Measuring local and global vibration modes in model plants

Model plants are extensively used in biological studies, and their mechanical behaviour needs to be better understood, in relation to studies in mechanoperception for instance. We present here the first approach to derive experimentally the modal parameters of two of these plants, Arabidopsis thaliana and Populus tremula × alba. A classical sinusoidal sweep excitation is used, with a measurement of displacements based on LKT optical flow tracking, followed by a bi-orthogonal decomposition (BOD). This allows us to estimate several modal frequencies for each plant, as well as the corresponding spatial localizations of deformation. Analyzing the modal frequencies, we show that global and local modes correspond to distinct ranges of frequencies and depend differently on plant size. Possible phenotyping applications are then discussed.     

A fractional derivative model for single-link mechanism vibration

A model for a flexible pinned-free link is defined, which is based on a set of linear uncoupled equations and which is even valid for large rotations. A stress-strain relationship based on fractional derivatives is used to define the material properties. Experimental findings and numerical results are compared.

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Sommario Viene definito un modello matematico lineare per lo studio della dinamica di un meccanismo a membro unico deformabile. Tale modello é costituito da equazioni disaccoppiate che rappresentano sia il moto del corpo rigido di riferimento sia i contributi modali alla vibrazione. La relazione tensione deformazione del materiale considerato é definita a mezzo di derivoidi. I risultati ottenuti numericamente sono confrontati con registrazioni sperimentali.

     

A model of wall pressure correlation for prediction of turbulence-induced vibration

The vibration response of a structure excited by a turbulent boundary layer is investigated experimentally and numerically. First, the wall pressure in a high speed acoustic wind tunnel is characterized and the cross-spectral density is approximated using a Corcos model with frequency dependent correlation lengths and a modified Chase model. Both models agree quite well with the measured cross spectrum. Second, based on these turbulence models, the vibration response is predicted and compared to measurements. At lower frequencies both models perform well. In a higher frequency region, however, the vibration response is greatest for length scales that are much longer than the one given by the convection velocity of the turbulence, and in this frequency region only the modified Chase model works effectively.     

基于分子动力学与耗散粒子动力学串行耦合的面心立方金属粗粒化模型

通过全原子分子动力学(MD)与等温耗散粒子动力学(DPD)的串行耦合,提出了面心立方金属粗粒化模型的建立方法。该方法将一定数量的原子粗粒化为单个介观 DPD 粒子,假设 DPD 粒子间作用势的表达式为Sutton-Chen势函数形式,利用遗传算法,以 MD和DPD计算的单晶金属常温(298 K)等温线相一致为目标,确定了DPD粒子间作用势函数的参数。对单晶铜纳米棒的轴向拉伸开展 MD 和 DPD 对比模拟,发现在纳米棒弹性响应阶段,两者计算结果吻合较好,而屈服应力和屈服应变存在一定差距。建议在优化 DPD势函数参数时,引入更多的材料力学响应信息,进一步提高介观DPD模型的准确性。     

A coarse-grained model of the myofibril: Overall dynamics and the evolution of sarcomere non-uniformities

A theoretical framework for predicting the macroscopic behavior of a muscle myofibril based on the collective behavior of sarcomeres is presented. The analysis is accomplished by rigorously transforming the nonlinear dynamics of an assemblage of sarcomeres into a partial differential equation for the probability distribution function of sarcomere lengths in the presence of stochastic temporal fluctuations and biological variability. This enables the study of biologically relevant specimens with reasonable computational effort. The model is validated by a comparison to quantitative experimental results. Further, it reproduces experimental observations that cannot be explained by standard single sarcomere models, and provides new insights into muscle function and muscle damage during cyclic loading. We show that the accumulation of overstretched sarcomeres, which is related to muscle damage, depends on a delicate interplay between the dynamics of a large number of sarcomeres and the load characteristics, such as its magnitude and frequency. Further, we show that biological variability rather than stochastic fluctuations are the main source for sarcomere non-uniformities.     

A novel fractional-order model and controller for vibration suppression in flexible smart beam

Nonlinear Dynamics - Vibration suppression represents an important research topic due to the occurrence of this phenomenon in multiple domains of life. In airplane wings, vibration can cause...     

逐孔起爆震动参数预报的BP神经网络模型

根据神经网络理论,结合逐孔起爆技术的特点,建立了爆破震动参数预报的BP网络模型。以某矿 山深孔台阶爆破为例,利用逐孔起爆过程中收集的原始资料和爆破震动监测数据,对建立的BP网络模型进 行了训练和应用。与实测值比较后发现,BP网络模型的预报结果更接近实测值。     

Free vibration analysis of elastic rods using global collocation

This paper investigates the performance of a novel global collocation method for the eigenvalue analysis of freely vibrated elastic structures when either basis or shape functions are used to approximate the displacement field. Although the methodology is generally applicable, numerical results are presented only for rods in which one-dimensional basis functions in the form of a power series, as well as equivalent Lagrange, Bernstein or Chebyshev polynomials are used. The new feature of the proposed methodology is that it can deal with any type of boundary conditions; therefore, the cases of two Dirichlet as well as one Dirichlet and one Neumann condition were successfully treated. The basic finding of this work is that all these polynomials lead to results identical to those obtained by the power series expansion; therefore, the solution depends on the position of the collocation points only.     

A reduced-order flow model for vocal fold vibration: From idealized to subject-specific models

We present a reduced-order model for fluid–structure interaction (FSI) simulation of vocal fold vibration during phonation. This model couples the three-dimensional (3D) tissue mechanics and a one-dimensional (1D) flow model that is derived from the momentum and mass conservation equations for the glottal airflow. The effects of glottal entrance and pressure loss in the glottis are incorporated in the flow model. We consider both idealized vocal fold geometries and subject-specific anatomical geometries segmented from the MRI images of rabbits. For the idealized vocal fold geometries, we compare the simulation results from the 1D/3D hybrid FSI model with those from the full 3D FSI simulation based on an immersed-boundary method. For the subject-specific geometries, we incorporate previously estimated tissue properties for individual samples and compare the results with those from the high-speed imaging experiment of in vivo phonation. In both setups, the comparison shows good agreement in the vibration frequency, amplitude, phase delay, and deformation pattern of the vocal fold, which suggests potential application of the present approach for future patient-specific modeling.     

An effective finite-element-based method for the computation of nonlinear normal modes of nonconservative systems

This paper addresses the numerical computation of nonlinear normal modes defined as two-dimensional invariant manifolds in phase space. A novel finite-element-based algorithm, combining the streamline upwind Petrov–Galerkin method with mesh moving and domain prediction–correction techniques, is proposed to solve the manifold-governing partial differential equations. It is first validated using conservative examples through the comparison with a reference solution given by numerical continuation. The algorithm is then demonstrated on nonconservative examples.     

A diffraction transducer for vibration analysis

The recently described ditfractographic technique¹, utilizing the diffraction of light passing through an aperture formed by two edges, one fixed as a reference, is used to determine small vibratory displacements. The transducer has little or no inertia, is noncontacting, and has high sensitivity and accuracy. A “time averaged” method is presented whereby peak amplitudes can be obtained with no readout instrumentation and no upper-frequency limit. Alternatively, a photodetector can be used to determine vibration amplitudes with frequency response limited only by the detector circuit.     

A model problem for vibration of thin elastic shells. Propagation and reflection of singularities

We consider an elementary model problem to represent some properties of vibration of thin elastic shells. As classical properties of compactness are not satisfied, there exists an essential spectrum Σ_ess. We study the propagation of singularities when the spectral parameter λ is an interior point of the segment formed by Σ_ess, exhibiting a deterioration of the regularity of the solutions with respect to the case λ out of Σ_ess (phenomena of resonance). We also give the reflection law of the singularities at the boundary of the domain.     

A vibration absorber for motorcycle handles

This paper describes the application of a vibration absorber to ameliorate the comfort of motorcycle handles. The concept of dynamical absorber is briefly summarised and a frequency response function is expressed as the ratio of vibration amplitudes (transmissibility). Some practical hints on the tuning strategy are also suggested in order to correctly define the absorber and then achieve the most effective vibration reduction. A specifically designed item is presented, with the peculiar characteristic of taking advantage of the damping properties of viscoelastic material undergoing shear deformations. An experimental verification of the good performances of the absorber is eventually given on the basis of both a modal analysis of a motorbike and the testing of its handle on an electrodynamical shaker.     

A nonlinear dynamic vibration model of cylindrical roller bearing considering skidding

Nonlinear Dynamics - This paper proposes a dynamic model to investigate the vibration response of a cylindrical roller bearing considering skidding. This model considers the frictional forces and...     

考虑局部非线性结构振动的模型预测控制

针对具有局部非线性的结构振动主动控制问题,首先,利用Newmark-β法推导了局部非线性结构动力响应的时域显式递推表达式。然后,基于该表达式,一方面建立了局部非线性结构振动预测模型,并借鉴模型的线性化思想对非线性环节进行处理,提出考虑局部非线性结构振动的模型预测控制算法;另一方面,在获取各仿真时刻的预测初始状态时,为避免直接对非线性动力学方程所有维度的完全迭代求解,推导了时域显式降维迭代方法,从而使在线计算效率得到显著提高。最后,分别以局部非线性弹簧振子系统在简谐激励作用下的无控动力学分析和含粘滞阻尼器毗邻框架建筑结构在地震激励作用下的受控振动为例,进行数值仿真,结果表明,本文算法计算准确且控制效果较好。     

A general vibration model of angle-ply laminated plates that accounts for the continuity of interlaminar stresses

This paper presents the generalisation of a well documented two-dimensional shear deformable laminated shell theory [Compos. Struct. 25 (1993) 165] that, based on a fixed number of unknown variables, was initially proposed for laminates made of specially orthotropic layers only. The theory is here specialised for laminated plates but is able to encompass monoclinic layers in a general multilayered configuration. Moreover, it is able to account for the interlaminar continuity of both displacements and transverse shear stresses. Higher-order effects, as shear deformation and rotary inertia, are naturally included into the formulation. In order to obtain the relevant governing differential equations, both Hamilton's variational principle and a recently proposed vectorial approach [Compos. Engng. 3 (1993) 3] have been independently used. The effectiveness of the present model is tested numerically by comparing its results with exact three-dimensional elasticity results obtained under the particular condition that the plates vibrate in cylindrical bending.     

A modified wake oscillator model for vortex-induced vibration of circular cylinders for a wide range of mass-damping ratio

In this paper, the behavior of an elastically mounted cylinder, subjected to vortex-induced vibrations (VIV), is investigated by a low-dimensional model. The classical wake oscillator model, as a standard model, predicts the behavior of the system at high mass-damping ratios but fails in modeling the system at low mass-damping ratios. A modified wake oscillator model is introduced in order to describe the response of the system over a wide range of mass-damping ratios. The results of this new model are compared to experimental results from the literature and shown to be in good agreement. The new model can describe most of the features of vortex-induced vibration phenomenology, such as the Griffin plot and lock-in domains.     

Optimal truncated model for vibration control design within a specified bandwidth

The work in this paper is directed at developing correction terms for a truncated structural dynamic model, which includes the effect on the structural response of both low and high frequency unmodelled vibration modes. The proposed model correction approach considers the corrected truncated model that only takes into account resonant modes within the bandwidth of interest and the optimised correction terms. The proposed approach is in contrast to the standard model correction approach that normally utilises a feedthrough correction term, taking into account only the unmodelled high frequency modes, while including all low frequency resonant modes into the truncated model. Thus, when one only interested in controlling vibration associated with a specified bandwidth of interest, the order of the corrected truncated model can be kept sufficiently low since the model does not have to include low and high frequency modes, leading to less complicated control design problems. Such active control within the specified bandwidth can be crucial for control tasks in the vibration minimisation at localised structural regions or in the noise reduction due to some coupled structural–acoustic modes. The procedures for calculating the optimal correction terms which include the lower and higher order mode contributions are outlined for both analytical and experimental models, allowing the procedures to be used for a wide range of theoretical and practical applications.     

A nonlocal strain gradient shell model incorporating surface effects for vibration analysis of functionally graded cylindrical nanoshells

In this paper, a novel size-dependent functionally graded(FG) cylindrical shell model is developed based on the nonlocal strain gradient theory in conjunction with the Gurtin-Murdoch surface elasticity theory. The new model containing a nonlocal parameter, a material length scale parameter, and several surface elastic constants can capture three typical types of size effects simultaneously, which are the nonlocal stress effect, the strain gradient effect, and the surface energy effects. With the help of Hamilton's principle and first-order shear deformation theory, the non-classical governing equations and related boundary conditions are derived. By using the proposed model, the free vibration problem of FG cylindrical nanoshells with material properties varying continuously through the thickness according to a power-law distribution is analytically solved, and the closed-form solutions for natural frequencies under various boundary conditions are obtained. After verifying the reliability of the proposed model and analytical method by comparing the degenerated results with those available in the literature, the influences of nonlocal parameter, material length scale parameter, power-law index, radius-to-thickness ratio, length-to-radius ratio, and surface effects on the vibration characteristic of functionally graded cylindrical nanoshells are examined in detail.     

Chaotic vibration of a nonlinear full-vehicle model

The present work investigates the chaotic responses of a nonlinear seven degree-of-freedom ground vehicle model. The disturbances from the road are assumed to be sinusoid and the time delay between the disturbances is investigated. Numerical results show that the responses of the vehicle model could be chaotic. With the bifurcation phenomenon detected, the chaotic motion is confirmed with the dominant Lyapunov exponent. The results can be useful in dynamic design of a vehicle.