Vibration of Beams Subjected to End and Axially Distributed Loading

1970 ◽  
Vol 12 (1) ◽  
pp. 70-72 ◽  
Author(s):  
D. F. Pilkington ◽  
J. B. Carr
Keyword(s):  
Lower Bound ◽  
Fundamental Frequency ◽  
Approximate Analysis ◽  
Hinged Beams ◽  
Good Agreement

This Note describes an approximate analysis which determines a lower bound to the fundamental frequency of beams subjected to both end and axially distributed loads. Comparison with results for the fixed-free and hinged-hinged beams gives good agreement.

Electrothermally Tunable Bridge Resonator

2016 ◽  
Author(s):  
Amal Z. Hajjaj ◽  
Nouha Alcheikh ◽  
Abdallah Ramini ◽  
Md Abdullah Al Hafiz ◽  
Mohammad I. Younis
Keyword(s):  
Fundamental Frequency ◽  
Beam Theory ◽  
Element Model ◽  
Bernoulli Beam ◽  
Electrothermal Actuation ◽  
Wide Range ◽  
Simulation Results ◽  
Dc Current ◽  
Euler Bernoulli Beam ◽  
Good Agreement

This paper demonstrates experimentally, theoretically, and numerically a wide-range tunability of an in-plane clamped-clamped microbeam, bridge, and resonator compressed by a force due to electrothermal actuation. We demonstrate that a single resonator can be operated at a wide range of frequencies. The microbeam is actuated electrothermally, by passing a DC current through it. We show that when increasing the electrothermal voltage, the compressive stress inside the microbeam increases, which leads eventually to its buckling. Before buckling, the fundamental frequency decreases until it drops to very low values, almost to zero. After buckling, the fundamental frequency increases, which is shown to be as high as twice the original resonance frequency. Analytical results based on the Galerkin discretization of the Euler Bernoulli beam theory are generated and compared to the experimental data and to simulation results of a multi-physics finite-element model. A good agreement is found among all the results.

Collective Behavior of Networks with Linear (VLSI) Integrate-and-Fire Neurons

1999 ◽  
Vol 11 (3) ◽  
pp. 633-652 ◽  
Author(s):  
Stefano Fusi ◽  
Maurizio Mattia
Keyword(s):  
Lower Bound ◽  
Numerical Simulations ◽  
Fixed Points ◽  
Collective Behavior ◽  
Emission Process ◽  
Current Opinion ◽  
Integrate And Fire ◽  
Excitatory Network ◽  
Good Agreement ◽  
Integrate And Fire Neuron

We analyze in detail the statistical properties of the spike emission process of a canonical integrate-and-fire neuron, with a linear integrator and a lower bound for the depolarization, as often used in VLSI implementations (Mead, 1989). The spike statistics of such neurons appear to be qualitatively similar to conventional (exponential) integrate-and-fire neurons, which exhibit a wide variety of characteristics observed in cortical recordings. We also show that, contrary to current opinion, the dynamics of a network composed of such neurons has two stable fixed points, even in the purely excitatory network, corresponding to two different states of reverberating activity. The analytical results are compared with numerical simulations and are found to be in good agreement.

Lower-bound calculations of the bearing capacity of eccentrically loaded footings in cohesionless soil

2012 ◽  
Vol 49 (3) ◽  
pp. 298-310 ◽  
Author(s):  
Sven Krabbenhoft ◽  
Lars Damkilde ◽  
Kristian Krabbenhoft
Keyword(s):  
Lower Bound ◽  
Bearing Capacity ◽  
Cohesionless Soil ◽  
Vertical Force ◽  
The Finite Element Method ◽  
Eccentric Load ◽  
Perfectly Plastic ◽  
Coulomb Failure ◽  
Coulomb Failure Criterion ◽  
Good Agreement

Lower-bound calculations based on the finite element method are used to determine the bearing capacity of a strip foundation subjected to a vertical, eccentric load on cohesionless soil with varying surcharges. The soil is assumed perfectly plastic following the Mohr–Coulomb failure criterion. The results are reported as tables and graphs showing the bearing capacity as a function of the eccentricity and surcharge. Normalised interaction diagrams in the vertical force versus moment plane have been produced. The results from the analysis are in reasonable agreement with existing methods for smaller eccentricities, whereas for greater eccentricities (e > 0.25B–0.3B, where B is the width of the foundation), the lower-bound values in general — and especially for greater surcharges — are considerably smaller than the bearing capacities predicted by existing methods. For the special case of no surcharge, the results are in very good agreement with results obtained by the effective-width approach originally proposed by Meyerhof.

Interaction of Critical Pressures and Critical Concentrated Loads Acting on Shallow Spherical Shells

1966 ◽  
Vol 33 (3) ◽  
pp. 612-616 ◽  
Author(s):  
Ta-Cheng Loo ◽  
R. M. Evan-Iwanowski
Keyword(s):  
Lower Bound ◽  
Residual Stresses ◽  
Concentrated Loads ◽  
Spherical Shells ◽  
Die Pressing ◽  
Geometrical Imperfections ◽  
Hand Test ◽  
Experimental Values ◽  
Geometry Parameter ◽  
Good Agreement

In this paper the critical combinations of uniform pressures and concentrated loads at the apex acting on shallow spherical shells have been determined analytically and experimentally. The Dini-Bessel expansion of unknown functions, proposed first in [4], have been applied to the problem on hand. Test specimens void of initial geometrical imperfections and negligible residual stresses have been fabricated in the laboratory by using the die-pressing technique. The analytically calculated critical combinations are in good agreement with those determined experimentally. The theoretical lower-bound, or the cut-off values, of the geometry parameter, μ, is found to be near the experimental values. The existence of the analytical and experimental cut-off values of γ2 indicates that there is a lower bound of the values of uniform pressures such that a shell does not exhibit a snap-through instability when subjected for any combinations of concentrated loads and uniform pressures below its cut-off value.

On the Bounds of Eigenvalues of a Clamped Plate in Tension

1958 ◽  
Vol 25 (1) ◽  
pp. 52-56
Author(s):  
R. K. Kaul ◽  
S. G. Tewari
Keyword(s):  
Lower Bound ◽  
Variational Method ◽  
Fundamental Frequency ◽  
Lower Bounds ◽  
Mode Shape ◽  
Present Method ◽  
Auxiliary Problem ◽  
Square Plate ◽  
Edge Tension

Abstract In this paper, use is made of Temple’s generalizations of Kato’s theorem for the determination of close lower bounds to the fundamental frequency of oscillation of a clamped square plate subjected to uniform biaxial edge tension. The success of the method depends upon the solution of an auxiliary problem governing the residual mode shape; and in the present case, this mode is determined by using the variational method of Ritz. The principle of computation of the number ϵV2 (which corresponds to the ratio of the elastic energies in the residual and the tentative mode) is explained, and the value of the lower bound is determined by using the inequality (1 − ρ/β)(ρ/α − 1) ≤ ϵV2. The results are compared with those obtained previously by Weinstein and Chien, and it is shown that the present method leads to much closer bounds.

A CONDUCTION MODEL OF THE ELECTRORHEOLOGICAL EFFECT

1994 ◽  
Vol 08 (20n21) ◽  
pp. 2731-2745 ◽  
Author(s):  
P. ATTEN ◽  
J.-N. FOULC ◽  
N. FELICI
Keyword(s):  
Large Scale ◽  
Low Frequency ◽  
Approximate Analysis ◽  
Conduction Model ◽  
Electrorheological Effect ◽  
Nonlinear Conduction ◽  
Surface Conduction ◽  
Solid Spheres ◽  
Good Agreement ◽  
Conduction Properties

A conduction model is proposed to explain the electrorheological effect under D.C. or low frequency A.C. fields. An approximate analysis taking into account the bulk conduction of the solid and the nonlinear conduction properties of the liquid is confirmed by experiments on large scale spheres. A good agreement between measurements and predictions is also obtained when air replaces the liquid. Finally the predictions are extended to the case of surface conduction of the solid spheres.

Compact Diplexer with High Isolation and Wide Stopband Based on SIRs

Frequenz ◽  
2017 ◽  
Vol 71 (5-6) ◽  
Author(s):  
Bo Zhou ◽  
Xin-Yi Wang ◽  
Feng Wei ◽  
Lei Chen
Keyword(s):  
Fundamental Frequency ◽  
Bandpass Filters ◽  
High Isolation ◽  
Electric Length ◽  
Rejection Level ◽  
S Parameters ◽  
Good Agreement

AbstractA compact microstrip diplexer with a high isolation and improved out-of-band performance is proposed in this paper. The proposed diplexer is based on cascaded-quadruplet (CQ) bandpass filters (BPFs), which is composed of λ/4 stepped-impedance resonators (SIRs). By employing the edge and quasi-lumped coupling topology, a compact diplexer with improved passband selectivity can be achieved. Meanwhile, by appropriately adjusting the impedance and electric length ratios of SIRs, the stopband can be extended to 20 GHz with a rejection level of 10 dB, which is 12.7 times of the fundamental frequency. The predicted results on S parameters are compared with the measured ones and good agreement is achieved.

Lower Bounds for the Buckling Loads and the Fundamental Frequencies of Elastic Bodies

1974 ◽  
Vol 41 (1) ◽  
pp. 151-154 ◽  
Author(s):  
C. H. Popelar
Keyword(s):  
Lower Bound ◽  
Elastic Body ◽  
Fundamental Frequency ◽  
Lower Bounds ◽  
Upper Bound ◽  
Elastic Stability ◽  
Buckling Load ◽  
Buckling Loads ◽  
Fundamental Frequencies ◽  
Elastic Bodies

Within the classical theory of elastic stability a lower bound to the buckling load of an elastic body is presented. The Timoshenko load is shown to be a better upper bound to the buckling load than the Rayleigh load. By appropriate modifications of the potential and complementary energies, these bounds are applicable to the fundamental frequency of an elastic body. The application of the bounds is illustrated.

Oscillations of a gas in a closed tube near half the fundamental frequency

1987 ◽  
Vol 183 ◽  
pp. 147-161 ◽  
Author(s):  
R. Althaus ◽  
H. Thomann
Keyword(s):  
Boundary Layer ◽  
Fundamental Frequency ◽  
Atmospheric Pressure ◽  
Nonlinear Effects ◽  
Viscous Effects ◽  
Sinusoidal Motion ◽  
Closed Tube ◽  
Resonant Part ◽  
Theoretical Results ◽  
Good Agreement

The oscillations are driven by the sinusoidal motion of a piston at one end of the tube. Near half the fundamental frequency the first overtone, driven by nonlinear effects, becomes resonant. For small boundary-layer friction the amplitude of this resonant part is comparable with the non-resonant acoustic solution and shocks are formed. Theoretical results are compared with pressure signals measured at the closed end of the tube. The viscous effects are large for air at atmospheric pressure and the nonlinear effects remain small. Experiments with xenon, sulphurhexafluoride (SF6) and Freon RC-318 (C4F8) were therefore conducted and shocks formed as predicted. The comparison of the nonlinear theory by Keller (1975) with the experiments shows very good agreement.

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