Random Response Analysis of Vibration Transfer Path Systems with Translational and Rotational Motions

2013 ◽  
Vol 423-426 ◽  
pp. 1543-1547
Author(s):  
Wei Zhao ◽  
Na Zhou ◽  
Yi Min Zhang
Keyword(s):  
Random Vibration ◽  
Response Analysis ◽  
Random Response ◽  
First Order ◽  
Transfer Path ◽  
Mathematical Expressions ◽  
Path System ◽  
Rotational Motions ◽  
Vector Valued Functions ◽  
Vector Valued

This paper based on the generalized probabilistic perturbation finite element method solves the random response analysis problem of vibration transfer path systems with translational and rotational motions. The effective random response analysis approaches are achieved using Kronecker algebra, matrix calculus, generalized second moment technique of vector-valued functions and matrix-valued functions. For the vibration transfer path system with multi-dimensional paths, the random response is described correctly and expressly in time domain as uncertain factors, which include mass, damping, stiffness and position, are considered. The mathematical expressions of the first order and second order moments for the random vibration response of vibration transfer path are obtained. According to the corresponding numerical example, the results of calculation are consistent with the results of Monte-Carlo simulation, which shows the method is feasible theoretically.

scholarly journals Reliability Analysis of Random Vibration Transmission Path Systems

2017 ◽  
Vol 2017 ◽  
pp. 1-6 ◽  
Author(s):  
Wei Zhao ◽  
Yi-Min Zhang
Keyword(s):  
Random Vibration ◽  
Vibration Source ◽  
Vibration Transmission ◽  
Transmission Path ◽  
Transfer Path ◽  
Practical Project ◽  
Mathematical Expressions ◽  
The Matrix ◽  
Path System ◽  
Element Theory

The vibration transmission path systems are generally composed of the vibration source, the vibration transfer path, and the vibration receiving structure. The transfer path is the medium of the vibration transmission. Moreover, the randomness of transfer path influences the transfer reliability greatly. In this paper, based on the matrix calculus, the generalized second moment technique, and the stochastic finite element theory, the effective approach for the transfer reliability of vibration transfer path systems was provided. The transfer reliability of vibration transfer path system with uncertain path parameters including path mass and path stiffness was analyzed theoretically and computed numerically, and the correlated mathematical expressions were derived. Thus, it provides the theoretical foundation for the dynamic design of vibration systems in practical project, so that most random path parameters can be considered to solve the random problems for vibration transfer path systems, which can avoid the system resonance failure.

Nonselfadjoint Schrödinger operators with singular first-order coefficients

1984 ◽  
Vol 96 (3-4) ◽  
pp. 323-329 ◽  
Author(s):  
Tosio Kato
Keyword(s):  
Schrödinger Operators ◽  
Schrodinger Operators ◽  
Real Vector ◽  
First Order ◽  
Vector Valued Functions ◽  
Complex Valued ◽  
Vector Valued

SynopsisSchrödinger operators of the form T = (i grad + b(x))2 + a(x) · grad + q(x) in Rm are considered, where a, b ate real vector-valued functions and q is a scalar complex-valued function. It is shown that T is essentially quasi-m-accretive in L2(Rm) if (1 + #x2223;∣)−1a ∈ L4 + L∞, div a ∈ L∞, , and Re q ≧ 0. The proof is elementary.

Random Response of Thick Laminated Rectangular Plates

1991 ◽  
Vol 113 (3) ◽  
pp. 286-291 ◽  
Author(s):  
R. S. Srinivasan ◽  
P. A. Krishnan
Keyword(s):  
Plate Theory ◽  
Order Theory ◽  
Response Analysis ◽  
Refined Theory ◽  
Rectangular Plates ◽  
Random Response ◽  
Refined Plate Theory ◽  
First Order ◽  
White Noise Excitation ◽  
First Order Theory

The present paper deals with the random response analysis of clamped thick laminated rectangular plates subjected to white noise excitation. The refined plate theory postulated by Reddy has been used. The analysis has been done using an integral equation technique. The random response results obtained for istropic square plates based on different plate theories (viz.) classical theory, first order theory and refined theory, have been compared. A parametric study has been conducted for angle ply and cross ply plates by varying the lay up of layers and a/h ratios.

Random Response Analysis of a Large-Size Cooling Tower Subjected to the Stationary Earthquake Motion

2013 ◽  
Vol 423-426 ◽  
pp. 1589-1593
Author(s):  
Jia Ning Zhu ◽  
Ya Zhou Xu ◽  
Guo Liang Bai ◽  
Rui Wen Li
Keyword(s):  
Power Spectrum ◽  
Random Vibration ◽  
Cooling Tower ◽  
Response Spectrum ◽  
Power Spectrum Density ◽  
Random Response ◽  
Large Size ◽  
Earthquake Motion ◽  
Spectrum Density ◽  
Random Vibration Theory

The response of a large-size cooling tower with 250m high subjected to the seismic action are investigated by both random vibration theory and response spectrum method. Shell element is taken to model the tower body, and beam element is used for the circular foundation and supporting columns. The earthquake motion input is a colored filtered white noise model and mode superposition method is adopted to analyze the random response of the large-size cooling tower. The paper presents the power spectrum density functions (PDF) and standard deviation of the displacement of the top and characteristic node, and the analysis results indicate that the results of the stationary random vibration theory and the response spectrum method are the same order of magnitude. The power spectrum density function of the bottom node stress is obviously bigger than the one at the top and the throat, and the random response of meridonal stress is dominated at the top. In addition, the peak frequency position of the power spectrum density function is different from the corresponding stress.

scholarly journals Farkas-Type Results for Vector-Valued Functions with Applications

2017 ◽  
Vol 173 (2) ◽  
pp. 357-390 ◽  
Author(s):  
N. Dinh ◽  
M. A. Goberna ◽  
M. A. López ◽  
T. H. Mo
Keyword(s):  
Vector Valued Functions ◽  
Vector Valued

scholarly journals Diameter-preserving linear bijections of function spaces

2001 ◽  
Vol 70 (3) ◽  
pp. 323-336 ◽  
Author(s):  
T. S. S. R. K. Rao ◽  
A. K. Roy
Keyword(s):  
Maximal Ideal ◽  
Convex Set ◽  
Compact Convex ◽  
Extreme Points ◽  
Continuous Functions ◽  
Ideal Space ◽  
Function Algebras ◽  
Compact Convex Set ◽  
Vector Valued Functions ◽  
Vector Valued

AbstractIn this paper we give a complete description of diameter-preserving linear bijections on the space of affine continuous functions on a compact convex set whose extreme points are split faces. We also give a description of such maps on function algebras considered on their maximal ideal space. We formulate and prove similar results for spaces of vector-valued functions.

scholarly journals THE LOCAL NON-HOMOGENEOUS Tb THEOREM FOR VECTOR-VALUED FUNCTIONS

2014 ◽  
Vol 57 (1) ◽  
pp. 17-82 ◽  
Author(s):  
TUOMAS P. HYTÖNEN ◽  
ANTTI V. VÄHÄKANGAS
Keyword(s):  
Singular Integrals ◽  
Local Version ◽  
Square Functions ◽  
Property A ◽  
Martingale Differences ◽  
Umd Spaces ◽  
Function Lattice ◽  
Vector Valued Functions ◽  
Vector Valued ◽  
Similar Extension

AbstractWe extend the local non-homogeneous Tb theorem of Nazarov, Treil and Volberg to the setting of singular integrals with operator-valued kernel that act on vector-valued functions. Here, ‘vector-valued’ means ‘taking values in a function lattice with the UMD (unconditional martingale differences) property’. A similar extension (but for general UMD spaces rather than UMD lattices) of Nazarov-Treil-Volberg's global non-homogeneous Tb theorem was achieved earlier by the first author, and it has found applications in the work of Mayboroda and Volberg on square-functions and rectifiability. Our local version requires several elaborations of the previous techniques, and raises new questions about the limits of the vector-valued theory.

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