Even harmonic resonance - an unusual problem

We demonstrate the variations of single harmonic resonance enhancement during high-order harmonics generation in zinc-containing atomic and molecular species at the conditions of single-color and two-color pumps of laser-induced plasmas by applying different laser sources. We show how selenides of this metal notably modify the enhancement of single (9th, 15th or 16th) harmonic compared with purely atomic zinc plasmas. The variations of single harmonic enhancement are demonstrated using fixed (806 nm) and tunable (1280–1440 nm) radiation.

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Nonlinear Vibrations of Two-Span Composite Laminated Plates with Equal and Unequal Subspan Lengths

Advances in Applied Mathematics and Mechanics ◽

10.4208/aamm.oa-2016-0121 ◽

2017 ◽

Vol 9 (6) ◽

pp. 1485-1505

Author(s):

Lingchang Meng ◽

Fengming Li

Keyword(s):

Multiple Scales ◽

Equations Of Motion ◽

Primary Resonance ◽

Laminated Plates ◽

Laminated Plate ◽

Composite Laminated Plate ◽

Vibration Localization ◽

Composite Laminated Plates ◽

Localization Phenomenon ◽

Harmonic Resonance

AbstractThe nonlinear transverse vibrations of ordered and disordered two-dimensional (2D) two-span composite laminated plates are studied. Based on the von Karman's large deformation theory, the equations of motion of each-span composite laminated plate are formulated using Hamilton's principle, and the partial differential equations are discretized into nonlinear ordinary ones through the Galerkin's method. The primary resonance and 1/3 sub-harmonic resonance are investigated by using the method of multiple scales. The amplitude-frequency relations of the steady-state responses and their stability analyses in each kind of resonance are carried out. The effects of the disorder ratio and ply angle on the two different resonances are analyzed. From the numerical results, it can be concluded that disorder in the length of the two-span 2D composite laminated plate will cause the nonlinear vibration localization phenomenon, and with the increase of the disorder ratio, the vibration localization phenomenon will become more obvious. Moreover, the amplitude-frequency curves for both primary resonance and 1/3 sub-harmonic resonance obtained by the present analytical method are compared with those by the numerical integration, and satisfactory precision can be obtained for engineering applications and the results certify the correctness of the present approximately analytical solutions.

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Impedance analysis for the investigation of the behaviors of piezoelectric quartz crystal in the liquid at harmonic resonance

Sensors and Actuators B Chemical ◽

10.1016/s0925-4005(00)00338-5 ◽

2000 ◽

Vol 67 (1-2) ◽

pp. 68-75 ◽

Cited By ~ 11

Author(s):

Anhong Zhou ◽

Jingdong Zhang ◽

Qingji Xie ◽

Shouzhuo Yao

Keyword(s):

Quartz Crystal ◽

Impedance Analysis ◽

Piezoelectric Quartz ◽

Piezoelectric Quartz Crystal ◽

Harmonic Resonance

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Harmonic Resonance Frequency Factor of Spur Gear System and Oscillation Reduction Approaches

Volume 7: Engineering Education and Professional Development ◽

10.1115/imece2007-43188 ◽

2007 ◽

Author(s):

Jianping Wang ◽

Pengfei Li ◽

Ziying Wu ◽

Minghong Zhang

Keyword(s):

Parametric Excitation ◽

Linear Time ◽

Primary Resonance ◽

Frequency Factor ◽

Multiple Scale ◽

Transmission Error ◽

Spur Gear ◽

High Order ◽

Time Varying ◽

Harmonic Resonance

In this study, a non-linear time-varying dynamic model of a spur gear pair system is used to investigate the dynamic behavior of the system by means of multiple scale approach. Both time-varying stiffness, transmission error and tooth backlash clearance of the system are taken into account in the model. The mesh stiffness fluctuation is developed as high order Fourier series and tooth backlash clearance is fitted by high order polynomial function. The frequency factors of the system are investigated and the frequency-response equations at the case of internal and external excitation, parametric excitation and combined excitation are obtained. The peak value of the amplitude of the primary resonance, super and sub harmonic resonance and combination harmonic under internal, external and parametric excitation are researched. The approaches of vibration reduction are investigated. Finally an example is investigated using the presented process and the results indicate the sensitivity and correctness of the presented analysis approaches.

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