Static and dynamic response of elastic suspended cables with thermal effects

The influence of the higher order modes of vibrations on the dynamic response of a suspension bridge is studied for two cases of loading. The first case is when the bridge is subjected to wind loading on the suspended cables and the bridge deck. The second case is when the bridge is subjected to a moving load on the bridge deck. The dynamic responses of the bridge deck and the suspended cables considering some higher order modes of vibrations are compared with the bridge response when it is modeled by the first dominant modes for each case of loading. It is shown that the influence of the higher order modes when the suspension bridge is subjected to wind loading is more significant than in the case when the bridge is subjected to a moving load. Therefore, it is recommended to investigate the influence of some higher order modes on the dynamic response of the suspension bridges and not always to depend on the response estimated from the first dominant modes of vibration.

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Nonlinear Dynamics of Suspended Cables under Periodic Excitation in Thermal Environments: Two-to-One Internal Resonance

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127421501534 ◽

2021 ◽

Vol 31 (10) ◽

pp. 2150153

Author(s):

Yaobing Zhao ◽

Henghui Lin

Keyword(s):

Thermal Effects ◽

Numerical Solutions ◽

Time History ◽

Phase Portraits ◽

Periodic Excitation ◽

Internal Resonances ◽

Chaotic Motions ◽

Temperature Changes ◽

Thermal Environments ◽

Suspended Cables

The temperature change is a non-negligible factor in examining the vibration behaviors of the cable structures. For this reason, the paper aims at investigating the thermal effects on suspended cables’ resonant responses considering two-to-one internal resonances. Firstly, a nonlinear continuous condensed model of the suspended cable under periodic excitation in thermal environments is adopted. Then, a multidimensional discretized model is constructed via the Galerkin method. Following the multiple scaling procedure, the modulation equations with both polar and Cartesian forms are obtained, which are solved numerically. A complete dynamic scenario is presented through bifurcation diagrams, phase portraits, time history curves, Fourier spectra, and Poincaré sections in three internal resonant cases. Numerical examples show that a small change in the static configuration due to thermal effects induces some noticeable changes in dynamic behaviors. The response amplitude, the nonlinear spring behavior, the resonant and stability region, the multi-periodic and chaotic motions are all dependent on temperature changes. Additional Hopf bifurcations might be found due to temperature changes, and it may lead to some more complicated dynamic characteristics. A good agreement between the perturbation and numerical solutions is observed to confirm the results’ correctness and accuracy.

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Temperature Effects on Dynamic Properties of Suspended Cables Subjected to Dual Harmonic Excitations

Shock and Vibration ◽

10.1155/2021/8883036 ◽

2021 ◽

Vol 2021 ◽

pp. 1-13

Author(s):

Yaobing Zhao ◽

Panpan Zheng ◽

Henghui Lin ◽

Chaohui Huang

Keyword(s):

Thermal Effects ◽

Dynamic Properties ◽

Time History ◽

Excitation Amplitude ◽

Phase Portraits ◽

Temperature Variations ◽

Thermal Environments ◽

Dynamical Behaviors ◽

Harmonic Excitations ◽

Suspended Cables

The paper aims at studying the influences of temperature on the suspended cables’ dynamical behaviors subjected to dual harmonic excitations in thermal environments. Significantly, the quadratic nonlinearity and the corresponding secondary resonances are considered. By introducing a tension variation factor, the nonlinear vibration equations of motion could be obtained based on the condensation model. By using Galerkin’s procedure, the continuous model of the nonlinear system is reduced to a set of infinite models with quadratic and cubic nonlinearities. By using the multiple scales method, the resultant reduced model is solved and the stability analysis is also presented in two simultaneous resonance cases. Nonlinear dynamical behaviors with thermal effects are presented using bifurcation diagrams, time-history curves, phase portraits, frequency spectrums, and Poincaré sections. The numerical results show that thermal effects induce different scenarios. The sensitivities of linear (natural frequency) and nonlinear (quadratic and cubic) coefficients to temperature variations are different. The temperature may increase or decrease the response amplitudes depending on the excitation amplitude and the sag-to-span ratio. The inflection point is shifted and exhibited at a smaller or larger excitation amplitude in thermal environments. The resonant range between two Pitchfork bifurcations seems to be reduced when the temperature is decreasing. The response amplitude is very sensitive to temperature, and even an opposite spring behavior may be exhibited due to warming/cooling conditions. However, the periodic motions seem independent of temperature variations.

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Thermal Considerations in Lens Regulator Systems

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100068783 ◽

1970 ◽

Vol 28 ◽

pp. 358-359

Author(s):

K.C. Newton

Keyword(s):

Electron Microscope ◽

Thermal Effects ◽

Environmental Control ◽

Reference Networks ◽

Better Than

Thermal effects in lens regulator systems have become a major problem with the extension of electron microscope resolution capabilities below 5 Angstrom units. Larger columns with immersion lenses and increased accelerating potentials have made solutions more difficult by increasing the power being handled. Environmental control, component choice, and wiring design provide answers, however. Figure 1 indicates with broken lines where thermal problems develop in regulator systemsExtensive environmental control is required in the sampling and reference networks. In each case, stability better than I ppm/min. is required. Components with thermal coefficients satisfactory for these applications without environmental control are either not available or priced prohibitively.

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Direct measurement of electron-diffraction-pattern intensities using an energy loss spectrometer

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100155311 ◽

1989 ◽

Vol 47 ◽

pp. 668-669

Author(s):

A. G. Jackson ◽

M. Rowe

Keyword(s):

Thermal Effects ◽

Dynamic Range ◽

Scattering Amplitude ◽

Dynamical Theory ◽

Site Symmetry ◽

Proof Of Concept ◽

Parallel Acquisition ◽

Kinematic Approximation ◽

Speed Up ◽

Structure Calculations

Diffraction intensities from intermetallic compounds are, in the kinematic approximation, proportional to the scattering amplitude from the element doing the scattering. More detailed calculations have shown that site symmetry and occupation by various atom species also affects the intensity in a diffracted beam. [1] Hence, by measuring the intensities of beams, or their ratios, the occupancy can be estimated. Measurement of the intensity values also allows structure calculations to be made to determine the spatial distribution of the potentials doing the scattering. Thermal effects are also present as a background contribution. Inelastic effects such as loss or absorption/excitation complicate the intensity behavior, and dynamical theory is required to estimate the intensity value.The dynamic range of currents in diffracted beams can be 104or 105:1. Hence, detection of such information requires a means for collecting the intensity over a signal-to-noise range beyond that obtainable with a single film plate, which has a S/N of about 103:1. Although such a collection system is not available currently, a simple system consisting of instrumentation on an existing STEM can be used as a proof of concept which has a S/N of about 255:1, limited by the 8 bit pixel attributes used in the electronics. Use of 24 bit pixel attributes would easily allowthe desired noise range to be attained in the processing instrumentation. The S/N of the scintillator used by the photoelectron sensor is about 106 to 1, well beyond the S/N goal. The trade-off that must be made is the time for acquiring the signal, since the pattern can be obtained in seconds using film plates, compared to 10 to 20 minutes for a pattern to be acquired using the digital scan. Parallel acquisition would, of course, speed up this process immensely.

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