Dynamical instability of laminated plates with external cutout

A method to study dynamical instability and non-linear parametric vibrations of symmetrically laminated plates of complex shapes and having different cutouts is proposed. The first-order shear deformation theory (FSDT) and the classical plate theory (CPT) are used to formulate a mathematical statement of the given problem. The presence of cutouts essentially complicates the solution of buckling problem, since the stress field is non-uniform. At first, a plane stress analysis is carried out using the variational Ritz method and the R-functions theory. The obtained results are applied to investigate buckling and parametric vibrations of laminated plates. The developed method uses the R-functions theory, and it may be directly employed to study laminated plates of arbitrary forms and different boundary conditions. Besides, the proposed method is numerical-analytical, what greatly facilitates a solution of similar-like non-linear problems. In order to show the advantage of the developed approach, instability zones and response curves for the layered cross- and angle-ply plates with external cutouts are constructed and discussed.     

Harvesting vibrations via 3D phononic isolators

We report on the existence of unidirectional phononic band gaps that may span over extended regions of the Brillouin zone and can find application in trapping elastic (acoustic) waves in properly designed multilayered 3D structures. Phononic isolators operate as a result of asymmetrical wave transmission through a slab of a crystallographic phononic structure with broken mirror symmetry. Due to the use of lossless materials in the crystal, the absorption rate is dramatically enhanced when the proposed isolator is placed next to a vibrational harvesting cell.     

Nonlocal three-dimensional theory of elasticity with application to free vibration of functionally graded nanoplates on elastic foundations

In the present work, a three-dimensional (3D) elastic plate model capturing the small scale effects is developed for the free vibration of functionally graded (FG) nanoplates resting on elastic foundations. The theoretical model is formulated employing the nonlocal differential constitutive relations of Eringen in conjunction with the 3D equations of motion of elasticity.The material properties are assumed to vary continuously along the thickness of the nanoplate in accordance with the power law formulation. Through extending the generalized differential quadrature (GDQ) method to the three-dimensional case, the governing equations are simultaneously discretized in every three coordinate directions and are then recast to the standard form of an eigen value problem. Solving the acquired problem, the natural frequencies of the nanoplates with different boundary conditions are calculated. The convergence behavior of the numerical results is checked out and comparison studies are conducted to make sure of the accuracy and reliability of the present model. Finally, the dependence of the vibration behavior of the nanoplate on edge conditions, elastic coefficients of the foundation, scale coefficient, mode number, material and geometric parameters are discussed.     

Investigating the effect of interphase and surrounding resin on carbon nanotube free vibration behavior

The free vibration analysis of a carbon nanotube (CNT) embedded in a volume element is performed using 3D finite element (FE) and analytical models. Three approaches consist of molecular and continuum mechanics FE methods and continuum analytical method are employed to simulate the CNT, interphase region and surrounding matrix. The bonding between CNT and polymer is treated as non-perfect bonding using van der Waals and triple phase material interaction in first and second approaches. In analytical approach a perfect bonding is assumed between nanotube and matrix. First, natural frequencies of CNT under different boundary conditions and aspect ratios are obtained by three approaches and the results are compared with published data. The results show the frequency response variations of CNT in GHz to THz range. Subsequently, vibration behaviors of CNT/polymer are evaluated and the results revealed the importance of interphase region role in the performance of nanocomposites. The results also showed the convergence of the natural frequencies for 1–2.5% of CNT volume in high aspect ratios using three methods, so that the interphase effects is negligible. In addition, it is observed that the molecular method due to interphase role has proper performance in vibration behavior investigation of volume elements.     

Comparative DFT study of Raman spectra of phosphorus-containing dendrimers built from thiophosphoryl,cyclotriphosphazene and phthalocyanine cores

The FT Raman spectra of the zero and first generations of phosphorus-containing dendrimers built from thiophosphoryl, cyclotriphosphazene and phthalocyanine core with terminal oxybenzaldehyde groups have been recorded and analyzed. The structural optimization and normal mode analysis were performed for dendrimers on the basis of the density functional theory (DFT). The calculated geometrical parameters, harmonic vibrational frequencies and Raman scattering activities are predicted in a good agreement with the experimental data. The experimental Raman spectra of dendrimers were interpreted by means of potential energy distribution. Relying on DFT calculations the lines of the cores, repeating units and terminal groups of dendrimers were assigned.The influence of the encirclement on the line frequencies and intensities was studied and due to the predictable, controlled and reproducible structure of dendrimers the information, usually inaccessible is obtained. The strong line at 1600 cm⁻¹ show marked changes of intensity in dependence of aldehyde (CHO) or azomethyne (CHN) substituents in the aromatic ring. The polarizabilities and lipophilicity of dendrimers were estimated.     

Damping analysis of nonwoven natural fibre-reinforced polypropylene composites used in automotive interior parts

The aim of this work is to evaluate the dynamic properties of nonwoven flax, hemp, kenaf and glass fibre-reinforced polypropylene (PP) composites. Also, the influence of some parameters, such as the type of reinforcement, the fibre/matrix weight ratio, the fibre orientation and the porosity content, on the damping behaviour of these nonwoven composites is investigated. To this end, a free flexural vibrations analysis was conducted to experimentally identify their natural frequencies and their associated loss factors. The obtained results show that the nonwoven composites reinforced by natural fibres present higher loss factors compared with those of the glass-PP composite. These interesting damping properties make these nonwoven composites very attractive for automotive applications where the dissipation of vibrations is highly requested.     

On the Role of Symmetry in Vibrational Strong Coupling: The Case of Charge‐Transfer Complexation

It is well known that symmetry plays a key role in chemical reactivity. Here we explore its role in vibrational strong coupling (VSC) for a charge‐transfer (CT) complexation reaction. By studying the trimethylated‐benzene–I₂ CT complex, we find that VSC induces large changes in the equilibrium constant K_DA of the CT complex, reflecting modifications in the ΔG° value of the reaction. Furthermore, by tuning the microfluidic cavity modes to the different IR vibrations of the trimethylated benzene, ΔG° either increases or decreases depending only on the symmetry of the normal mode that is coupled. This result reveals the critical role of symmetry in VSC and, in turn, provides an explanation for why the magnitude of chemical changes induced by VSC are much greater than the Rabi splitting, that is, the energy perturbation caused by VSC. These findings further confirm that VSC is powerful and versatile tool for the molecular sciences.     

Shape stability of a gas bubble in a soft solid

Predicting the onset of non-spherical oscillations of bubbles in soft matter is a fundamental cavitation problem with implications to sonoprocessing, polymeric materials synthesis, and biomedical ultrasound applications. The shape stability of a bubble in a Kelvin-Voigt viscoelastic medium with nonlinear elasticity, the simplest constitutive model for soft solids, is analytically investigated and compared to experiments. Using perturbation methods, we develop a model reducing the equations of motion to two sets of evolution equations: a Rayleigh-Plesset-type equation for the mean (volume-equivalent) bubble radius and an equation for the non-spherical mode amplitudes. Parametric instability is predicted by examining the natural frequency and the Mathieu equation for the non-spherical modes, which are obtained from our model. Our theoretical results show good agreement with published experiments of the shape oscillations of a bubble in a gelatin gel. We further examine the impact of viscoelasticity on the time evolution of non-spherical mode amplitudes. In particular, we find that viscosity increases the damping rate, thus suppressing the shape instability, while shear modulus increases the natural frequency, which changes the unstable mode. We also explain the contributions of rotational and irrotational fields to the viscoelastic stresses in the surroundings and at the bubble surface, as these contributions affect the damping rate and the unstable mode. Our analysis on the role of viscoelasticity is potentially useful to measure viscoelastic properties of soft materials by experimentally observing the shape oscillations of a bubble.     

中性线修正型变截面梁类构件压电控制

传统绝对节点坐标法(absolute nodal coordinate formulation,ANCF)在变截面梁类构件建模过程中常以几何中位线等效构造单元中性线,难以对变截面单元位移场状态进行精确描述.为解决此类问题,本文以中细型变截面梁类构件为研究对象,深入考虑变截面结构几何因素及复合材料属性对变截面梁类构件中性...     

Chatter mitigation using the nonlinear tuned vibration absorber

A passive vibration absorber, termed the nonlinear tuned vibration absorber (NLTVA), is designed for the suppression of chatter vibrations. Unlike most passive vibration absorbers proposed in the literature for suppressing machine tool vibrations, the NLTVA comprises both a linear and a nonlinear restoring force. Its linear characteristics are tuned in order to optimize the stability properties of the machining operation, while its nonlinear properties are chosen in order to control the bifurcation behavior of the system and guarantee robustness of stable operation. In this study, the NLTVA is applied to turning machining.