Static and dynamic analysis of functionally graded fluid-infiltrated porous skew and elliptical nanoplates using an isogeometric approach

The analysis of static bending and free and forced vibration responses of functionally graded fluid-infiltrated porous (FGFP) skew and elliptical nanoplates placed on Pasternak’s two-parameter elastic foundation is performed for the first time using isogeometric analysis (IGA) based on the non-uniform rational B-splines (NURBSs) basis function. Three types of porosity distributions affect the mechanical characteristics of materials: symmetric distribution, upper asymmetric distribution, and lower asymmetric distribution. The stress–strain relationship for Biot porous materials was determined using the elastic theory. The general equations of motion of the nanoplates were established using the four-unknown shear deformation plate theory in conjunction with the nonlocal elastic theory and Hamilton’s principle. A computer program that uses IGA to determine the static bending and free and forced vibration of a nanoplate was developed on MATLAB software platform. The accuracy of the computational program was validated via numerical comparison with confidence assertions. This set of programs presents the influence of the following parameters on the static bending and free and forced vibrations of nanoplates: porosity distribution law, porosity coefficient and geometrical parameters, elastic foundation, deviation angle, nonlocal coefficient, different boundary conditions, and Skempton coefficients. The numerical findings demonstrated the uniqueness of the FGFP plate’s behavior when the porosities are saturated with liquid compared with the case without liquid. The findings of this study have significant implications for engineers involved in the design and fabrication of the aforementioned type of structures. Furthermore, this can form the basis for future research on the mechanical responses of the structures.     

A finite element modeling-based approach to predict vibrations transmitted through different body segments of the operator within the workspace of a small tractor

Agricultural tractor drivers are subjected to high levels of whole-body vibrations and hand arm vibrations during most part of the farm activities due to unevenness of field surface, uneasy posture, improper workplace design, moving parts of the tractor, and other unavoidable circumstances. The comfort level of the operator inside a dynamic tractor is dependent on the level of vibration generated inside the different human body segments. In the present study, a finite element modeling was proposed to predict vertical vibrations (Z-axis) and frequencies at the different body segments of the seated small tractor operator. The forces required for different controls of the tractor were measured to be used as input parameters in the finite element modeling. The maximum mean forces of the brake (172.8 N) and clutch (153.2 N) were used as the input parameters for the simulation study. The simulated results were validated with the field measured values of vertical accelerations at selected body segments of the operator. The simulation could successfully predict vertical vibrations at selected points of interest (i.e., foot, leg, thigh, lower arm, upper arm, back, and head) except the chest of the body, as the buttock of the operator model was fixed (degree of freedom is equal to zero) in the simulation. The obtained results were compared with the international standards ISO 2631-1 (1985/1997) and ISO 5349-1 (2001) to assess the vibration characteristics at the different body segments of the operator. The foot, leg, lower arm, and upper arm of the operator were subjected to vertical vibration frequencies from 10 to 200 Hz. Most of the resonance of vertical accelerations occurred in one-third octave bands of 20–80 Hz frequencies. The thigh, chest, back, and head of the operator were exposed to vibration frequencies below 40 Hz during field operation. At these parts of the body, the vertical acceleration resonated at lower frequencies, between 2 and 8 Hz.     

A comparative study of the eigenvalue solutions for mass-loaded beams under classical boundary conditions

A comparative study of the eigenfrequency analysis for an Euler–Bernoulli beam carrying a concentrated mass at an arbitrary location is presented in this short note. The dimensionless frequency equation for different combinations of classical boundary conditions is obtained by satisfying the differential equations of motion and by imposing the corresponding boundary and compatibility conditions. Two formulation methods have been commonly used for the boundary-value problem. One is to adopt a single frame originated from the beam's left-end, while another is by dual frames associated with the concentrated mass. It is found that the forms derived by dual frames are more compact than the corresponding expressions by using the single frame. Nevertheless, the comparison for all the cases shows that the dual-frame expressions need more time to obtain the same set of eigenvalues if compared with the time by using the single-frame expressions.     

Pseudospectral method for assessing stability robustness for linear time-periodic delayed dynamical systems

The article presents a pseudospectral approach to assess the stability robustness of linear time-periodic delay systems, where periodic functions potentially present discontinuities and the delays may also periodically vary in time. The considered systems are subject to linear real-valued time-periodic uncertainties affecting the coefficient matrices, and the presented method is able to fully exploit structure and potential interdependencies among the uncertainties. The assessment of robustness relies on the computation of the pseudospectral radius of the monodromy operator, namely, the largest Floquet multiplier that the system can attain within a given range of perturbations. Instrumental to the adopted novel approach, a solver for the computation of Floquet multipliers is introduced, which results into the solution of a generalized eigenvalue problem which is linear w.r.t. (samples of) the original system matrices. We provide numerical simulations for popular applications modeled by time-periodic delay systems, such as the inverted pendulum subject to an act-and-wait controller, a single-degree-of-freedom milling model and a turning operation with spindle speed variation.     

High-Performance Unidirectional Manipulation of Microdroplets by Horizontal Vibration on Femtosecond Laser-Induced Slant Microwall Arrays

The high-performance unidirectional manipulation of microdroplets is crucial for many vital applications including water collection and bioanalysis. Among several actuation methods (e.g., electric, magnetic, light, and thermal actuation), mechanical vibration is pollution-free and biocompatible. However, it suffers from limited droplet movement mode, small volume range (V_Max/V_Min < 3), and low transport velocity (≤11.5 mm s⁻¹) because the droplet motion is a sliding state caused by the vertical vibration on the asymmetric hydrophobic microstructures. Here, an alternative strategy is proposed—horizontal vibration for multimode (rolling, bouncing/reverse bouncing, converging/diffusing, climbing, 90^o turning, and sequential transport), large-volume-range (V_Max/V_Min ≈ 100), and high-speed (≈22.86 mm s⁻¹) unidirectional microdroplet manipulation, which is ascribed to the rolling state on superhydrophobic slant microwall arrays (SMWAs) fabricated by the one-step femtosecond laser oblique ablation. The unidirectional transport mechanism relies on the variance of viscous resistance induced by the difference of contact area between the microdroplet and the slant microwalls. Furthermore, a circular, curved, and “L”-shaped SMWA is designed and fabricated for droplet motion with particular paths. Finally, sequential transport of large-volume-range droplets and chemical mixing microreaction of water-based droplets are demonstrated on the SMWA, which demonstrates the great potential in the field of microdroplet manipulation.     

Active tuned mass damper for damping of offshore wind turbine vibrations

An active tuned mass damper (ATMD) is employed for damping of tower vibrations of fixed offshore wind turbines, where the additional actuator force is controlled using feedback from the tower displacement and the relative velocity of the damper mass. An optimum tuning procedure equivalent to the tuning procedure of the passive tuned mass damper combined with a simple procedure for minimizing the control force is employed for determination of optimum damper parameters and feedback gain values. By time domain simulations conducted in an aeroelastic code, it is demonstrated that the ATMD can be used to further reduce the structural response of the wind turbine compared with the passive tuned mass damper and this without an increase in damper mass. A limiting factor of the design of the ATMD is the displacement of the damper mass, which for the ATMD, increases to compensate for the reduction in mass. Copyright © 2016 John Wiley & Sons, Ltd.     

Thermo-mechanical vibration analysis of rotating nonlocal nanoplates applying generalized differential quadrature method

In this study, thermal and small-scale effects on the flapwise bending vibrations of a rotating nanoplate, which can be the basis of nano-turbine design, have been analyzed. The nano-turbine is made of an orthotropic nanoplate with a setting angle that is modeled based on the classical plate theory (CPT) with cantilever boundary conditions. The axial forces are also included in the model as the true spatial variation due to the rotation and temperature change. The governing equations and boundary conditions are derived according to Hamilton's principle and the governing equations are solved with the aid of the generalized differential quadrature method. The effects of small-scale parameter, nondimensional angular velocity, temperature change, and setting angles in the first four nondimensional frequencies are discussed. Due to the consideration of the rotating effects, results of this study are applicable in nano-machines, such as nano-motors, nano-rotor, and other rotating nano-structures. Also, by considering the effect of thermal loading on rotation of a nanoplate, the results are useful in the design of nano-turbines.     

裂纹转子弯扭耦合瞬态振动影响因素研究

针对两端刚性支承的Jeffcott转子，推导了裂纹转子的弯扭耦合振动非线性微分方程，通过数值仿真手段，分析了升速过程中弯振和扭振的瞬态特性，并详细探讨了加速度、裂纹减小刚度、裂纹夹角、质量偏心以及阻尼系数等因素对弯扭耦合振动瞬态特性的影响。研究表明，升速过程中，随着加速度增大，弯振和扭振各共振峰值减小，而对应转速增加。各共振峰值均随着△kq的增加而增大，当△kq超过某值后，峰值急剧增加。β在0～2π范围内变化时，各共振峰值呈现不同周期的正余弦变化。质量偏心主要影响临界峰值，对其它各峰值影响很小。各峰值均随阻尼系数的增加而降低，阻尼系数较小时，峰值减小率更大。     

A p‐version,first order shear deformation,finite element for geometrically non‐linear vibration of curved beams

A p‐version, hierarchical finite element for curved, moderately thick, elastic and isotropic beams is introduced. The convergence properties of the element are analysed and some results are compared with results published elsewhere or calculated using a commercial finite element package. It is verified that, with the proposed element, shear locking does not affect the computation of the natural frequencies and that low dimensional, accurate models are obtainable. Geometrically non‐linear vibrations due to finite deformations, which occur for harmonic excitations with frequencies close to the first three natural frequencies of vibration, are investigated using Newmark's method. The influence of the thickness, longitudinal inertia and curvature radius on the dynamic behaviour of curved beams are studied. Copyright © 2004 John Wiley & Sons, Ltd.     

Vibration Characteristics of Fatigue Damage of Beam-Type Structural Components

We consider free vibration of an elastic cantilever beam with a closing edge crack. The crack is simulated by an elastic pivot whose compliance is taken to be finite and is determined from the energy equivalence criterion. An algorithm has been constructed for sequential calculation of the beam vibration modes for each beam vibration cycle, whereas the number of cycles is limited. It is demonstrated that the beam vibration modes other than the initially preset one are induced during the crack opening and closing. The distinct features of such modes have been studied. We have analyzed the sensitivity of the vibration-damage characteristics which are determined from the assessment of nonlinear distortions of the displacement, acceleration, and strain waveform of the cross sections of the beam with a closing crack.