( 26 ) On the theorem of Riemann-Roch for adjoint systems on Kiihlerian varieties

Author(s):  
Kunihiko Kodaira
Keyword(s):  
AIAA Journal ◽  
1999 ◽  
Vol 37 ◽  
pp. 933-938
Author(s):  
H. W. Song ◽  
L. F. Chen ◽  
W. L. Wang

Author(s):  
Timothy W. Dimond ◽  
Amir A. Younan ◽  
Paul Allaire

Experimental identification of rotordynamic systems presents unique challenges. Gyroscopics, generally damped systems, and non-self-adjoint systems due to fluid structure interaction forces mean that symmetry cannot be used to reduce the number of parameters to be identified. Rotordynamic system experimental measurements are often noisy, which complicates comparisons with theory. When linearized, the resulting dynamic coefficients are also often a function of excitation frequency, as distinct from operating speed. In this paper, a frequency domain system identification technique is presented that addresses these issues for rigid-rotor test rigs. The method employs power spectral density functions and forward and backward whirl orbits to obtain the excitation frequency dependent effective stiffness and damping. The method is highly suited for use with experiments that employ active magnetic exciters that can perturb the rotor in the forward and backward whirl directions. Simulation examples are provided for excitation-frequency reduced tilting pad bearing dynamic coefficients. In the simulations, 20 and 50 percent Gaussian output noise was considered. Based on ensemble averages of the coefficient estimates, the 95 percent confidence intervals due to noise effects were within 1.2% of the identified value. The method is suitable for identification of linear dynamic coefficients for rotordynamic system components referenced to shaft motion. The method can be used to reduce the effect of noise on measurement uncertainty. The statistical framework can also be used to make decisions about experimental run times and acceptable levels of measurement uncertainty. The data obtained from such an experimental design can be used to verify component models and give rotordynamicists greater confidence in the design of turbomachinery.


AIAA Journal ◽  
1966 ◽  
Vol 4 (12) ◽  
pp. 2221-2222 ◽  
Author(s):  
S. NEMAT-NASSER ◽  
G. HERRMANN

2005 ◽  
Vol 2 (3) ◽  
pp. 527-534 ◽  
Author(s):  
Krzysztof Fujarewicz ◽  
◽  
Marek Kimmel ◽  
Andrzej Swierniak ◽  

Author(s):  
Chin An Tan ◽  
Heather L. Lai

Extensive research has been conducted on vibration energy harvesting utilizing a distributed piezoelectric beam structure. A fundamental issue in the design of these harvesters is the understanding of the response of the beam to arbitrary external excitations (boundary excitations in most models). The modal analysis method has been the primary tool for evaluating the system response. However, a change in the model boundary conditions requires a reevaluation of the eigenfunctions in the series and information of higher-order dynamics may be lost in the truncation. In this paper, a frequency domain modeling approach based in the system transfer functions is proposed. The transfer function of a distributed parameter system contains all of the information required to predict the system spectrum, the system response under any initial and external disturbances, and the stability of the system response. The methodology proposed in this paper is valid for both self-adjoint and non-self-adjoint systems, and is useful for numerical computer coding and energy harvester design investigations. Examples will be discussed to demonstrate the effectiveness of this approach for designs of vibration energy harvesters.


Author(s):  
Radu Serban ◽  
Antonio Recuero

We present an adjoint sensitivity method for hybrid discrete—continuous systems, extending previously published forward sensitivity methods (FSA). We treat ordinary differential equations (ODEs) and differential-algebraic equations (DAEs) of index up to two (Hessenberg) and provide sufficient solvability conditions for consistent initialization and state transfer at mode switching points, for both the sensitivity and adjoint systems. Furthermore, we extend the analysis to so-called hybrid systems with memory where the dynamics of any given mode depend explicitly on the states at the last mode transition point. We present and discuss several numerical examples, including a computational mechanics problem based on the so-called exponential model (EM) constitutive material law for steel reinforcement under cyclic loading.


2016 ◽  
Vol 60 (3) ◽  
pp. 615-633 ◽  
Author(s):  
Sonja Currie ◽  
Thomas T. Roth ◽  
Bruce A. Watson

AbstractA self-adjoint first-order system with Hermitian π-periodic potential Q(z), integrable on compact sets, is considered. It is shown that all zeros of are double zeros if and only if this self-adjoint system is unitarily equivalent to one in which Q(z) is π/2-periodic. Furthermore, the zeros of are all double zeros if and only if the associated self-adjoint system is unitarily equivalent to one in which Q(z) = σ2Q(z)σ2. Here, Δ denotes the discriminant of the system and σ0, σ2 are Pauli matrices. Finally, it is shown that all instability intervals vanish if and only if Q = rσ0 + qσ2, for some real-valued π-periodic functions r and q integrable on compact sets.


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