A Complex Modal Analysis Method for Damped Vibration Systems (The Representation in the Second Order Differential Form of a Modal Equation and its Use for Practical Application)

1985 ◽  
Vol 107 (1) ◽  
pp. 13-18
Author(s):  
Y. Inoue ◽  
T. Fujikawa
Keyword(s):  
Modal Analysis ◽  
Damping Ratio ◽  
Second Order ◽  
Response Analysis ◽  
Modal Damping Ratio ◽  
Vibration Problems ◽  
Modal Mass ◽  
Modal Equation ◽  
Damped Vibration Systems ◽  
Complex Modal

Second order uncoupled differential equations for the general damped vibration systems are derived theoretically. The equations are written in a form similar to the classical real modal equations by using the natural frequency, the modal damping ratio, and the newly defined complex modal mass. Introducing supplementary variables, the response analysis is carried out in a similar manner to the real modal analysis. By comparing these equations to the classical ones, physical meanings of the derived equations are clarified. For the vibration problems near the resonant point, approximate complex modal equations are derived which have almost the same form as the classical one. Some applications of the proposed method to vibration problems are discussed.

Complex Modal Analysis of Non-Self-Adjoint Hybrid Serpentine Belt Drive Systems

2000 ◽  
Vol 123 (2) ◽  
pp. 150-156 ◽  
Author(s):  
Lixin Zhang ◽  
Jean W. Zu ◽  
Zhichao Hou
Keyword(s):  
Modal Analysis ◽  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
Mode Shapes ◽  
Belt Drive ◽  
Serpentine Belt ◽  
Complex Modal Analysis ◽  
Drive Systems ◽  
Complex Modal

A linear damped hybrid (continuous/discrete components) model is developed in this paper to characterize the dynamic behavior of serpentine belt drive systems. Both internal material damping and external tensioner arm damping are considered. The complex modal analysis method is developed to perform dynamic analysis of linear non-self-adjoint hybrid serpentine belt-drive systems. The adjoint eigenfunctions are acquired in terms of the mode shapes of an auxiliary hybrid system. The closed-form characteristic equation of eigenvalues and the exact closed-form solution for dynamic response of the non-self-adjoint hybrid model are obtained. Numerical simulations are performed to demonstrate the method of analysis. It is shown that there exists an optimum damping value for each vibration mode at which vibration decays the fastest.

Towards a Technique for Nonlinear Modal Analysis

2012 ◽  
Author(s):  
Simon A. Neild ◽  
Andrea Cammarano ◽  
David J. Wagg
Keyword(s):  
Normal Form ◽  
Modal Analysis ◽  
Equations Of Motion ◽  
Transformation Process ◽  
Second Order ◽  
Identity Transformation ◽  
Modal Testing ◽  
System Response ◽  
Weakly Nonlinear ◽  
Nonlinear Modal Analysis

In this paper we discuss a theoretical technique for decomposing multi-degree-of-freedom weakly nonlinear systems into a simpler form — an approach which has parallels with the well know method for linear modal analysis. The key outcome is that the system resonances, both linear and nonlinear are revealed by the transformation process. For each resonance, parameters can be obtained which characterise the backbone curves, and higher harmonic components of the response. The underlying mathematical technique is based on a near identity normal form transformation. This is an established technique for analysing weakly nonlinear vibrating systems, but in this approach we use a variation of the method for systems of equations written in second-order form. This is a much more natural approach for structural dynamics where the governing equations of motion are written in this form as standard practice. In fact the first step in the method is to carry out a linear modal transformation using linear modes as would typically done for a linear system. The near identity transform is then applied as a second step in the process and one which identifies the nonlinear resonances in the system being considered. For an example system with cubic nonlinearities, we show how the resulting transformed equations can be used to obtain a time independent representation of the system response. We will discuss how the analysis can be carried out with applied forcing, and how the approximations about response frequencies, made during the near-identity transformation, affect the accuracy of the technique. In fact we show that the second-order normal form approach can actually improve the predictions of sub- and super-harmonic responses. Finally we comment on how this theoretical technique could be used as part of a modal testing approach in future work.

Preliminary microzonation of the Memphis, Tennessee, area

1982 ◽  
Vol 72 (3) ◽  
pp. 1011-1024
Author(s):  
Sunil Sharma ◽  
William D. Kovacs
Keyword(s):  
United States ◽  
Soil Properties ◽  
Damping Ratio ◽  
Ground Surface ◽  
Strong Motion ◽  
Response Analysis ◽  
Borehole Data ◽  
Central United States ◽  
Hazardous Zone ◽  
High Level

abstract The city of Memphis, which is situated very close to the inferred epicenter of one of the three major 1811 to 1812 earthquakes, is in a potentially hazardous zone which will be susceptible to the usual seismic hazards. By recognizing the high level of seismicity in the New Madrid area, this study attempts to microzone the potential hazards by considering the following subjects: (i) the seismicity of the central United States; (ii) design earthquakes; and (iii) response analysis which allows construction of the necessary microzonation maps. The seismicity of the region is evaluated from state-of-the-art literature as there is no recorded strong-motion data available for the central United States. Synthetically generated accelerograms, simulating the design earthquakes, were used to represent the ground motions which were applied at a depth of 45 m, below ground surface, at numerous sites in Memphis. The soil stratigraphy was conceptualized from borehole data, made available by local sources, and dynamic soil properties estimated from available empirical correlations. The results of the response analysis were transformed into microzonation maps depicting: (i) zones showing qualitative estimates of ground response; (ii) zones showing the natural frequency of the soils; (iii) zones showing the peak spectral acceleration for 2 per cent damping ratio; and (iv) zones of liquefaction potential. These maps are useful for preliminary design and are not intended to be used on a quantitative basis. Further investigation is necessary in determining the stratigraphy and soil properties for a site-specific design and analysis.

High Frequency Analysis of a Dynamically Coupled Parallel Plate System

2017 ◽  
Author(s):  
Dean R. Culver ◽  
Earl Dowell
Keyword(s):  
Modal Analysis ◽  
Frequency Analysis ◽  
High Frequency ◽  
Parallel Plate ◽  
Damping Ratio ◽  
Parallel Plates ◽  
Linear Spring ◽  
Stiffness And Damping ◽  
Plate System

The behavior of a system comprised of two parallel plates coupled by a discrete, linear spring and damper is studied. Classical Modal Analysis (CMA) is used to illustrate this behavior, while specifically observing the effects of varying the stiffness and damping ratio of the coupling elements. Conditions under which the coupling may be approximated as rigid are identified. Additionally, conditions under which the coupling displacement reaches its maximum and minimum values are identified. This work also lays the groundwork for extending Asymptotic Modal Analysis (AMA) to systems with discrete, elastic, and dissipative coupling.

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