The Proportional-Damping Matrix of Arbitrarily Damped Linear Mechanical Systems

2002 ◽  
Vol 69 (5) ◽  
pp. 649-656 ◽  
Author(s):  
J. Angeles ◽  
S. Ostrovskaya
Keyword(s):  
Stiffness Matrix ◽  
Mechanical Systems ◽  
Least Square ◽  
Simultaneous Diagonalization ◽  
Single Degree Of Freedom ◽  
Practical Applications ◽  
Single Degree ◽  
Damping Matrix ◽  
Damped System ◽  
Damped Systems

The vibration of linear mechanical systems with arbitrary damping is known to pose challenging problems to the analyst, for these systems cannot be analyzed with the techniques pertaining to their undamped counterparts. It is also known that a class of damped systems, called proportionally damped, can be analyzed with the same techniques, which mimic faithfully those of single-degree-of-freedom systems. For this reason, in many instances the system at hand is assumed to be proportionally damped. Nevertheless, this assumption is difficult to justify on physical grounds in many practical applications. What this assumption brings about is a damping matrix that admits a simultaneous diagonalization with the stiffness matrix. Proposed in this paper is a decomposition of the damping matrix of an arbitrarily damped system allowing the extraction of the proportionally damped component, which, moreover, approximates optimally the original damping matrix in the least-square sense. Finally, we show with examples that conclusions drawn from the proportionally damped approximation of an arbitrarily damped system can be dangerously misleading.

Diagonal Dominance and the Decoupling Approximation in Damped Discrete Linear Systems

2007 ◽  
Author(s):  
Matthias Morzfeld ◽  
Nopdanai Ajavakom ◽  
Fai Ma
Keyword(s):  
Diagonal Element ◽  
Diagonal Dominance ◽  
Damping Matrix ◽  
Damped System ◽  
Modal Damping ◽  
Principal Coordinates ◽  
Discrete Linear Systems ◽  
Modal Coupling ◽  
Decoupling Approximation ◽  
Damped Systems

The principal coordinates of a non-classically damped linear system are coupled by nonzero off-diagonal element of the modal damping matrix. In the analysis of non-classically damped systems, a common approximation is to ignore the off-diagonal elements of the modal damping matrix. This procedure is termed the decoupling approximation. It is widely accepted that if the modal damping matrix is diagonally dominant, then errors due to the decoupling approximation must be small. In addition, it is intuitively believed that the more diagonal the modal damping matrix, the less will be the errors in the decoupling approximation. Two quantitative measures are proposed in this paper to measure the degree of being diagonal dominant in modal damping matrices. It is demonstrated that, over a finite range, errors in the decoupling approximation can continuously increase while the modal damping matrix becomes more and more diagonal with its off-diagonal elements decreasing in magnitude continuously. An explanation for this unexpected behavior is presented. Within a practical range of engineering applications, diagonal dominance of the modal damping matrix may not be sufficient for neglecting modal coupling in a damped system.

An Analysis of Pulse Control for Simple Mechanical Systems

1985 ◽  
Vol 107 (2) ◽  
pp. 123-131 ◽  
Author(s):  
Z. Prucz ◽  
T. T. Soong ◽  
A. Reinhorn
Keyword(s):  
Control Algorithm ◽  
Control Method ◽  
Excitation Frequency ◽  
Mechanical Systems ◽  
System Response ◽  
Control Parameters ◽  
Pulse Control ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
On Line

An efficient pulse control method for insuring safety of simple mechanical systems is developed and its sensitivity to the excitation frequency content and to various control parameters is studied. The control algorithm, consisting of applying pulse forces in a feedback fashion, is designed to insure that maximum system response is limited to safe values at all times. It is shown that the proposed algorithm is simple to implement and is efficient in controlling peak response in terms of on-line computation and pulse energy required. The technique is illustrated and analyzed for a single-degree-of-freedom linear system.

An Efficient Method for Compensating Truncated Higher Modes in Structural Dynamics Modification

1986 ◽  
Vol 200 (1) ◽  
pp. 41-48 ◽  
Author(s):  
K R Chung ◽  
C W Lee
Keyword(s):  
Structural Dynamics ◽  
Efficient Method ◽  
Curve Fitting ◽  
Modal Parameters ◽  
Frequency Range ◽  
Single Degree Of Freedom ◽  
Higher Modes ◽  
Numerical Example ◽  
Single Degree ◽  
Damped Systems

An efficient method for compensating the effects of the truncated higher modes in structural dynamics modification (SDM) is developed to predict the accurate modal parameters of locally modified structures. The effects of the truncated higher modes are represented by a fictitious, effective mode residing beyond the frequency range of interest. The modal parameters are then easily obtained by the iterative single degree-of-freedom curve-fitting technique developed for lightly damped systems. A numerical example demonstrates the effectiveness of the improved SDM technique.

scholarly journals ALGORITMA SIMULASI NUMERIK GETARAN DIRRECT INLINE HARMONICAL CAM FOLLOWER PADA VALVE TRAIN MANIFOLD MOTOR DIESEL

2021 ◽  
Vol 2 ◽  
pp. 45-51
Author(s):  
Abdul Hadi ◽  
B G Tentua
Keyword(s):  
Random Process ◽  
Degree Of Freedom ◽  
Least Square ◽  
Valve Train ◽  
Single Degree Of Freedom ◽  
Ordinary Least Square ◽  
Single Degree ◽  
Level Data ◽  
Data Record ◽  
Cam Follower

Abstrak Penelitian ini dibuat untuk mengetahui getaran vertical direct inline dari suatu mekanisme ekivalen cam follower dengan profil cam harmonik pada suatu manifold -valve train motor diesel. Masalahnya dimulai dengan penentuan koefisien redaman viscous dan koefisien kekakuan pegas ekivalen sistem yang mana sulit ditentukan secara langsung. Oleh karena secara praktis dapat dipandang bahwa sinyal sistem adalah bersifat deterministick random process maka untuk mengatasi kesulitan ini dilakukan suatu analisa gabungan deduksi dan induksi yaitu dalam model estimasi ordinary least square (OLS) dan simulasi numerik Newton-Rhapson dengan mengacu pada data record hasil pengukuran eksperimental respon getaran yang ditunjukkan oleh sensor accelerometer. Sinyal getaran respon sistem dengan model mekanik single degree of freedom (1-dof) ini kenudian diolah baik dalam domain waktu atau domain frekuensi dengan menerapkanLaplace Transform dan Fast Furrior Transform (FFT). Hasilnya menunjukan bahwa komputasi numerik itu dapat dibuat untuk mengetahui harga-harga koefisien redaman viscous ekivalen,  koefisien kekakuan pegas ekivalen dan initial tensiom clearance ekivalen sedemikian hingga selanjutnya respon dinamik sinyal getaran sistem dapat diestimasi dengan menerapkan metode simulasi numerik Runge-Kutta order ke-empat. Algoritma hasil formulasinya dengan demikian dapat menjadi lebih general untuk menjawab berbagai persoalan amplitude getaran pada level data percepatan eksitasi ekivalen multi input multi output (MIMO) dalam berbagai variasi sistem cam-follower yang diberikan sebagaimana dimaksud. 

scholarly journals Vibration Control of Fractionally-Damped Beam Subjected to a Moving Vehicle and Attached to Fractionally-Damped Multiabsorbers

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Hashem S. Alkhaldi ◽  
Ibrahim M. Abu-Alshaikh ◽  
Anas N. Al-Rabadi
Keyword(s):  
Dynamic Response ◽  
Fractional Derivatives ◽  
Single Degree Of Freedom ◽  
Moving Vehicle ◽  
Single Degree ◽  
Damping Characteristics ◽  
The Laplace Transform ◽  
Fractional Differential ◽  
Damped Systems ◽  
Special Case

This paper presents the dynamic response of Bernoulli-Euler homogeneous isotropic fractionally-damped simply-supported beam. The beam is attached to multi single-degree-of-freedom (SDOF) fractionally-damped systems, and it is subjected to a vehicle moving with a constant velocity. The damping characteristics of the beam and SDOF systems are described in terms of fractional derivatives. Three coupled second-order fractional differential equations are produced and then they are solved by combining the Laplace transform with the decomposition method. The obtained numerical results show that the dynamic response decreases as (a) the number of absorbers attached to the beam increases and (b) the damping-ratios of used absorbers and beam increase. However, there are some critical values of fractional derivatives which are different from unity at which the beam has less dynamic response than that obtained for the full-order derivatives model. Furthermore, the obtained results show very good agreements with special case studies that were published in the literature.

Simplified seismic code design procedure for friction-damped steel frames

1999 ◽  
Vol 26 (1) ◽  
pp. 55-71 ◽  
Author(s):  
Yaomin Fu ◽  
Sheldon Cherry
Keyword(s):  
Design Procedure ◽  
Steel Structures ◽  
Lateral Force ◽  
Building Codes ◽  
Degree Of Freedom ◽  
Friction Damper ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Damped System ◽  
Seismic Force

This paper describes the development of a proposed seismic design procedure for friction-damped steel structures, which employs the lateral force provisions used in many modern building codes. Closed-form expressions are first derived that relate the normalized response of a single degree of freedom friction-damped system with the system parameters, such as bracing stiffness ratio, damper slip ratio, and frame member ductility. A parametric analysis is then used to reveal that the seismic displacement of a friction-damped frame can be controlled by combining the frame stiffness with the bracing stiffness of the friction damper component, while the seismic force can be controlled by the damper slip force. A force modification factor (equivalent to the code R-factor) and displacement estimate for a friction-damped system are next determined. The single degree of freedom results are subsequently used to develop expressions for dealing with the multi degree of freedom situation, which permits the seismic lateral force design procedure adopted by many current building codes to be applied to friction-damped systems. The proposed procedure allows the frame response to be controlled so that the displacement can be limited to small magnitudes and the overall structural shape to an essentially straight-line deformation. Design examples illustrate that friction-damped frame systems are economical and offer a better overall response performance than that provided by conventional systems under the design earthquake.Key words: passive energy dissipation system, friction damper, steel frame, design procedure, static analysis.

scholarly journals Size/Layout Optimization of Truss Structures Using Vibrating Particles System Meta-heuristic Algorithm and its Improved Version

2021 ◽  
Author(s):  
Ali Kaveh ◽  
Masoud Khosravian
Keyword(s):  
Free Vibration ◽  
Heuristic Algorithm ◽  
Optimization Problems ◽  
Truss Structures ◽  
Equilibrium Conditions ◽  
Single Degree Of Freedom ◽  
Search Spaces ◽  
Single Degree ◽  
New Process ◽  
Damped Systems

Vibrating Particles System (VPS) optimization is a newly made meta-heuristic algorithm to optimize problems by inspiration of the free vibration of viscous-damped systems with single degree of freedom. The agents are modeled as particles which systematically proceed toward their equilibrium conditions that are reached by the existing population and historically best position. To enhance the performance of the VPS algorithm, Enhanced Vibrating Particles System (EVPS) applies a new process for updating agent’s positions. This paper tries to improve the EVPS algorithm with the aim of reduction in the regulatory parameters’ effect on the algorithm's performance by reducing the regulatory parameters. To evaluate the performance of the proposed method, it is applied to four optimization problems of truss structures including mixed of discrete and continuous design search spaces with displacement, stress and buckling constraints. As a result, the proposed algorithm is a suitable method and more research can be done on it.

Four-Position Synthesis for Spatial Mechanisms With Two Independent Loops

1992 ◽  
Author(s):  
Chien H. Chiang ◽  
Wei Hua Chieng ◽  
David A. Hoeltzel
Keyword(s):  
Rigid Body ◽  
Mathematical Models ◽  
Analytical Methods ◽  
Degree Of Freedom ◽  
Single Degree Of Freedom ◽  
Practical Applications ◽  
Single Degree ◽  
Spatial Mechanisms ◽  
Position Synthesis ◽  
Independent Loops

Abstract Mathematical models that have been employed to synthesize spatial mechanisms for rigid body guidance have been found to be too complicated to implement in practical applications, especially for four-position guidance synthesis. This paper describes simple analytical methods for synthesizing single degree-of-freedom spatial mechanisms having two independent loops for four precision positions. In addition, prescribed timing has been simultaneously considered for several spatial mechanisms.

Single Degree of Freedom Forced Vibration System

2021 ◽  
pp. 41-79
Keyword(s):  
Forced Vibration ◽  
Influence Factor ◽  
Initial Conditions ◽  
Degree Of Freedom ◽  
Transient Solution ◽  
Vibration System ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Damped System ◽  
Arbitrary Loading

This chapter concerns the study of forced vibration of a single degree of freedom system, treating undamped and damped system under harmonic, periodic, and arbitrary loading with different cases and examples. Passing by all components of the general solution of an undamped forced system, which are a transient solution, depends only on initial conditions, transient solution due to the load at the end the stationary solution. In this chapter, a study of the dynamic influence factor depends on the ration between load frequency and structure one is presented.

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