scholarly journals Modal Analysis of Pseudo-Schell Model Sources

Photonics ◽  
2021 ◽  
Vol 8 (10) ◽  
pp. 449
Author(s):  
Massimo Santarsiero ◽  
Rosario Martínez-Herrero ◽  
Gemma Piquero ◽  
Juan Carlos González de Sande ◽  
Franco Gori
Keyword(s):  
Modal Analysis ◽  
Closed Form ◽  
Exponential Function ◽  
Intensity Distribution ◽  
Radial Coordinate ◽  
Mode Amplitude ◽  
Peculiar Property ◽  
Near Zone

All pseudo-Schell model sources have been shown to possess the same continuous set of circularly symmetric modes, all of them presenting a conical wavefront. For keeping energy at a finite level, the mode amplitude along the radial coordinate is modulated by a decreasing exponential function. A peculiar property of such modes is that they exist in the Laplace transform’s realm. After a brief discussion of the near-zone, we pass to the far-zone, where the field can be evaluated in closed form. The corresponding features of the intensity distribution 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.

Modal Analysis of Multi-Stepped Distributed-Parameter Rotor-Bearing Systems Using Exact Dynamic Elements

2001 ◽  
Vol 123 (3) ◽  
pp. 401-403 ◽  
Author(s):  
Seong-Wook Hong ◽  
Jong-Heuck Park
Keyword(s):  
Modal Analysis ◽  
Closed Form ◽  
Complete Analysis ◽  
Distributed Parameter ◽  
Analysis Method ◽  
Closed Form Solutions ◽  
Analysis Scheme ◽  
Rotor Bearing ◽  
The Matrix ◽  
Transcendental Functions

Although the exact dynamic elements have been suggested by the authors [1] and proved to be useful for the dynamic analysis of distributed-parameter rotor-bearing systems, difficulty remains in computation because of the presence of transcendental functions in the matrix. This paper proposes a complete analysis scheme for the exact dynamic elements, a generalized modal analysis method, to obtain exact and closed form solutions of time and frequency domain responses for multi-stepped distributed-parameter rotor-bearing systems. A numerical example is provided for validating the proposed method.

Explicit formulae for stationary distributions of stress release processes

2000 ◽  
Vol 37 (2) ◽  
pp. 315-321 ◽  
Author(s):  
K. Borovkov ◽  
D. Vere-Jones
Keyword(s):  
Closed Form ◽  
Stationary Distribution ◽  
Exponential Function ◽  
Markov Models ◽  
Risk Process ◽  
Stress Release ◽  
Stationary Distributions ◽  
Explicit Formulae ◽  
Tectonic Forces ◽  
Release Processes

Stress release processes are special Markov models attempting to describe the behaviour of stress and occurrence of earthquakes in seismic zones. The stress is built up linearly by tectonic forces and released spontaneously when earthquakes occur. Assuming that the risk is an exponential function of the stress, we derive closed form expressions for the stationary distribution of such processes, the moments of the risk, and the autocovariance function of the reciprocal risk process.

Modal Analysis for the Active Multi-Layer Beams by Using Spectrally Formulated Exact Eigenfunctions

1999 ◽  
Author(s):  
Usik Lee ◽  
Joohong Kim
Keyword(s):  
Modal Analysis ◽  
Closed Form ◽  
Dynamic Characteristics ◽  
Equations Of Motion ◽  
Hamilton’S Principle ◽  
Analysis Method ◽  
Hamilton's Principle ◽  
Numerical Examples ◽  
Coupled Equations ◽  
Fully Coupled

Abstract In this paper, a modal analysis method (MAM) is introduced for the active multi-layer laminate beams. Two types of active multi-layer laminate beams are considered: the elastic-viscoelastic-piezoelectric three-layer beams and the elastic-piezoelectric two-layer beams. The dynamics of the multi-layer laminate beams are represented by a set of fully coupled equations of motion, derived by using Hamilton’s principle. The exact eigenfunctions are spectrally formulated and the orthogonality of eigenfunctions is derived in a closed form. The present MAM is evaluated through some numerical examples. It is shown that the dynamic characteristics obtained by the present MAM certainly converge to the exact ones obtained by SEM as the number of eigenfunctions superposed in MAM is increased. The modal analysis results are also compared with the results obtained by FEM.

Closed-Form Transient Response of Distributed Damped Systems, Part I: Modal Analysis and Green’s Function Formula

1996 ◽  
Vol 63 (4) ◽  
pp. 997-1003 ◽  
Author(s):  
Bingen Yang
Keyword(s):  
Green’S Function ◽  
Modal Analysis ◽  
Closed Form ◽  
Distributed System ◽  
Transient Response ◽  
Green's Function ◽  
Eigenfunction Expansion ◽  
Distributed Parameter ◽  
Modal Expansion ◽  
Damped Systems

An analytical method is developed for closed-form estimation of the transient response of complex distributed parameter systems that are nonproportionally damped, and subject to arbitrary external, initial, and boundary excitations. A new modal analysis leads to the Green’s function formula for the distributed system and an eigenfunction expansion of the system Green’s function. The legitimacy of the modal expansion is also shown.

scholarly journals NDF of the near-field of a strip source in orthogonal directions

2020 ◽  
Author(s):  
Rocco Pierri ◽  
Raffaele Moretta
Keyword(s):  
Inverse Problems ◽  
Closed Form ◽  
Degrees Of Freedom ◽  
Near Field ◽  
Closed Form Expression ◽  
Main Difficulty ◽  
Form Expression ◽  
Independent Functions ◽  
Near Zone

<div><div>In the manuscript, we address the problem of evaluating the</div><div>number of degrees of freedom (NDF) of the field radiated by a strip source along all the directions orthogonal to it. </div><div>The NDF represents at the same time the number of independent functions required to represent the data with a given degree of accuracy, and the dimension of the unknowns subspace that can be stably reconstructed. For such reason, the knowledge of the NDF gives insight on the forward and on the inverse problems and it represents one of the metrics to evaluate the achievable performance in the inversion.</div></div><div>The main difficulty arises since in near-zone the eigenvalue</div><div>problem that must be solved for the computation of the NDF,</div><div>involves a non-convolution and non-bandlimited kernel. In the paper, we show how to overcome this drawback and how to obtain a closed-form expression of the NDF which highlights the role played by the configuration parameters.</div>

scholarly journals Coordinate-free exponentials of general multivector in Cl(p,q) algebras for p+q=3

2021 ◽  
Author(s):  
Arturas Acus ◽  
Adolfas Dargys
Keyword(s):  
Signal Processing ◽  
Differential Equations ◽  
Automatic Control ◽  
Closed Form ◽  
Exponential Function ◽  
Free Form ◽  
Hyperbolic Function ◽  
Main Difficulty ◽  
Geometric Algebras ◽  
And Robotics

Closed form expressions in real Clifford geometric algebras Cl(0,3), Cl(3,0), Cl(1,2), and Cl(2,1) are presented in a coordinate-free form for exponential function when the exponent is a general multivector. The main difficulty in solving the problem is connected with an entanglement (or mixing) of vector and bivector components a and a in a form (a-a), i≠ j≠ k . After disentanglement, the obtained formulas simplify to the well-known Moivre-type trigonometric/hyperbolic function for vector or bivector exponentials. The presented formulas may find wide application in solving GA differential equations, in signal processing, automatic control and robotics.

scholarly journals Extension of generalized integro-exponential function and its application in study of Chen distribution

2017 ◽  
Vol 11 (2) ◽  
pp. 434-450 ◽  
Author(s):  
Tibor Pogány ◽  
Gauss Cordeiro ◽  
Muhammad Tahir ◽  
Hari Srivastava
Keyword(s):  
Power Series ◽  
Closed Form ◽  
Series Expansion ◽  
Exponential Function ◽  
Generating Functions ◽  
Power Series Expansion ◽  
Quantile Function ◽  
Mathematical Properties ◽  
Lifetime Model ◽  
Two Parameter

In 2000 Chen introduced a two-parameter lifetime model and has reported only a few mathematical properties moments, quantile and generating functions, among others. In this article, we derive a power series expansion for newly introduced real upper parameter generalized integro-exponential function Eps(z) extending certain Milgram's findings. By our novel results we derive closed-form expressions for the moments, generating function, R?nyi entropy and power series for the quantile function of the Chen distribution.

Analytical modal analysis of thin-film flat lenses

2005 ◽  
Vol 219 (1) ◽  
pp. 55-59 ◽  
Author(s):  
H R Hamidzadeh ◽  
L Moxey
Keyword(s):  
Thin Film ◽  
Analytical Solution ◽  
Dynamic Response ◽  
Modal Analysis ◽  
Closed Form ◽  
Material Properties ◽  
Mathieu Equation ◽  
Free Vibrations ◽  
Mode Shapes ◽  
Closed Form Solutions

The free vibrations of circular and elliptical thin-film lens are investigated. In particular, linear closed-form solutions for free vibrations of these structures were achieved and modal analysis was performed. The vibration response of the thin-film membranes were mathematically modelled using the Mathieu equation. Numerical results for various nodal diameters were computed. For the limited case, when an elliptical lens becomes circular, an excellent comparison was established with the available analytical solution. Experimental analyses were conducted to determine the effects of various parameters, such as material properties, membrane pre-strain rate, and the geometry, on natural frequency and mode shapes of these structures. The comparison verified the adequacy of linear solutions to predict the dynamic response of thin-film lenses.

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