A transfer matrix formulation of an electromechanical Helmholtz resonator

2005 ◽  
Vol 118 (3) ◽  
pp. 1944-1944 ◽  
Author(s):  
Fei Liu ◽  
Lou Cattafesta ◽  
Mark Sheplak ◽  
Stephen Horowitz ◽  
Toshi Nishida
Keyword(s):  
Transfer Matrix ◽  
Helmholtz Resonator ◽  
Matrix Formulation

Dynamic Simulation of Compressor Station Operation Including Centrifugal Compressor and Gas Turbine

1991 ◽  
Vol 113 (2) ◽  
pp. 300-311 ◽  
Author(s):  
K. K. Botros ◽  
P. J. Campbell ◽  
D. B. Mah
Keyword(s):  
Dynamic Simulation ◽  
Transfer Matrix ◽  
Numerical Technique ◽  
Nonlinear Partial Differential Equations ◽  
Field Measurements ◽  
Compressor Station ◽  
Algebraic Equations ◽  
Gas Dynamics Equations ◽  
Matrix Formulation ◽  
Simulation Results

Dynamic simulation of the operation of a compressor station requires mathematical modeling of the dynamic behavior of the compressor unit and various piping elements. Such models consist of large systems of nonlinear partial differential equations describing the pipe flow together with nonlinear algebraic equations describing the quasi-steady flow through various valves, constrictions, and compressors. In addition, the models also include mathematical descriptions of the control system, which consists of mixed algebraic and ordinary differential (mad) equations with some inequalities representing controllers’ limits. In this paper a numerical technique for the solution of the gas dynamics equations is described, based on the transfer matrix formulation relating the state vector time difference at one side of an element to that on the other side. This approach facilitates incorporation of all element transfer matrices into an overall transfer matrix according to the system geometric connectivity. The paper also presents simulation results and comparison with actual field measurements of three case histories: (1) simulation of a compressor surge protection control process; (2) unit startup; and (3) slow transient of a compressor station responding to changes in the discharge pressure set point. Good agreement between simulation results and field measurements is demonstrated.

Wave Localization in Multi-Coupled Periodic Structures: Application to Truss Beams

1996 ◽  
Vol 49 (2) ◽  
pp. 65-86 ◽  
Author(s):  
Christophe Pierre ◽  
Matthew P. Castanier ◽  
Wan Joe Chen
Keyword(s):  
Lyapunov Exponents ◽  
Transfer Matrix ◽  
Periodic Structures ◽  
Wave Localization ◽  
Matrix Formulation ◽  
Wave Type ◽  
Recent Developments ◽  
Propagation Of Waves ◽  
Dynamics Problems ◽  
Localized Waves

A tutorial and a review of recent developments in the area of localization in linear structural dynamics problems are presented. Particular emphasis is placed on multi-coupled nearly periodic structures, which carry more than one wave type. First, background on perfectly periodic structures is provided, including both the wave and modal descriptions of the dynamics. A wave transfer matrix formulation for disordered periodic structures is then presented, which is well suited to the analysis of localized dynamics. Next, stochastic analysis tools are introduced that allow one to quantify the degree of localization in an asymptotic sense. Means of calculating these localization factors as the Lyapunov exponents of the system wave transfer matrix are discussed. Finally, the general theory is illustrated on an example multi-coupled structure - a planar truss beam which carries four pairs of waves. The propagation of waves in the disordered structure is examined, and Lyapunov exponents are calculated. In addition to the localization of the incident wave, significant mixing of the various wave types occurs, causing the leakage of energy to the least localized waves, and enabling sustainment of motion according to the smallest Lyapunov exponent.

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