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1

Wave propagation and free vibration of FG graphene platelets sandwich curved beam with auxetic core resting on viscoelastic foundation via DQM

Al Mukahal F. H. H., Sobhy Mohammed

Archives of Civil and Mechanical Engineering

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2022

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Vol. 22, no. 1

art. no. e12, 2022

EN

A novel shear and normal deformations theory is presented in this article to illustrate the wave propagation and free vibration of three-layer sandwich curved beams subjected to elevated temperature and moisture environments and resting on viscoelastic foundation. The upper and lower layers are made of metal matrix reinforced with functionally graded (FG) graphene platelets (GPLs). While, the core layer is made of auxetic honeycomb structures. For the layers to be more bonded, the matrix of the face layers and the auxetic layer are both made of aluminum material. The volume fraction of GPLs is varied through the thickness of the face layers according to a layer-wise rule. The modified Halpin–Tsai model is used to describe the effective material properties of the face layers. Four types of GPLs distribution are considered in the present analysis. The differential quadrature method (DQM) is employed to discretize the equations of motion and then converted to a system of algebraic equations. This system can be solved to obtain the natural frequencies of the sandwich curved beams. Whereas, the wave dispersion relations are determined by solving the motion equations analytically. Convergence and comparison examples are presented to adjust and validate the present solution. In addition, comprehensive parametric studies are performed to investigate the effects of the weight fraction of GPLs, temperature, moisture concentrations, core thickness, boundary conditions, and viscoelastic foundation stiffness on the natural frequency, wave frequency and phase velocity of the honeycomb sandwich curved beams.

2

The use of genetic algorithm for identification of vibration model on the example of Bernoulli-Euler beam

Cekus D., Waryś P.

Vibrations in Physical Systems

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2010

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Vol. 24

75--80

EN

In the paper, in the discrete-continuous model, the spring constants replacing the rotational and translational restrained end of the Bernoulli-Euler beam have been identified on the basis experimental investigations and formulation of optimization problem. The mathematical model of free vibration problem of analyzed system has been formulated and solved according to the Lagrange multiplier formalism. Frequencies and mode shapes of free vibration, which have been obtained from the experimental investigations, have been used to formulate optimization problem. Optimization has been based on the genetic algorithm. The presented proceeding’s stages allow identification any parameters of discrete-continuous systems.

PL

W pracy na podstawie przeprowadzonych badań eksperymentalnych oraz sformułowania zadania optymalizacyjnego zidentyfikowano stałe sprężystości sprężyn rotacyjnej i translacyjnej zastępujących w modelu dyskretno-ciągłym zamocowanie jednostronne belki Bernoulliego-Eulera. Model matematyczny zagadnienia drgań swobodnych analizowanego układu został sformułowany i rozwiązany zgodnie z formalizmem mnożników Lagrange’a. Jako rezultat przeprowadzonych badań eksperymentalnych otrzymano częstości i postacie drgań własnych, które wykorzystano do sformułowania zagadnienia optymalizacyjnego. Algorytm optymalizacyjny bazował na algorytmie genetycznym. Przedstawione etapy postępowania pozwalają na identyfikację dowolnych parametrów układów dyskretno-ciągły.

3

Longitudinal vibrations of an elastically connected double-rod complex system. Part 2, Forced vibrations

Oniszczuk Z.

Vibrations in Physical Systems

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2006

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Vol. 22

297--302

4

Free vibration of a two member column loaded by a stretching rod

Tomski L., Szmidla J., Gołebiowska-Rozanow M.

Vibrations in Physical Systems

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2004

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Vol. 21

379--382

EN

The problem of free vibrations of two-member column loaded by a stretching road is considered in the paper. An influence of rigidity asymmetry on the bending between stretching element of the system and column rods is analysed. An influence of rigid mounting of the loading element on the critical load and on the course of free vibration frequency in relation to the external load is also analysed. Numerical computations are supported by appropriate results of experimental investigations.