多孔压电分流超材料及其带隙特性研究

设计了一种新型多孔压电分流超材料构型,以单、双孔元胞构型为例,研究了其带隙特性和有限周期振动传递特性,并与未开孔压电分流超材料板进行了对比分析.计算结果表明:与未开孔压电超材料相比,两种构型在低频处的压电局域共振带隙频率更低,带宽变窄,且均会在高频范围内出现额外带隙,随着孔宽δ的增大,额外带隙数量逐渐增多;对应特定的孔...     

超材料混凝土的带隙特征及对冲击波的衰减效应

借鉴超材料的研究思路,在混凝土中引入谐振骨料,设计出具有消波特性的超材料混凝土。首先,通过结构动力学方法计算超材料混凝土的有效质量,从而建立了超材料混凝土带隙起始频率及截止频率的简化模型,并给出了带隙起始频率及截止频率的理论表达式。然后,分析了涂层弹性模量、芯柱密度、基体密度、骨料体积占比和芯柱边长与软涂层厚度比对超材料混凝土带隙特征的影响。最后,采用数值模拟的方法,对比了超材料混凝土和普通混凝土对冲击波的衰减效应。研究结果表明:(1)低弹性模量涂层能够形成低频带隙,但带隙宽度较窄,而高弹性模量涂层能够形成较宽的带隙,但带隙起始频率较高;(2)通过选择高密度芯柱材料和低密度基体材料,可以得到低频、宽带隙特征;(3)通过增大骨料体积占比和芯柱边长与软涂层厚度比可以实现扩宽带隙的目的;(4)与普通混凝土相比,超材料混凝土对冲击波具有更好的衰减作用。     

Bistable attachments for wideband nonlinear vibration attenuation in a metamaterial beam

Nonlinear Dynamics - This work investigates the amplitude-dependent dynamics of a locally resonant metamaterial beam with bistable attachments. The concept that was previously demonstrated for a...     

The constrained elastic beam

Summary The theory of variational inequalities is applied to the problem of equilibrium of a constrained elastic beam. Existence, unicity and regularity of solutions are discussed.

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Sommario La teoria delle disequazioni variazionali è applicata al problema dell'equilibrio della trave elastica soggetta a vincoli. Si trattano le questioni di esistenza, unicità e regolarità della soluzione.

     

Nonlinear vibration of a beam with asymmetric elastic supports

Nonlinear Dynamics - Under the conditions of horizontal placement and only considering geometric nonlinearity, depending on the boundary constraints, primary resonances of an elastic beam exhibit...     

Tunable three-dimensional nonreciprocal transmission in a layered nonlinear elastic wave metamaterial by initial stresses

In this work, the three-dimensional(3 D) propagation behaviors in the nonlinear phononic crystal and elastic wave metamaterial with initial stresses are investigated.The analytical solutions of the fundamental wave and second harmonic with the quasilongitudinal(qP) and quasi-shear(qS1 and qS2) modes are derived. Based on the transfer and stiffness matrices, band gaps with initial stresses are obtained by the Bloch theorem.The transmission coefficients are calculated to support the band gap prope...     

Emergent scale behaviour in the effective equations for an elastic metamaterial

Asymptotic homogenisation of an elastic metamaterial consisting of a series of plates interspaced by a fluid is considered. It is shown that the usual method must be extended by the inclusion of a second macroscale, the “emergent scale”, in order to correctly capture the behaviour of this metamaterial at low frequency. The leading order solutions for plane wave propagation are found and the effective constitutive equations derived. At leading order, the dispersion curves for plane wave propagation depend on the direction of propagation and the branch associated with the emergent scale is dispersive. The effective constitutive equations contain some terms, associated with the shear normal to the plates, for which stress is not proportional to strain but rather depends on the third derivative of the normal displacement with respect to transverse position. These terms are not present in the usual form of the Willis equations and the effective fields are non-analytic functions of frequency as the frequency tends to zero.     

Natural vibration of a sandwich beam on an elastic foundation

The natural vibration of an elastic sandwich beam on an elastic foundation is studied. Bernoulli’s hypotheses are used to describe the kinematics of the face layers. The core layer is assumed to be stiff and compressible. The foundation reaction is described by Winkler’s model. The system of equilibrium equations is derived, and its exact solution for displacements is found. Numerical results are presented for a sandwich beam on an elastic foundation of low, medium, or high stiffness __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 5, pp. 57–63, May 2006.     

On the large amplitude oscillations of a thin elastic beam

This paper is concerned with the finite amplitude, free, planar oscillations of a thin elastic beam. By assuming the motion to be inextensional but at the same time recognizing the existence of a resultant normal force acting on each cross-section of the beam a system of governing equations is derived which is manageable but still meaningful. For the case of the simply-supported beam a finite difference, Galerkin, and (regular) perturbation solutions are explicitly obtained. The results are compared and discussed. In the course of obtaining the various solutions it is found that an additional simplification in the form of the governing equations is possible. This simplification turns out to be quite important from a general point of view of obtaining approximate analytical solutions.