Blow-up of solution for beam equation with delay and dynamic boundary conditions

In this paper, we consider an elastic beam equation with delay, source term, and boundary conditions together with some suitable initial data. Using the Faedo-Galerkin approximation and some estimates, we get the local existence of solution. Moreover, we obtain the finite time blow-up of solution by constructing suitable Lyapunov functionals.     

Self-trapped dynamics of a hollow Gaussian beam in metamaterials

We present a systematic investigation on the dynamics of a hollow Gaussian beam (HGB) in metamaterials. We predict self-trapped propagation of HGBs and evolution of the beam is highly influenced by dimensionless dispersion coefficient (κ), which determines the strength of dispersion over diffraction. The evolutions of HGBs such as disappearance of single ringed intensity pattern and appearance of patterns with a central bright spot are achievable with less propagation distance in metamaterials with higher values of κ. On the other hand, metamaterials with low values of κ can preserve single ring intensity distribution over a long propagation distance without focusing. When the strength of dispersion over diffraction increases, it significantly influences the evolution of the beam and may lead to the formation of tightly focussed beam with high peak intensity at the center. The phenomenon of tight focussing is found to have some applications in trapping of nanosized particles.     

Influence of the torsional vibration of the periodically attached perpendicular beam resonator on the flexural band of a Euler-Bernoulli beam

The bending and torsional vibration of the periodic perpendicular cantilever beam-mass resonators (PCBMR) is idealized as translational and rotational oscillators attached to the main beam. In this paper, the effect of that torsional vibration of the PCBMR on the dynamics of an infinitely long Euler-Bernoulli beam is evaluated. The band-structure is explored by implementing the transfer matrix method in conjunction with Bloch-Floquet's theorem. The combination of the translational and rotational oscillator modifies the relative position of the coupling coefficient in the transfer matrix, which plays a pivotal role in the band-gap formation. The flexural band-structure is highly sensitive to the torsional vibration while the radius of gyration of the tip mass is considerably higher than the length of the PCBMR. Ill-tuning leads to split and reduction of attenuation band to 50%; whereas, around 38% elongation of the attenuation band in the low frequency regime can be achieved by proper tuning.     

Biomolecular Release Stimulated by Electrochemical Signals at a Very Small Potential Applied

DNA release electrochemically stimulated by applying ?10 mV on the modified electrode was studied. The release process was based on the local (interfacial) pH change produced upon H₂O₂ reduction electrocatalyzed by the immobilized microperoxidase‐11. SiO₂ nanoparticles attached to the electrode surface and functionalized with trigonelline and boronic acid species changed their electrical charge from positive to negative upon the interfacial pH change, thus allowing electrostatic adsorption of negatively charged DNA on the positive interface and then its repulsion/release from the negative interface. The loaded/released DNA molecules were labeled with a fluorescent dye to allow easy detection of the released DNA molecules. The important feature of the developed system is the controlled DNA release upon applying very small electrical potential on the modified electrode.     

Influence of friction and asymmetric freeplay on the limit cycle oscillation in aeroelastic system: An extended Hénon’s technique to temporal integration

Nonlinear effects such as friction and freeplay on the control surfaces can affect aeroelastic dynamics during flight. In particular, these nonlinearities can induce limit cycle oscillations (LCO), changing the system stability, and because of this it is essential to employ computational methods to predict this type of motion during the aircraft development cycle. In this context, the present article presents a matrix notation for describing the Hénon’s method used to reduce errors when considering piecewise linear nonlinearities in the numerical integration process. In addition, a new coordinate system is used to write the aeroelastic system of equations. The proposal defines a displacement vector with generalized and physical variables to simplify the computational implementation of the Hénon’s technique. Additionally, the article discusses the influence of asymmetric freeplay and friction on the LCO of an airfoil with control surface. The results show that the extended Hénon’s technique provides more accurate LCO predictions, that friction can change the frequency and amplitude of these motions, and the asymmetry of freeplay is important to determine the LCO behavior.     

椭球粒子声辐射力计算及分析

针对水下椭球粒子,以声散射理论为基础,采用分波序列的方法,建立了椭球粒子声辐射力的理论计算模型。进而根据声辐射力计算公式,以刚性椭球粒子和液体椭球粒子为例,计算并分析不同Bessel波束作用下椭球粒子的轴向声辐射力函数特征。数值仿真计算结果表明,对于刚性椭球粒子,扁平椭球粒子相对于细长椭球粒子更有助于激发负声辐射力；对于液体椭球粒子,细长椭球粒子相对于扁平椭球粒子更加容易产生负声辐射力；对于不同介质的椭球粒子,不同的入射波束激发的负声辐射力的效果也存在明显的差异。该结果为复杂的尺寸和介质粒子声操控技术提供了理论的可行性。     

平顶飞秒激光经圆锥透镜在熔融石英中成丝及超连续辐射

实验研究了平顶飞秒激光经圆锥透镜后在熔融石英中的成丝及超连续辐射.与高斯飞秒激光的成丝对比发现,平顶飞秒激光可以获得在圆锥透镜焦深区域内强度分布更为均匀的等离子体细丝,这一特征更有利于飞秒激光在固体介质中进行微纳加工等领域的应用.并且,在不损伤熔融石英的条件下,平顶飞秒激光成丝可以获得更高能量、更高转换效率的超连续辐射,这是因为若产生光强相近的细丝,平顶飞秒激光所需的初始激光能量更高,此激光能量下产生的细丝长度更长、均匀性更好.     

双稳态结构中的1/2次谐波共振及其对隔振特性的影响

以典型的双稳态系统——屈曲梁结构为例,基于等效模型,结合解析、数值和实验手段,研究了双稳态结构中的1/2次谐波共振特性、演化过程、参数调节规律及其对隔振特性的影响.研究发现,当非线性刚度系数或激励幅值增加到一定程度时,系统会在一定带宽下产生显著的1/2次谐波共振;随着激励幅值增加,阻尼系统的1/2次谐波遵循“产生-增强-衰退-消失”的过程,该过程对峰值频率和峰值传递率有重要影响;适当提高非线性强度能有效改善双稳态结构隔振特性.针对双稳态屈曲梁结构开展的实验验证了1/2次谐波特性和隔振特性变化规律.     

Anti-wear beam effects on gas–solid hydrodynamics in a circulating fluidized bed

Anti-wear beams installed on water walls of circulating fluidized bed (CFB) boilers are one of the most effective ways to protect against water-wall erosion. Beam effects from, for example, beam size and superficial gas velocity were investigated on gas–solid hydrodynamics in a CFB test rig using CFD simulations and experimental methods. The downward flow of the wall layer solids is observed to be disrupted by the beam but is then restored some distance further downstream. When falling solids from the wall layer hit the anti-wear beam, the velocity of the falling solids decreases rapidly. A fraction of the solids accumulates on the beam. Below the beams, the falling solids have reduced velocities but upward-moving solids were observed on the wall. The effect of the beam increases with width and superficial gas velocity. Wear occurs mainly above the beam and its variation with width is different above to below the beam. There is an optimum width that, when combined with beam height, results in less erosion.