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The dynamic response of periodically restrained flexural structures, modeled as Euler–Bernoulli beams supported by flexible and dissipative supports at equally spaced points, to moving loads is investigated. Bloch–Floquet theorem and modal analysis are used to examine the dispersion relation and band structure of the infinitely long periodic beam and the frequency spectrum of the finite beam, respectively. It is shown that the natural frequencies of the finite beam fall within the propagation bands of the corresponding infinite beam and get closer to each other as the number of spans increases ultimately covering the propagation bands. The dynamic response to moving load is obtained via a novel method based on Floquet transformation in the frequency domain for infinite periodic beams and through modal summation for finite periodic beams. Through numerical examples, the effect of boundary conditions, e.g. support stiffness and damping, and the impact of moving load speed on the flexural response as well as the energy stored and dissipated within the supports are discussed. [ABSTRACT FROM AUTHOR]

Abstract The subject of this article is analysis of transverse vibrations of beams which geometric and material properties vary periodically along the longitudinal axis. The aim is to present averaged models that take into account the shear deformation and geometric non-linearity, and to analyse transverse vibrations of such beams in moderately large deflection range. As the theoretical foundations, we use Timoshenko beam theory with von Kármán-type non-linearity. This results in obtaining new differential equations with constant coefficients, some of which explicitly depend on the beam inhomogeneity period size. Then, a reasonably simplified model is proposed to describe the vibrations of the considered beams in the low frequency range. The differential equations are transformed into a system of algebraic equations according to the Galerkin method. The response of the beam to transverse harmonic load is investigated by means of a pseudo arc-length continuation scheme. Non-linear coupling between vibration modes and the possibility of superharmonic resonance occurrence are taken into account. As an example of application, few special cases of beam geometry and boundary conditions are examined and compared. The results have the potential application to structural vibration control. [ABSTRACT FROM AUTHOR]

Abstract Wave propagation control in piezoelectric meta-structures has been developed in recent years, which focuses on coupling proper electric media via piezoelectric materials for elastic wave filtering properties within a low frequency range. In order to develop broadband band gaps and diversified wave propagation characteristics of mechanical meta-structures for different complex practical applications, the research proposes an innovative piezoelectric beam meta-structure using electronic negative capacitance dual-adjacent/staggered electrical connections. In the proposed meta-structures, a unit periodic cell composed of four adjacent primitive periodic cells (including four piezoelectric patches with different polarization directions) are connected to negative capacitance circuit shunts using electrical dual-adjacent/staggered patterns. Based on the Timoshenko beam theory and wave propagation theory, a theoretical modeling of the proposed meta-structure is established for evaluating wave propagation properties. Furthermore, wave attenuation performance of the proposed structure is investigated and compared with the traditional meta-structure with negative capacitance independent electronic networks in which negative capacitance shunts are independently applied to single piezoelectric patch or bimorph piezoelectric patches within a unit primitive periodic cell. Results show that the proposed innovative meta-structure utilizes less negative capacitance shunts for achieving better wave attenuation performance, and has more stable negative capacitance control system in practical applications. [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]

A topology optimization method is developed for microstructure design of heterogeneous periodic beam structure aiming at its extreme or specified effective stiffness. The effective stiffness is calculated using a FEM formulation of asymptotic homogenization method for heterogeneous periodic beam. Sensitivity of stiffness to the density design variable is derived analytically based on the solution of unit cell problems under corresponding generalized strain fields. Implementation of optimization procedure is generalized to take full advantage of commercial FEM software capabilities, with several examples presented to demonstrate its effectiveness. It is shown here the proposed method is extendible to periodic truss beam design. [ABSTRACT FROM AUTHOR]

Abstract: To determine the flexural vibration band gaps in periodic beams, the theoretical equations are derived by employing the Bloch–Floquet theorem and then solved by the use of the differential quadrature method. Moreover, a comprehensive parametric study is also conducted to highlight the influences of shear deformation, geometrical parameters and material parameters on the gaps. The results show that the method is efficient and accurate and that the bandwidth can be enlarged by changing the geometrical or material parameters. The existence of vibration gaps lends a new insight into vibration isolation applications in areas such as mechanical and civil engineering. [Copyright &y& Elsevier]

In this paper mathematical modelling of vibrations and stability problems for slender visco-elastic periodic beams is considered. In order to take into account the effect of microstructure a certain non-asymptotic approach is applied, called the tolerance modelling method. This technique allows to replace the equation with non-continuous, highly oscillating, periodic coefficients by a system of differential equations with constant coefficients. Moreover, the derived equations describe the effect of microstructure on the overall behaviour of the beams under consideration. In the framework of the tolerance modelling governing equations of two different tolerance models can be obtained – the standard and the general, under weakened assumptions. To evaluate the proposed general tolerance model obtained results are compared with results calculated within the known asymptotic homogenization, i.e. by the asymptotic model. In this note mathematical models describing investigated beams are only presented and illustrated by a simple example. [ABSTRACT FROM AUTHOR]