Nonreciprocal acoustics and dynamics in the in-plane oscillations of a geometrically nonlinear lattice.
Nonreciprocal acoustics and dynamics in the in-plane oscillations of a geometrically nonlinear lattice.
复制标题
几何非线性晶格面内振荡的不可逆声学和动力学。
作者：
Zhen Zhang;I. Koroleva;L. Manevitch;L. Bergman;A. Vakakis
我们研究了具有固定边界条件的非线性晶格的动力学和声学，该晶格由有限数量的通过线性弹簧耦合的粒子组成，经历面内振荡。这种晶格的强非线性的来源是由耦合线性弹簧的面内拉伸产生的几何效应。它已被证明，在低能量的限制，晶格产生了一个强非线性的声学真空，这是一个介质与零声速的定义在经典声学。声真空具有强烈的非局域耦合效应和一组正交的非线性驻波[或非线性正常模式（NNM）]，其模式形状与相应的线性晶格的模式相同;然而，与线性情况相反，除了具有最高波长的一个以外，所有NNM都是不稳定的。此外，晶格支持两种类型的波，即，对应于粒子的主要轴向振荡的近线性声波（称为“L波”）和对应于具有局部包络的粒子的主要横向振荡波包的强非线性局部传播脉冲（称为“NL脉冲”）。我们证明了在晶格的动力学和声学中存在非线性非互易现象。在低能极限下，研究了两种相反的情况。第一种情况引起非互易动力学，并对应于集体的，空间上延伸的横向加载的晶格，导致激发的个人，主要是横向NNM，而第二种情况下引起非互易声学考虑的晶格的响应空间本地化，横向脉冲或位移激励。我们证明了强烈的和经常性的能量交换之间的直接激发的NNM和其他NNM具有较高的波数，因此，从小到大波数的非互易能量交换建立。此外，我们表明存在的非互易波相互作用现象的形式不可逆的有针对性的能量转移从L波NL脉冲在这两种类型的波的碰撞。额外的非互惠声学以复杂的“级联过程”以及L波和静止离散呼吸者之间的非互惠相互作用的形式被发现。计算结果证实了理论预言的晶格动力学向低能非线性声真空态的强非定域性跃迁。
We study the dynamics and acoustics of a nonlinear lattice with fixed boundary conditions composed of a finite number of particles coupled by linear springs, undergoing in-plane oscillations. The source of the strongly nonlinearity of this lattice is geometric effects generated by the in-plane stretching of the coupling linear springs. It has been shown that in the limit of low energy the lattice gives rise to a strongly nonlinear acoustic vacuum, which is a medium with zero speed of sound as defined in classical acoustics. The acoustic vacuum possesses strongly nonlocal coupling effects and an orthogonal set of nonlinear standing waves [or nonlinear normal modes (NNMs)] with mode shapes identical to those of the corresponding linear lattice; in contrast to the linear case, however, all NNMs except the one with the highest wavelength are unstable. In addition, the lattice supports two types of waves, namely, nearly linear sound waves (termed "L waves") corresponding to predominantly axial oscillations of the particles and strongly nonlinear localized propagating pulses (termed "NL pulses") corresponding to predominantly transverse oscillating wave packets of the particles with localized envelopes. We show the existence of nonlinear nonreciprocity phenomena in the dynamics and acoustics of the lattice. Two opposite cases are examined in the limit of low energy. The first gives rise to nonreciprocal dynamics and corresponds to collective, spatially extended transverse loading of the lattice leading to the excitation of individual, predominantly transverse NNMs, whereas the second case gives rise to nonreciprocal acoutics by considering the response of the lattice to spatially localized, transverse impulse or displacement excitations. We demonstrate intense and recurring energy exchanges between a directly excited NNM and other NNMs with higher wave numbers, so that nonreciprocal energy exchanges from small-to-large wave numbers are established. Moreover, we show the existence of nonreciprocal wave interaction phenomena in the form of irreversible targeted energy transfers from L waves to NL pulses during collisions of these two types of waves. Additional nonreciprocal acoustics are found in the form of complex "cascading processes, as well as nonreciprocal interactions between L waves and stationary discrete breathers. The computational studies confirm the theoretically predicted transition of the lattice dynamics to a low-energy state of nonlinear acoustic vacum with strong nonlocality.