History and use of panels or other rigid supports for easel paintings

2020 ◽  
pp. 49-116
Author(s):  
Noëlle Streeton
Keyword(s):  
Rigid Supports

Limit-Cycle Analysis of Three-Dimensional Flexible Shaft/Rigid Rotor/Autobalancer System With Symmetric Rigid Supports

2016 ◽  
Vol 138 (3) ◽  
Author(s):  
DaeYi Jung ◽  
H. A. DeSmidt
Keyword(s):  
Limit Cycle ◽  
Three Dimensional ◽  
Design Parameters ◽  
Rigid Rotor ◽  
Modal Shape ◽  
Flexible Shaft ◽  
Flexible Mode ◽  
Automatic Balancing ◽  
Rigid Supports ◽  
Limit Cycle Behavior

In recent years, there has been much interest in the use of automatic balancing devices (ABD) in rotating machinery. Autobalancers consist of several freely moving eccentric balancing masses mounted on the rotor, which, at certain operating speeds, act to cancel rotor imbalance. This “automatic balancing” phenomenon occurs as a result of nonlinear dynamic interactions between the balancer and rotor wherein the balancer masses naturally synchronize with the rotor with appropriate phase to cancel the imbalance. However, due to inherent nonlinearity of the autobalancer, the potential for other undesirable nonsynchronous limit-cycle behavior exists. In such situations, the balancer masses do not reach their desired synchronous balanced positions resulting in increased rotor vibration. To explore this nonsynchronous behavior of ABD, the unstable limit-cycle analysis of three-dimensional (3D) flexible shaft/rigid rotor/ABD/rigid supports described by the modal coordinates has been investigated here. Essentially, this paper presents an approximate harmonic analytical solution to describe the limit-cycle behavior of ABD–rotor system interacting with flexible shaft, which has not been fully considered by ABD researchers. The modal shape of flexible shaft is determined by using well-known fixed–fixed boundary condition due to symmetric rigid supports. Here, the whirl speed of the ABD balancer masses is determined via the solution of a nonlinear characteristic equation. Also, based upon the analytical limit-cycle solutions, the limit-cycle stability of three primary design parameters for ABD is assessed via a perturbation and Floquet analysis: the size of ABD balancer mass, the ABD viscous damping, and the relative axial location of ABD to the imbalance rotor along the shaft. The coexistence of the stable balanced synchronous condition and undesirable nonsynchronous limit-cycle is also studied. It is found that for certain combinations of ABD parameters and rotor speeds, the nonsynchronous limit-cycle can be made unstable, thus guaranteeing asymptotic stability of the synchronous balanced condition at the supercritical shaft speeds between each flexible mode. Finally, the analysis is validated through numerical simulation. The findings in this paper yield important insights for researchers wishing to utilize ABD in flexible shaft/rigid rotor systems and limit-cycle mitigation.

scholarly journals Effect of intermediate supports location on natural frequencies of multiple cracked continuous beams

2018 ◽  
Author(s):  
Do Nam ◽  
Nguyen Tien Khiem ◽  
Le Khanh Toan ◽  
Nguyen Thi Thao ◽  
Pham Thi Ba Lien
Keyword(s):  
General Solution ◽  
Free Vibration ◽  
Natural Frequencies ◽  
Continuous Beam ◽  
Cracked Beam ◽  
Continuous Beams ◽  
Simplified Method ◽  
Rigid Supports ◽  
Natural Frequency Analysis ◽  
Eigenfrequency Spectrum

The present paper deals with free vibration of multiple cracked continuous beams with intermediate rigid supports. A simplified method is proposed to obtain general solution of free vibration in cracked beam with intermediate supports that is then used for natural frequency analysis of the beam in dependence upon cracks and support locations. Numerical results show that the support location or ratio of span lengths in combination with cracks makes a significant effect on eigenfrequency spectrum of beam. The discovered effects of support locations on eigenfrequency spectrum of cracked continuous beam are useful for detecting not only cracks but also positions of vanishing deflection on the beam.

scholarly journals Modeling of Constructions’ Structurally Nonlinear Oscillations Using Chebyshev's Polynomials

Mechanika ◽  
2020 ◽  
Vol 26 (4) ◽  
pp. 331-337
Author(s):  
Sergey Gridnev ◽  
Yuri Skalko ◽  
Alexandr Shimanovsky
Keyword(s):  
Nonlinear Oscillations ◽  
Continuous System ◽  
Initial Boundary ◽  
Nonlinear Boundary Conditions ◽  
Building Structures ◽  
Deformed State ◽  
Floating Bridge ◽  
Elastic Couplings ◽  
Initial Boundary Value ◽  
Rigid Supports

A numerical algorithm for solving initial-boundary value problems with nonlinear boundary conditions was developed and implemented. The algorithm is constructed with reference to modeling of oscillations of an elastically supported deformable rod with limit stops at the ends under the action of a moving variable force. Such a rod is the design scheme of a number of building structures, including the span structure of a floating bridge of continuous system with limiting rigid supports at the ends. Chebyshev's polynomials were used to improve the computational schemes for realizing the practical problems of modeling constructive-nonlinear oscillations of building structures. The solution does not lose stability for large values of the elasticity coefficients of elastic couplings. Using the developed approach, it is possible to perform virtual computing experiments to skip a variety of movable loads on the floating bridge to analyze its deformed state and to make well-grounded design decisions.

Free Vibrations of Constrained Beams

1952 ◽  
Vol 19 (4) ◽  
pp. 471-477
Author(s):  
Winston F. Z. Lee ◽  
Edward Saibel
Keyword(s):  
Natural Frequencies ◽  
Degree Of Approximation ◽  
Free Vibrations ◽  
Frequency Equation ◽  
Continuous Beam ◽  
Concentrated Mass ◽  
Simple Manner ◽  
Natural Modes ◽  
Modes Of Vibration ◽  
Rigid Supports

Abstract A general expression is developed from which the frequency equation for the vibration of a constrained beam with any combination of intermediate elastic or rigid supports, concentrated masses, and sprung masses can be found readily. The method also is extended to the case where the constraint is a continuous elastic foundation or uniformly distributed load of any length. This method requires only the knowledge of the natural frequencies and natural modes of the beam supported at the ends in the same manner as the constrained beam but not subjected to any of the constraints between the ends. The frequency equation is obtained easily and can be solved to any desired degree of approximation for any number of modes of vibration in a quick and simple manner. Numerical examples are given for a beam with one concentrated mass, for a beam with one sprung mass, and a continuous beam with one sprung mass.

Using Analytical/Numerical Matching With Finite Element Analysis to Solve a Fluid-Loaded Structural Dynamics Problem

2000 ◽  
Author(s):  
Christopher D. Park ◽  
Linda P. Franzoni
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Original Problem ◽  
Lower Boundary ◽  
Fluid Loading ◽  
Computationally Efficient ◽  
Principle Of Superposition ◽  
Element Analysis ◽  
Loading Effects ◽  
Rigid Supports

Abstract Two model problems are solved using a combination of Analytical/Numerical Matching (ANM) and Finite Element Analysis (FEA). The first problem is that of a thick, finite length beam driven by the motion of a small rigid support attached to its lower boundary. The second problem is a thick, infinitely long fluid-loaded beam driven by the motion of periodically spaced rigid supports (identical to the support of the first problem). The ANM process divides an original problem into local, matching, and global sub-problems through the use of a smooth force and the principle of superposition. In the two model problems presented, the same high-resolution local (in vacuo) problem is solved using FEA. The fluid loading effects can be accounted for entirely by the global problem. The problems presented show that ANM is a computationally efficient method that retains the high accuracy needed near structural discontinuities.

scholarly journals Hybrid Lipid-Polymer Bilayers: pH-Mediated Interactions between Hybrid Vesicles and Glass

Polymers ◽  
2020 ◽  
Vol 12 (4) ◽  
pp. 745
Author(s):  
Keith L. Willes ◽  
Jasmyn R. Genchev ◽  
Walter F. Paxton
Keyword(s):  
Quartz Crystal ◽  
Solution Ph ◽  
Polymer Vesicles ◽  
Polymer Bilayers ◽  
Poly Ethylene Oxide ◽  
Ph Dependent ◽  
Poly Ethylene ◽  
Glass Surfaces ◽  
Rigid Supports ◽  
Hybrid Bilayers

One practical approach towards robust and stable biomimetic platforms is to generate hybrid bilayers that incorporate both lipids and block co-polymer amphiphiles. The currently limited number of reports on the interaction of glass surfaces with hybrid lipid and polymer vesicles—DOPC mixed with amphiphilic poly(ethylene oxide-b-butadiene) (PEO-PBd)—describe substantially different conclusions under very similar conditions (i.e., same pH). In this study, we varied vesicle composition and solution pH in order to generate a broader picture of spontaneous hybrid lipid/polymer vesicle interactions with rigid supports. Using quartz crystal microbalance with dissipation (QCM-D), we followed the interaction of hybrid lipid-polymer vesicles with borosilicate glass as a function of pH. We found pH-dependent adsorption/fusion of hybrid vesicles that accounts for some of the contradictory results observed in previous studies. Our results show that the formation of hybrid lipid-polymer bilayers is highly pH dependent and indicate that the interaction between glass surfaces and hybrid DOPC/PEO-PBd can be tuned with pH.

Eigenfrequencies of Continuous Plates With Arbitrary Number of Equal Spans

1979 ◽  
Vol 46 (3) ◽  
pp. 656-662 ◽  
Author(s):  
Isaac Elishakoff ◽  
Alexander Sternberg
Keyword(s):  
Arbitrary Number ◽  
Wave Number ◽  
Analytical Technique ◽  
Simply Supported ◽  
Isotropic Plates ◽  
Simple Support ◽  
Transcendental Equations ◽  
Rigid Supports ◽  
Numerical Complexity

An approximate analytical technique is developed for determination of the eigenfrequencies of rectangular isotropic plates continuous over rigid supports at regular intervals with arbitrary number of spans. All possible combinations of simple support and clamping at the edges are considered. The solution is given by the modified Bolotin method, which involves solution of two problems of the Voigt-Le´vy type in conjunction with a postulated eigenfrequency/wave-number relationship. These auxiliary problems yield a pair of transcendental equations in the unknown wave numbers. The number of spans figures explicitly in one of the transcendental equations, so that numerical complexity does not increase with the number of spans. It is shown that the number of eigenfrequencies associated with a given pair of mode numbers equals that of spans. The essential advantage of the proposed method is the possibility of finding the eigenfrequencies for any prescribed pair of mode numbers. Moreover, for plates simply supported at two opposite edges and continuous over rigid supports perpendicular to those edges, the result is identical with the exact solution.

Laser-sealed arteriotomy: a reliable aneurysm model

1987 ◽  
Vol 67 (2) ◽  
pp. 284-287 ◽  
Author(s):  
Matthew R. Quigley ◽  
Kenneth Heiferman ◽  
Hau C. Kwaan ◽  
Danko Vidovich ◽  
Peter Nora ◽  
...  
Keyword(s):  
Blood Pressure ◽  
Carotid Artery ◽  
Systolic Blood Pressure ◽  
Systemic Hypertension ◽  
Chi Square ◽  
Content Type ◽  
Small Arteries ◽  
Rigid Supports ◽  
Aneurysm Model ◽  
Fine Print

✓ Laser-assisted vascular anastomosis (LAVA) is associated with a significant aneurysm problem when it is applied to small arteries. The etiology of this phenomenon was investigated by creating arteriotomies of different lengths and orientation in the rat carotid artery and sealing them with the milliwatt CO2 laser. It was found that increasing the arteriotomy length from 0.5 to 1.0 mm significantly raised aneurysm occurrence (4/17 vs. 25/28, chi-square: p < 0.001) regardless of orientation. Systemic hypertension (systolic blood pressure ≥ 170 mm Hg) also significantly affected the aneurysm rate among the 0.5-mm arteriotomy group, raising aneurysm occurrence from 23.5% (4/17) to 100% (14/14) (p < 0.001). Assuming that the stay-sutures used for LAVA's act as rigid supports, the rate of aneurysm occurrence must be related to the distance between sutures. This phenomenon has been exploited to create a reliable aneurysm model.

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