibrating responses of elastic structures

1988 ◽  
Vol 21 (3) ◽  
pp. 190-197
Author(s):  
Yu-An Fu
Keyword(s):  
Rigid Body ◽  
Harmonic Excitation ◽  
Body Motion ◽  
Shake Table ◽  
Reciprocating Motion ◽  
Friction Forces ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Analytical Expressions ◽  
Vibrating Response

By using simulated friction forces, analytical expressions were derived from the sliding-vibrating response of a single degree of freedom system under harmonic excitation or the "disadvantageous period reciprocating motion", taking the mass of the sliding base into consideration. Some of the general laws were studied and some new characteristics determined which had previously been ignored by assuming rigid body motion. The analysis methods adopted in this paper have been confirmed in comparison with the results of model tests on a shake table.

A Simplified Analysis Method for Elasto-Plastic Seismic Response Using the Energy Balance Equation of a Maximum Hysteresis Loop

2015 ◽  
Author(s):  
Gaku Nakamura ◽  
Yukihiko Okuda ◽  
Shoichi Ebato ◽  
Hiroshi Niwa ◽  
Tadashi Iijima ◽  
...  
Keyword(s):  
Energy Balance ◽  
Seismic Response ◽  
Degree Of Freedom ◽  
Integration Scheme ◽  
Analysis Method ◽  
Maximum Displacement ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Simplified Analysis ◽  
Vibration Tests

With increasing magnitude of design earthquake ground motions, it is necessary to develop methods of evaluating the seismic safety margin that are more exact than the current methods. However, a standard nonlinear analysis method requires step by step calculations of the numerical time integration scheme to obtain the seismic response. The authors present a new simplified analysis method of elasto-plastic seismic response. The proposed method is formulated by the energy balance between the input energy and the dissipated energy of an equivalent single degree of freedom model for actual equipment. Assuming the harmonic resonance of the single degree of freedom model, the maximum displacement response can be estimated conservatively. To verify the proposed method, static tests and vibration tests with cantilever-type specimens were performed. The vibration tests were conducted with sine, sweep down sine and random waves to verify the conservativeness of the proposed method. Comparisons of the maximum displacement between the tests and the proposed method show the conservative estimation of the displacement by the proposed method.

scholarly journals A novel semi-empirical supervised model of vortex-induced vertical force on a flat closed-box bridge deck

2019 ◽  
Vol 15 (1) ◽  
pp. 155014771982684
Author(s):  
Xiaoxia Tian ◽  
Jingwen Yan
Keyword(s):  
Model Simulation ◽  
Correlation Coefficients ◽  
Coefficient Of Determination ◽  
Vertical Force ◽  
Validity And Reliability ◽  
Maximum Displacement ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Proposed Model ◽  
Semi Empirical

This study presents a novel single-degree-of-freedom model of vortex-induced vertical force, which is based on supervised learning. There are three steps in the process of modeling. First, a hypothesis function based on the Taylor expansion is applied to describe the complicated of vortex-induced vertical force. Second, this hypothesis function is optimized by spectrum and correlation analysis. The terms in this function are deleted when they meet one of the following cases: the frequency amplitudes are close to 0; the correlation coefficients with the vortex-induced vertical force are less than 0.3; the correlation coefficients with other low-order terms are more than 0.8. Third, the validity and reliability of the optimized function are verified by comparative and residual analysis. The process of optimization makes the proposed model simple and well describes the main characteristics of vortex-induced vertical forces. Moreover, the maximum displacement is accurately predicted according to the proposed model. Simulation results show that the proposed model has a high coefficient of determination ( R2) compared with Scanlan’s and Zhu’s models, which means that the proposed model is more suitable to describe vortex-induced vertical forces.

Computational Approaches to the Min-Max Response of Dynamic Systems With Incompletely Prescribed Input Functions

1967 ◽  
Vol 34 (1) ◽  
pp. 87-90 ◽  
Author(s):  
Eugene Sevin ◽  
Walter Pilkey
Keyword(s):  
Dynamic Systems ◽  
Initial Conditions ◽  
Restoring Force ◽  
Maximum Displacement ◽  
Single Degree Of Freedom ◽  
Load Duration ◽  
Analytical Technique ◽  
Single Degree ◽  
Forcing Function ◽  
Total Impulse

Linear, nonlinear, and dynamic programming formulations are developed for the solution of the min-max response of a single-degree-of-freedom dynamic system with incompletely prescribed input functions. The problem is: Given an oscillator whose equation of motion is mx¨ + g(x, x˙) = f(t), subject to stated initial conditions, and acted upon by a forcing function, f(t), which is nonnegative, and of specified finite duration and total impulse, find the particular forces which produce the least possible maximum displacement of the oscillator, and find this bounding value. Previously, Sevin developed an analytical technique for the solution which is inherently dependent upon a linear undamped form for the restoring force g(x, x˙). In the current work, an alternate statement of the problem is presented which lends itself to tractable computational formulations involving less stringent restrictions on g(x, x˙). Results obtained by dynamic and linear programming for specified forms of g(x, x˙) are given as functions of load duration.

scholarly journals The Response of Nonlinear Single-Degree-of-Freedom Systems to Modulated High-Frequency Input

2006 ◽  
Vol 61 (10-11) ◽  
pp. 541-555
Author(s):  
Atef F. El-Bassiouny
Keyword(s):  
Carrier Frequency ◽  
Phase Modulation ◽  
Evolution Equations ◽  
Multiple Scales ◽  
Degree Of Freedom ◽  
Response Curves ◽  
Single Degree Of Freedom ◽  
First Order ◽  
Single Degree ◽  
Jump Phenomena

In this paper we study the response of single-degree-of-freedom with cubic, quartic and quintic nonlinearities to an amplitude-modulated excitation whose carrier frequency is much higher than the natural frequency of the system. The only restriction on the amplitude modulation is that it contains frequencies much lower than the carrier frequency of the excitation. The method of multiple scales is used to derive two coupled first-order ordinary differential equations that describe the evolution of the amplitude and phase with damping, nonlinearities and resonances. The evolution equations are used to determine the steady-state motions, while representative frequency-response curves are presented for each resonance. Stability analysis of the amplitude and phase modulation equations for both cases are performed. The bending of the response curves leads to multi-valued solutions and hence to jump phenomena.

Dynamic Axisymmetric Buckling of Shallow Conical Shells Subjected to Impulsive Loads

1965 ◽  
Vol 32 (1) ◽  
pp. 129-134 ◽  
Author(s):  
R. E. Fulton
Keyword(s):  
Conical Shell ◽  
Strain Energy ◽  
Maximum Displacement ◽  
Spherical Cap ◽  
Single Degree Of Freedom ◽  
Conical Shells ◽  
Simply Supported ◽  
Single Degree ◽  
Impulsive Loads ◽  
Axisymmetric Buckling

A theoretical investigation is made of the axisymmetric snap-through buckling of a shallow conical shell subjected to an idealized impulse applied uniformly over the surface of the shell. The shell is assumed to behave as a single-degree-of-freedom system, and a study is made of the strain energy at maximum displacement: i.e., zero velocity. Under certain conditions this equilibrium position becomes unstable and the shell can snap through (or buckle). Nonlinear strain displacement equations are used and solutions are obtained for clamped and simply supported boundaries at the edge of the shell. Results for the cone are compared with similar results for a shallow spherical cap having the same rise as the cone. This comparison indicates that the spherical shell can resist a larger impulse than the conical shell before buckling.

Identification of Structural Parameters by Wavelet Transform of Acceleration Response

1999 ◽  
Author(s):  
Akira Sone ◽  
Ryutaro Segawa ◽  
Shizuo Yamamoto ◽  
Arata Masuda ◽  
Hiroaki Hata
Keyword(s):  
Wavelet Transform ◽  
Numerical Simulations ◽  
Structural Model ◽  
Structural Parameters ◽  
Degree Of Freedom ◽  
Acceleration Response ◽  
Single Degree Of Freedom ◽  
Displacement Response ◽  
Single Degree ◽  
Stiffness And Damping

Abstract The method to identify structural parameters of multi-degree of freedom structures by the wavelet transform of displacement response is previously proposed However, the vibration of structure is measured by the accelerometers. Therefore, if it is possible to identify structural parameters by the wavelet transform of only acceleration responses, it is very useful. In this paper, the method to identify structural parameters such as stiffness and damping by wavelet transform of acceleration responses is presented. To verify the applicability of the proposed method, numerical simulations using the single degree of freedom structure and the four-degree-of-freedom structure and the experiments using simple structural model are conducted. From both results, it has been clear that the proposed method can give the good estimation for the structural parameters.

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