Dynamic Snap-Through of Imperfect Viscoelastic Shallow Arches

1968 ◽  
Vol 35 (2) ◽  
pp. 289-296 ◽  
Author(s):  
N. C. Huang ◽  
W. Nachbar
Keyword(s):  
Lower Bound ◽  
Critical Load ◽  
Critical Loads ◽  
Jump Discontinuity ◽  
Closed Form Expression ◽  
Antisymmetric Mode ◽  
Form Expression ◽  
Shallow Arches ◽  
Voigt Model ◽  
Good Agreement

Dynamic snap-through or dynamic buckling of imperfect viscoelastic shallow arches with hinged ends is considered under step loads of infinite duration. Attention is principally devoted to the influence both of small imperfections and of small amounts of damping, acting together, on the critical loads. For the problem considered, the Voigt model is used for viscoelasticity, the deflection is represented by the first two harmonic modes, and imperfections have the shape of the second (antisymmetric) mode. Results obtained by numerical integration of the differential equations show that the critical load exhibits a jump discontinuity in the limit for vanishing imperfection. Critical loads for slightly imperfect and elastic (inviscid) arches are slightly higher than those from the saddle-point formula of Hoff and Bruce [1, p. 276], confirming that the formula gives a lower bound on the critical load. However, critical loads for arches with slight imperfection and slight viscosity are considerably higher than for the slightly imperfect elastic arches. Another closed-form expression is shown to be in good agreement with these results. For finite amounts of viscosity, the critical loads tend rapidly to the values obtained for infinite viscosity, which are the same as the critical loads for quasi-static buckling. Apart from the jump discontinuity at zero, the critical load for any viscosity decreases continuously and monotonically with imperfection.

Reliability optimization for non-repairable series-parallel systems with a choice of redundancy strategies and heterogeneous components: Erlang time-to-failure distribution

2020 ◽  
pp. 1748006X2095257
Author(s):  
Meisam Sadeghi ◽  
Emad Roghanian ◽  
Hamid Shahriari ◽  
Hassan Sadeghi
Keyword(s):  
Lower Bound ◽  
Closed Form ◽  
System Reliability ◽  
Parallel Systems ◽  
Closed Form Expression ◽  
Erlang Distribution ◽  
Time To Failure ◽  
Form Expression ◽  
Integrodifference Equation ◽  
Cold Standby

The redundancy allocation problem (RAP) of non-repairable series-parallel systems considering cold standby components and imperfect switching mechanism has been traditionally formulated with the objective of maximizing a lower bound on system reliability instead of exact system reliability. This objective function has been considered due to the difficulty of determining a closed-form expression for the system reliability equation. But, the solution that maximizes the lower bound for system reliability does not necessarily maximize exact system reliability and thus, the obtained system reliability may be far from the optimal reliability. This article attempts to overcome the mentioned drawback. Under the assumption that component time-to-failure is distributed according to an Erlang distribution and switch time-to-failure is exponentially distributed, a closed-form expression for the subsystem cold standby reliability equation is derived by solving an integrodifference equation. A semi-analytical expression is also derived for the reliability equation of a subsystem with mixed redundancy strategy. The accuracy and the correctness of the derived equations are validated analytically. Using these equations, the RAP of non-repairable series-parallel systems with a choice of redundancy strategies is formulated. The proposed mathematical model maximizes exact system reliability at mission time given system design constraints. Unlike most of the previous formulations, the possibility of using heterogeneous components in each subsystem is provided so that the active components can be of one type and the standby ones of the other. The results of an illustrative example demonstrate the high performance of the proposed model in determining optimal design configuration and increasing system reliability.

scholarly journals Triangular buckling patterns of twisted inextensible strips

2010 ◽  
Vol 467 (2125) ◽  
pp. 285-303 ◽  
Author(s):  
A. P. Korte ◽  
E. L. Starostin ◽  
G. H. M. van der Heijden
Keyword(s):  
Boundary Value Problem ◽  
Critical Load ◽  
Critical Loads ◽  
Equilibrium Shape ◽  
Boundary Value ◽  
Mode Number ◽  
Force Extension ◽  
Higher Modes ◽  
Post Buckling ◽  
Good Agreement

When twisting a strip of paper or acetate under high longitudinal tension, one observes, at some critical load, a buckling of the strip into a regular triangular pattern. Very similar triangular facets have recently been found in solutions to a new set of geometrically exact equations describing the equilibrium shape of thin inextensible elastic strips. Here, we formulate a modified boundary-value problem for these equations and construct post-buckling solutions in good agreement with the observed pattern in twisted strips. We also study the force–extension and moment–twist behaviour of these strips by varying the mode number n of triangular facets and find critical loads with jumps to higher modes.

A SEMI-ANALYTICAL MODEL OF TIME DEPENDENT PLASTIC STRAINS INDUCED DURING SHOT PEENING

2013 ◽  
Vol 05 (03) ◽  
pp. 1350027 ◽  
Author(s):  
J. DAVIS ◽  
M. RAMULU
Keyword(s):  
Plastic Strain ◽  
Order Differential Equation ◽  
Closed Form Expression ◽  
Plastic Strain Rate ◽  
Solid Model ◽  
Mathematical Form ◽  
Form Expression ◽  
Loading And Unloading ◽  
Inelastic Strains ◽  
Good Agreement

When a semi-infinite surface is shot peened the in-plane inelastic strains are zero because of compatibility. As a result, the in-plane residual stress and plastic strain are linearly related. These boundary conditions motivate a second order differential equation similar in mathematical form to a modified Kelvin solid model with a strain acceleration term. Solving the resulting equation gives a closed form expression for the plastic strain as a function of time. The plastic strain rate is solved by taking the derivative with respect to time. Comparisons with published finite element data show good agreement and are within 10% for most of the loading and unloading period.

EFFECT OF SUPPORT STIFFNESS ON STABILITY OF SHALLOW ARCHES

2010 ◽  
Vol 10 (05) ◽  
pp. 1099-1110 ◽  
Author(s):  
JIANGUO CAI ◽  
JIAN FENG
Keyword(s):  
Critical Load ◽  
Critical Loads ◽  
Virtual Work ◽  
Stiffness Coefficient ◽  
Rotational Stiffness ◽  
Initial Stiffness ◽  
Buckling Mode ◽  
Concentrated Load ◽  
Shallow Arches ◽  
Bifurcation Buckling

The nonlinear behavior and in-plane stability of parabolic shallow arches with elastic rotational supports are investigated. A central concentrated load is applied to create the compression in the supports. Nonlinear buckling analysis based on the virtual work formulation is carried out to obtain the critical load for both symmetric snap-through buckling and anti-symmetric bifurcation buckling. It is found that the effect of rotational stiffness of the elastic supports on the critical loads is significant. The critical load increases as either the initial stiffness coefficient α or the stiffening rate β increases. The effect of the stiffening rate β on the critical loads decreases, as the initial stiffness coefficient α increases. In addition, the influence of rotational stiffness on the bifurcation buckling is larger than that on the snap-through buckling. The limit of the geometric parameter λ between the bifurcation and snap-through buckling modes also increases with the increase in the stiffening rate β. In addition, the snap-through buckling mode governs the buckling of the arch with larger stiffening rates.

scholarly journals New Cad Model of the Microstrip Interdigital Capacitor

2004 ◽  
Vol 27 (4) ◽  
pp. 237-245 ◽  
Author(s):  
Nihad Dib ◽  
Qiu Zhangb ◽  
Ulrich Rohde
Keyword(s):  
Coplanar Waveguide ◽  
Circuit Theory ◽  
Closed Form Expression ◽  
Simple Circuit ◽  
Form Expression ◽  
Coupled Line ◽  
Interdigital Capacitor ◽  
Quarter Wavelength ◽  
Coupled Lines ◽  
Good Agreement

A new model for the microstrip line interdigital capacitor is proposed. This model consists of calculating the2N×2N Y-matrix of theNcoupled lines using the multiple coupled line tool. Then, this matrix is reduced to a2×2matrix using simple circuit theory. The capacitance at the end of each finger is taken into consideration using closed-form expression of the coplanar waveguide open-end capacitance. This model can predict the resonances that might appear around the quarter-wavelength frequency. These resonances are caused by the coupling between the fingers and exist only in capacitors with four fingers or more. Very good agreement is obtained between the results of our model and those obtained using the software HFSS and measurements.

scholarly journals Secrecy capacity optimization artificial noise: the ergodic secrecy capacity lower bound and optimal power allocation

2020 ◽  
Author(s):  
Yebo Gu ◽  
Zhilu Wu ◽  
Zhendong Yin ◽  
Bowen Huang
Keyword(s):  
Lower Bound ◽  
Channel Estimation ◽  
Closed Form ◽  
Power Allocation ◽  
Estimation Error ◽  
Closed Form Expression ◽  
Artificial Noise ◽  
Secrecy Capacity ◽  
Capacity Optimization ◽  
Form Expression

Abstract The secure transmission problem of MIMO wireless system in fading channels is studied in this paper. We add a secrecy capacity optimization artificial noise(SCO-AN) to the transported signal for improving the security performance of the system. The closed-form expression of secrecy capacity's lower bound is obtained. Base on the closed-form expression of secrecy capacity's lower bound, We optimize the power allocation between the information-bearing signal and the SCO-AN. By calculating, the optimal ratio of power alloation betwenn the information-bearing signal and the SCO-AN is obtained. Through simulation, the results shows the secrecy capacity increases with more receiving antennas and less eavesdropping antennas.And more power should be allocated to the SCO-AN with the increase of the colluding eavedroppers.More over, we study the effect of channel estimation error on power allocation between information-bearing signal and SCO-AN and find that more power should be allocated to decrease eavesdroppers capacity if the channel estimation is not perfect.

scholarly journals Exact Critical Loads for a Pinned Half-Sine Arch Under End Couples

2005 ◽  
Vol 72 (1) ◽  
pp. 147-148 ◽  
Author(s):  
Jen-San Chen ◽  
Jian-San Lin
Keyword(s):  
Closed Form ◽  
Cross Section ◽  
Critical Loads ◽  
Closed Form Expression ◽  
Radius Of Gyration ◽  
Form Expression ◽  
Shallow Arch ◽  
Initial Height ◽  
The Cross

In this note we show that for a pinned half-sine arch under end couples snap-through buckling will occur unsymmetrically if the initial height of the shallow arch is greater than 6.5466r, where r is the radius of gyration of the cross section. The closed-form expression for the critical couple can be obtained analytically.

scholarly journals Synthesizing of Planar and Conformal Double-Sided Parallel-Cross Dipoles FSS Based on Closed-Form Expression

IEEE Access ◽  
2021 ◽  
pp. 1-1
Author(s):  
Yassine Zouaoui ◽  
Larbi Talbi ◽  
Khelifa Hettak ◽  
Naresh K. Darimireddy
Keyword(s):  
Closed Form ◽  
Closed Form Expression ◽  
Form Expression

Distribution of Consensus in a Broadcasting-based Consensus-forming Algorithm

2021 ◽  
Vol 48 (3) ◽  
pp. 91-96
Author(s):  
Shigeo Shioda
Keyword(s):  
Distribution Function ◽  
Probability Density Function ◽  
Closed Form ◽  
Probability Density ◽  
Infinite Number ◽  
Stable Distribution ◽  
Random Variable ◽  
Cauchy Distribution ◽  
Closed Form Expression ◽  
Form Expression

The consensus achieved in the consensus-forming algorithm is not generally a constant but rather a random variable, even if the initial opinions are the same. In the present paper, we investigate the statistical properties of the consensus in a broadcasting-based consensus-forming algorithm. We focus on two extreme cases: consensus forming by two agents and consensus forming by an infinite number of agents. In the two-agent case, we derive several properties of the distribution function of the consensus. In the infinite-numberof- agents case, we show that if the initial opinions follow a stable distribution, then the consensus also follows a stable distribution. In addition, we derive a closed-form expression of the probability density function of the consensus when the initial opinions follow a Gaussian distribution, a Cauchy distribution, or a L´evy distribution.

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