Response of Beams and Plates to Random Loads

1957 ◽  
Vol 24 (1) ◽  
pp. 46-52
Author(s):  
A. C. Eringen
Keyword(s):  
Cross Correlation ◽  
External Pressure ◽  
Rectangular Plates ◽  
Circular Plates ◽  
Probable Number ◽  
Simply Supported ◽  
Random Loads ◽  
Stochastic Loading ◽  
Special Cases ◽  
The Cross

Abstract With the use of generalized harmonic analysis the problem of vibrating damped beams and plates under stochastic loading is solved. The resulting equations give the cross-correlation functions for displacements, stresses, moments, and so on, in terms of the cross-correlation function of external pressure. Mean square values of these functions are special cases of these results. Using a method due to Rice, we also calculate the probable number of times per unit time the random displacements or stresses will exceed a given value. The case of simply supported bars, cantilever bars, clamped circular plates, and simply supported rectangular plates are worked out in detail.

Maximum Stresses in Beams and Plates Vibrating at Resonance

1962 ◽  
Vol 84 (1) ◽  
pp. 149-155 ◽  
Author(s):  
Eric E. Ungar
Keyword(s):  
Simple Formula ◽  
Maximum Stress ◽  
Rectangular Plates ◽  
Circular Plates ◽  
Simply Supported ◽  
At Resonance ◽  
Design Calculations ◽  
Maximum Stresses

Expressions are derived which relate the maximum stresses encountered in simply supported beams and rectangular plates and in clamped circular plates vibrating at resonance to modal displacements and modal loadings. Computation of modal loadings from time-wise harmonic or random pressures is discussed. It is shown that the resonant maximum stress may be reasonably approximated by a simple formula suitable for conservative design calculations for all types of beams and plates.

Transition Mechanisms Attendant to Large Amplitude Parametric Vibrations of Rectangular Plates

1967 ◽  
Vol 89 (4) ◽  
pp. 619-625 ◽  
Author(s):  
J. H. Somerset
Keyword(s):  
Rectangular Plate ◽  
Large Amplitude ◽  
Strong Influence ◽  
Forced Vibrations ◽  
Rectangular Plates ◽  
Parametric Vibrations ◽  
Periodic Load ◽  
Simply Supported ◽  
Stochastic Loading ◽  
Parametric Oscillations

Experiments have been conducted to investigate the transition mechanisms attendant to the parametric vibrations of a simply supported rectangular plate subjected to a periodic load of the form P = P0 + P1 cos γt. It is found that the transition mechanisms, such as “jumps” within the zone and “dropout” from the zone, are influenced by the initial curvature of the plate and by interactions with the source of energy. Due to the possibility of transitions between the parametric oscillations and forced vibrations of the plate, “splitting” of the zone may occur. Preliminary experiments indicate that the transition mechanisms have a strong influence on the response of the plate to stochastic loading.

Exact Solution for Simply Supported and Multilayered Magneto-Electro-Elastic Plates

2001 ◽  
Vol 68 (4) ◽  
pp. 608-618 ◽  
Author(s):  
E. Pan
Keyword(s):  
Composite Structures ◽  
Three Dimensional ◽  
Layered Composite ◽  
Rectangular Plates ◽  
Elastic Plates ◽  
Homogeneous Solutions ◽  
Simply Supported ◽  
Special Cases ◽  
Multilayered Plates ◽  
Simple Formalism

Exact solutions are derived for three-dimensional, anisotropic, linearly magneto-electro-elastic, simply-supported, and multilayered rectangular plates under static loadings. While the homogeneous solutions are obtained in terms of a new and simple formalism that resemble the Stroh formalism, solutions for multilayered plates are expressed in terms of the propagator matrix. The present solutions include all the previous solutions, such as piezoelectric, piezomagnetic, purely elastic solutions, as special cases, and can therefore serve as benchmarks to check various thick plate theories and numerical methods used for the modeling of layered composite structures. Typical numerical examples are presented and discussed for layered piezoelectric/piezomagnetic plates under surface and internal loads.

Postbuckling Behavior of Unsymmetrically Layered Anisotropic Rectangular Plates

1974 ◽  
Vol 41 (1) ◽  
pp. 155-162 ◽  
Author(s):  
C. Y. Chia ◽  
M. K. Prabhakara
Keyword(s):  
Nonlinear Differential Equations ◽  
Fourier Method ◽  
Rectangular Plates ◽  
Postbuckling Behavior ◽  
Anisotropic Plates ◽  
Simply Supported ◽  
Aspect Ratios ◽  
Special Cases ◽  
Present Solution ◽  
Anisotropic Rectangular Plates

An analysis for the postbuckling behavior of unsymmetrically layered rectangular anisotropic plates is presented. Each layer is assumed to have arbitrary thickness, elastic properties, and orientation of orthotropic axes with respect to the plate axes. The governing nonlinear differential equations in the sense of von Karman are solved in conjunction with boundary conditions for clamped edges by use of the multiple Fourier method. In the case of simply supported edges, a solution based on the method is also obtained for unsymmetrical angle-ply plates. In the examples, a nine-term approximation to each series is used and load-deflection relations, bending moments, membrane forces are presented for clamped cross-ply and angle-ply and simply supported angle-ply plates with various aspect ratios. Numerical results obtained from the present solution are, in special cases, compared with available data.

scholarly journals Insights to enhance the examination of tool marks in human cartilage

2021 ◽  
Author(s):  
Matthias Weber ◽  
Anja Niehoff ◽  
Markus A. Rothschild
Keyword(s):  
Light Microscope ◽  
Cross Correlation ◽  
Costal Cartilage ◽  
Correlation Coefficients ◽  
Human Cartilage ◽  
Cut Marks ◽  
Tool Marks ◽  
The Cross ◽  
Cleaning Methods ◽  
The Individual

AbstractThis work deals with the examination of tool marks in human cartilage. We compared the effectiveness of several cleaning methods on cut marks in porcine cartilage. The method cleaning by multiple casts achieved the significantly highest scores (P = 0.02). Furthermore, we examined the grain-like elevations (dots) located on casts of cut cartilage. The results of this study suggest that the casting material forms these dots when penetrating cartilage cavities, which are areas where the strong collagen fibres leave space for the chondrocytes. We performed fixation experiments to avoid this, without success. In addition, 31 casting materials were compared regarding contrast under light-microscope and 3D tool marks scanner. Under the light-microscope, brown materials achieved significantly higher values than grey (P = 0.02) or black (P = 0.00) whereas under the 3D scanner, black materials reached higher contrast values than grey (P = 0.04) or brown (P = 0.047). To compare the accuracy and reproducibility of 6 test materials for cartilage, we used 10 knives to create cut marks that were subsequently scanned. During the alignment of the individual signals of each mark, the cross-correlation coefficients (Xmax) and lags (LXmax) were calculated. The signals of the marks in agarose were aligned with significantly fewer lags and achieved significantly higher cross-correlation coefficients compared to all tested materials (both P = 0.00). Moreover, we determined the cross-correlation coefficients (XC) for known-matches (KM) per material. Agarose achieved significantly higher values than AccuTrans®, Clear Ballistics™, and gelatine (all P = 0.00). The results of this work provide valuable insights for the forensic investigation of marks in human costal cartilage.

scholarly journals Detection and Localization for Multiple Stationary Human Targets Based on Cross-Correlation of Dual-Station SFCW Radars

2019 ◽  
Vol 11 (12) ◽  
pp. 1428 ◽  
Author(s):  
Yong Jia ◽  
Yong Guo ◽  
Chao Yan ◽  
Haoxuan Sheng ◽  
Guolong Cui ◽  
...  
Keyword(s):  
Cross Correlation ◽  
Continuous Wave ◽  
Coefficient Matrix ◽  
Constant False Alarm Rate ◽  
Localization Algorithm ◽  
Cfar Detection ◽  
Stepped Frequency ◽  
The Cross ◽  
The One ◽  
Detection And Localization

This paper demonstrates the feasibility of detection and localization of multiple stationary human targets based on cross-correlation of the dual-station stepped-frequency continuous-wave (SFCW) radars. Firstly, a cross-correlation operation is performed on the preprocessed pulse signals of two SFCW radars at different locations to obtain the correlation coefficient matrix. Then, the constant false alarm rate (CFAR) detection is applied to extract the ranges between each target and the two radars, respectively, from the correlation matrix. Finally, the locations of human targets is calculated with the triangulation localization algorithm. This cross-correlation operation mainly brings about two advantages. On the one hand, the cross-correlation explores the correlation feature of target respiratory signals, which can effectively detect all targets with different signal intensities, avoiding the missed detection of weak targets. On the other hand, the pairing of two ranges between each target and two radars is implemented simultaneously with the cross-correlation. Experimental results verify the effectiveness of this algorithm.

Sign in / Sign up

Export Citation Format

Share Document