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1

Effect of angular speed variations on the nonlinear vibrations of a rotational spring-mass system

Pakdemirli Mehmet

International Journal of Applied Mechanics and Engineering

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2024

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Vol. 29, no. 1

130--141

EN

A rotating spring-mass system is considered using polar coordinates. The system contains a cubic nonlinear spring with damping. The angular velocity harmonically fluctuates about a mean velocity. The dimensionless equations of motion are derived first. The velocity fluctuations resulted in a direct and parametric forcing terms. Approximate analytical solutions are sought using the Method of Multiple Scales, a perturbation technique. The primary resonance and the principal parametric resonance cases are investigated. The amplitude and frequency modulation equations are derived for each case. By considering the steady state solutions, the frequency response relations are derived. The bifurcation points are discussed for the problems. It is found that speed fluctuations may have substantial effects on the dynamics of the problem and the fluctuation frequency and amplitude can be adjusted as passive control parameters to maintain the desired responses.

2

Modification of the guitar bracing using optimization

Pilch Adam

Vibrations in Physical Systems

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2023

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Vol. 34, nr 2

art. no. 2023221

EN

The form of modern guitars were shaped by Spanish luthiers in the XIX century. Especially Antonio de Torres Jurado is the one, whose designs are an inspiration for modern constructions. From the very beginning, guitars are struggling with not sufficient sound levels for all the desired applications. Apart from electroacoustic amplification, there were several attempts to modify the construction of the sound hole or the soundboard. Higher sound pressure levels were often connected with distorted sound, sometimes not acceptable to musicians. In this paper, inequalities in the frequency characteristics of the sound generated by the guitar with modern sound holes are presented. Resonant frequencies of the soundboard were pointed as being responsible for the too high amplitude of sound in the 600-800 Hz frequency range. Using optimization and finite element method modelling, the best patterns of bracings were proposed to equalize the frequency spectrum and improve the sound of the instrument.

3

On some aspects of multiple scale method in problems of nonlinear dynamics

Awrejcewicz J., Starosta R., Sypniewska-Kamińska G.

Vibrations in Physical Systems

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2012

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Vol. 25

53--58

EN

Nonlinear vibrations of the two degree-of-freedom system near resonances are studied. The system is externally and kinematically driven. The dynamical problem is solved by an analytical multiple scales method (MS). This analytical approach gives very good results in solving problems of nonlinear dynamics and is more and more popular in last decades. The investigations are focused on correctness of MS method using various number of considered time scales. Namely, we show that in some cases the use of only two time scales is insufficient to detect all possible resonances exhibited by the studied system.

4

Parametrically excited non-linear systems: a comparison of two methods

El-Bassiouny A. F.

Mechanics and Mechanical Engineering

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2001

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Vol. 5, nr 1

21-40

EN

Subharmonic resonance of two-degree-of-freedom systems with cubic nonlinearities to multifrequency parametric excitations in the presence of three-to-one internal resonance is investigated. Two approximate methods (the multiple scales and the generalized synchronization) are used to construct a firs-order non-linear ordinary differential equations governing the modulation of the amplitudes and phases. Steady state solutions and their stability are computed for selected values of the system parameters. The results obtained by the two methods are in excellent agreement. Numerical solutions are carried out and graphical representations of the results are presented and discussed.