周期薄壁开口梁中的双耦合振动带隙

本文研究了由两种材料组合构成的周期性薄壁开口梁的弯曲和扭转双耦合振动。基于双耦合振动方程，给出了平面波展开法。当填充比不变时，晶格常数是影响带隙相对宽带的一个因素；当晶格常数和填充比不变时，杨氏模量是影响带隙宽带的主要因素，而不是密度。利用有限元法计算了有限周期结构的振动频率响应，在带隙频率范围内，振动衰减40dB左右。这些发现对于声子晶体的应用具有重要意义。     

Triply coupled vibrations of thin-walled open cross-section beams including rotary inertia effects

An exact analytical method is presented for predicting the undamped natural frequencies of beams with thin-walled open cross-sections having no axis of symmetry. The governing differential equations give a characteristic equation of the 12th order with real coefficients. The roots are found numerically and the exact boundary conditions are considered especially for free ends to obtain natural frequencies. The simpler cases of neglecting cross-sectional warping and/or rotary inertia are also dealt with. It is seen that when the effect of rotary inertia is neglected significant errors incur for some boundary conditions, cross-section thicknesses and mode numbers. This is more profound when the warping effect is taken into account.     

Acoustic waves in thin-walled elastic tube with polymeric solution

Acoustic waves in a pipe with polymeric liquid are investigated within a quasi-one-dimensional approach. Analysis of the dispersion equation has shown that rheological features lead to essential changes in both attenuation and speed of the sound. The results may find application in acoustic rheometry of polymeric liquids and for modeling of fast dynamic processes in polymer production technology.     

Non-linear free torsional vibrations of thin-walled beams with bisymmetric cross-section

A finite element method for studying non-linear free torsional vibrations of thin-walled beams with bisymmetric open cross-section is presented. The non-linearity of the problem arises from axial loads generated at moderately large amplitude torsional vibrations due to immovability of end supports. The derivation of the fundamental differential equation of the problem is based on the classical assumption of a thin-walled beam with a non-deformable cross-section. The non-linear eigenvalue problem is solved iteratively by series of linear eigenvalue problems until the required accuracy is obtained. Non-linear frequencies, fundamental mode shapes and axial loads computed for various amplitude of torsional vibrations of thin-walled I beams are included.     

Growth of Raman-Stokes waves in focused pump beams

A theoretical analysis of the process of forward and backward Raman-Stokes pulse growth in a focused pump beam is presented. The position of the peak of the Stokes pulse duration build-up is determined as a function of the focusing lens. Numerical integration of the propagation equations shows strong modulation in the backward Stokes wave and high efficiency     

Generation of internal waves in fluids by sound beams

The nonlinear interaction between internal and sound waves in a two-component fluid due to the time modulation of the convective component of fluid interface velocity is considered.     

Power flow in coupled bending and longitudinal waves in beams

In complex structures, curvature and impedance discontinuities (e.g., junctions) couple bending and longitudinal waves. Propagation losses for longitudinal waves are often much less than losses for bending waves, and damping treatments often less effective on longitudinal waves. When the dissipation in longitudinal waves is less than that on bending waves, longitudinal waves can provide an efficient means of power flow between bending waves generated at one location and bending waves that are a source of acoustic radiation at another location. In order to design and locate effective treatments, knowledge of the power flow in longitudinal as well as bending waves is required. The measurement of power in both bending and longitudinal waves when both waves are present is demonstrated. Measurements conducted on a straight beam and a T-beam are compared to predictions obtained using finite element methods. The effect of coupling between waves at the junction in a T-beam is illustrated using results from measurements of power flow.     

Localization of elastic waves in randomly disordered multi-coupled multi-span beams

Abstract

The wave localization in randomly disordered periodic multi-span continuous beams is studied. The transfer matrix method is used to deduce transfer matrices of two kinds of multi-span beams. To calculate the Lyapunov exponents in discrete dynamical systems, the algorithm for determining all the Lyapunov exponents in continuous dynamical systems presented by Wolf et al is employed. The smallest positive Lyapunov exponent of the corresponding discrete dynamical system is called the localization factor, which characterizes the average exponential rates of growth or decay of wave amplitudes along the randomly mistuned multi-span beams. For two kinds of disordered periodic multi-span beams, numerical results of localization factors are given. The effects of the disorder of span-length, the non-dimensional torsional spring stiffness and the non-dimensional linear spring stiffness on the wave localization are analysed and discussed. It can be observed that the localization factors increase with the increase of the coefficient of variation of random span-length and the degree of localization for wave amplitudes increases as the torsional spring stiffness and the linear spring stiffness increase.     

Self-similar counter-propagating beams of electromagnetic waves in nonlinear cubic media

We study the structure of the self-similar beams of counter-propagating electromagnetic waves in nonlinear cubic media. Eigenfrequencies of two-mirror quasi-optical resonators, whose eigen-modes are self-similar beams of counter-propagating waves, are found.     

Localization of elastic waves in randomly disordered multi-coupled multi-span beams

The wave localization in randomly disordered periodic multi-span continuous beams is studied. The transfer matrix method is used to deduce transfer matrices of two kinds of multi-span beams. To calculate the Lyapunov exponents in discrete dynamical systems, the algorithm for determining all the Lyapunov exponents in continuous dynamical systems presented by Wolf et al is employed. The smallest positive Lyapunov exponent of the corresponding discrete dynamical system is called the localization factor, which characterizes the average exponential rates of growth or decay of wave amplitudes along the randomly mistuned multi-span beams. For two kinds of disordered periodic multi-span beams, numerical results of localization factors are given. The effects of the disorder of span-length, the non-dimensional torsional spring stiffness and the non-dimensional linear spring stiffness on the wave localization are analysed and discussed. It can be observed that the localization factors increase with the increase of the coefficient of variation of random span-length and the degree of localization for wave amplitudes increases as the torsional spring stiffness and the linear spring stiffness increase.     

Transverse shear deformability in the dynamics of thin-walled composite beams: consistency of different approaches

The aim of this work is to describe an analysis of the transverse shear deformability in the dynamics of thin-walled composite beams. Some thin-walled-composite-beam models, which are derived by means of different approaches (principle of virtual works and principle of Hellinger-Reissner among others), show substantial discrepancies due to the employment of different constitutive equations based on the aforementioned approaches. In the following paragraphs a comparison of different schemes and hypotheses related to constitutive equations for thin-walled composite beams is performed.