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1

Vibration reduction assessment of layered acoustic metamaterial

Świrk Patrycja, Żyłka Wojciech, Leniowska Lucyna, Grochowina Marcin

Vibrations in Physical Systems

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2022

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Vol. 33, nr 2

art. no. 2022221

EN

Acoustic meta-materials offer an approach to reducing the vibration and noise transmission through layered panels. In this paper, the investigation of constructed meta-material for reduction of low-frequency vibration and noise is a major concern. The key concept underlying this approach is to construct the metamaterial as a highly-distributed system of tuned point masses that introduce instead of low resonance frequency one or more bands of higher frequency. They can be then successfully damped with passive methods. Using the modes method, a metamaterial system with distributed point masses integrated into the honeycomb core was designed to be a representative layered panel. To determine the dynamic response of the global sandwich panel, the metamaterial system was tested for 70 Hz and 120 Hz excitation. The obtained results confirm the possibility of tuning the considered layered meta-material to the excitation frequency and shifting low frequencies towards higher frequencies.

2

A discrete model for geometrically nonlinear free and forced vibrations of stepped and continuously segmented Euler-Bernoulli AFG beams (SAFGB) carrying point masses

Moukhliss Anass, Rahmouni Abdellatif, Bouksour Othman, Benamar Rhali

Diagnostyka

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2022

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Vol. 23, No. 4

art. no. 2022401

EN

A discrete model is applied to handle the geometrically nonlinear free and forced vibrations of beams consisting of several different segments whose mechanical characteristics vary in the length direction and contain multiple point masses located at different positions. The beam is presented by an N degree of freedom system (N-Dof). An approach based on Hamilton's principle and spectral analysis is applied, leading to a nonlinear algebraic system. A change of basis from the displacement basis to the modal basis has been performed. The mechanical behavior of the N-Dof system is described in terms of the mass tensor mij, the linear stiffness tensor kij, and the nonlinear stiffness tensor bijkl. The nonlinear vibration frequencies as functions of the amplitude of the associated vibrations in the free and forced cases are predicted using the single mode approach. Once the formulation is established, several applications are considered in this study. Different parameters control the frequency-amplitude dependence curve: the laws that describe the variation of the mechanical properties along the beam length, the number of added masses, the magnitude of excitation force, and so on. Comparisons are made to show the reliability and applicability of this model to non-uniform and non-homogeneous beams in free and forced cases.

3

A multimode approach to geometrically non-linear forced vibration of beams carrying point masses

Fakhreddine Hatim, Adri Ahmed, Chajdi Mohcine, Rifai Said, Benamar Rhali

Diagnostyka

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2020

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Vol. 21, No. 4

23--33

EN

The present work deals with the geometrically non-linear forced vibrations of beams carrying a concentric mass under different end conditions. Considering the axial strain energy and expanding the transverse displacement in the form of a finite series of spatial functions, the application of Hamilton's principle reduces the vibration problem to a non-linear algebraic system solved by an approximate method developed previously. In order to validate the approach, comparisons are made of the present solutions with those previously obtained by the finite element method. Focus is made here on the analysis of the non-linear stress distribution in the beam with an attached mass. The non-linear forced deflection shapes and their corresponding curvatures are presented for different magnitudes of the attached mass, different excitation levels and different vibration amplitudes.

4

On small vibrations of a damped Stieltjes string

Boyko O., Pivovarchik V.

Opuscula Mathematica

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2015

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Vol. 35, no. 2

143--159

EN

Inverse problem of recovering masses, coefficients of damping and lengths of the intervals between the masses using two spectra of boundary value problems and the total length of the Stieltjes string (an elastic thread bearing point masses) is considered. For the case of point-wise damping at the first counting from the right end mass the problem of recovering the masses, the damping coefficient and the lengths of the subintervals by one spectrum and the total length of the string is solved.

5

Periodic control of the bar with point mass

Bieda M., Piekarski Z.

Mechanics / AGH University of Science and Technology

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2008

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Vol. 27, no. 4

131-137

EN

The following article discusses the usage of optimization theory with quasi periodic control to form a vibrating bar with point mass that is situated on the bar's axis. The maximum principle was changed and used to calculate a numerical sample. The principle uses the new condition for optimisation containing several constituent hamiltonians. The hamiltonians facilitated the calculation of the quasi periodic controls. The result of the calculation was a numerical sample, which specified how the quasi-periodic cross-section of the bar depends on the mass and the point of the mass position along the bar's axis.

PL

W artykule zaprezentowano zastosowanie teorii optymalizacji z quasi-okresowym sterowaniem do kształtowania drgającego podłużnie pręta z masą punktową umieszczoną na jego osi. Do obliczeń wykorzystana została zmieniona zasada maksimum, w której występuje nowy warunek optymalności z sumą hamiltonianów składowych pozwalający wyznaczyć quasi-okresowe sterowania. W pracy przeliczony został numeryczny przykład, w którym określono, w jaki sposób quasi-okresowy przykrój poprzeczny pręta zależy od wielkości masy i punktu jej przyłożenia na osi tego pręta.