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• In the work dynamics of a 3-D periodic beam is investigated. • The beam is modelled by 6-node SFEs of smooth geometry optimised to predefined dynamic properties. • This results in the emergence of one common frequency band gap in the beam spectrum. • The common frequency band gap allows to use the beam a sound isolator or filter. • Numerical and optimisation results by TD-SFEM/FEM agree well with experimental ones by 1D-SLDV. This paper presents results of investigations on a three-dimensional (3-D) isotropic periodic beam. The beam can represent a vibroacoustic isolator of optimised dynamic characteristics in the case of its longitudinal, flexural and torsional behaviour. The optimisation process concerned both the widths as well as the positions of particular frequency band gaps that are present in the frequency spectrum of the beam. Since the dynamic behaviour of the beam is directly related to its geometry, through an optimisation process of the beam geometry, desired dynamic characteristics of the beam were successfully obtained. For the purpose of the optimisation process a new numerical model of the beam, based on the spectral finite element method in the time domain (TD-SFEM), was developed by the authors. This model enabled the authors to investigate the beam behaviour not only in a wide frequency spectrum, but also ensured a high accuracy of the model predictions. The accuracy of this modelling approach was checked against well-known analytical formulas. However, in the case of the optimised geometry of the beam for the verification of the correctness of the modelling approach a commercial finite element method (FEM) package was used. Finally, based on the results of numerical predictions and optimised geometry of the beam a sample for experimental verification was prepared. Experimental measurements were carried out by the authors by the application of one-dimensional (1-D) laser Doppler scanning vibrometry (LDSV). The results of experimental measurements obtained by the authors confirmed the correctness of the numerical predictions, showing a high degree of correspondence. [ABSTRACT FROM AUTHOR]

In this study, an Euler–Bernoulli beam carrying periodic arrays of meander-shaped beams is introduced. Each meander-shaped beam consists of several connected beam elements. Two models with different number of beam elements are considered. In each model, the effects of geometrical parameters on the lower and upper edges of the first three band gaps are investigated using the Adomian decomposition method. Results show that the wide band gaps at low frequency ranges can be obtained by changing the geometrical parameters. Furthermore, the band gaps are very close to each other for specific values of the geometrical parameters. Another advantage of this periodic beam is that its length is shorter than other types of periodic beams. These features make this periodic beam very useful in different applications of the band gap phenomenon such as vibration absorption. The finite element simulation (ANSYS software) is used to validate the analytical results and good agreement is found. [ABSTRACT FROM AUTHOR]

In this study, a new periodic beam model is introduced. This beam consists of the concentrated rigid masses and tapered beam elements with linearly variable width. The theoretical equations are derived by employing the Euler-Bernoulli beam and the Bloch–Floquet theorem and then solved using the generalized differential quadrature rule method to calculate the first two band gaps. The effects of the mass, mass moment of inertia and taper ratio on the widths and central frequencies of the first two band gaps are investigated. Results show that the wide band gaps at low frequency ranges can be obtained by changing the geometrical parameters. This is of interest for different applications of the band gap phenomenon such as broadband piezoelectric energy harvesting. Finally, the finite element simulation (ANSYS software) is used to validate the analytical method and good agreement is found. [ABSTRACT FROM AUTHOR]

This paper deals with the linear natural vibrations analysis of beams where the geometric and material properties vary periodically along the beam axis. In contrast with homogeneous prismatic beams, the frequency spectra of such beams are irregular as there exist enlarged intervals between some adjacent frequencies. Presented here are two averaged models of beams based on the tolerance modelling approach. The assumptions of classical Euler–Bernoulli and Timoshenko–Ehrenfest beam theories are adopted as the foundations. The resulting mathematical models are systems of differential equations with constant, weight-averaged coefficients. This makes it possible to apply any classical method of solution suitable for homogeneous beams, such as Galerkin orthogonalization. Here, emphasis is placed on the comparison of natural frequencies neighbouring the frequency band-gaps that are obtained from these two theories. Two basic cases of material and geometric property distribution in a periodicity cell are studied, and the natural frequencies and mode shapes are obtained for a simply supported beam. The results are supported by a comparison with the finite element method and partially exact solutions. [ABSTRACT FROM AUTHOR]