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Dynamic response of a machine tool structure varies along the tool path depending on the changes in its structural configurations. The productivity of the machine tool varies as a function of its frequency response function (FRF) which determines its chatter stability and productivity. This paper presents a computationally efficient reduced order model to obtain the FRF at the tool center point of a machine tool at any desired position within its work volume. The machine tool is represented by its position invariant substructures. These substructures are assembled at the contacting interfaces by using novel adaptations of constraint formulations. As the tool moves to a new position, these constraint equations are updated to predict the FRFs efficiently without having to use computationally costly full order finite element or modal models. To facilitate dynamic substructuring, an improved variant of standard component mode synthesis method is developed which automates reduced order determination by retaining only the important modes of the subsystems. Position-dependent dynamic behavior and chatter stability charts are successfully simulated for a virtual three axis milling machine, using the substructurally synthesized reduced order model. Stability lobes obtained using the reduced order model agree well with the corresponding full-order system.

Bandgaps are frequency intervals of no wave propagation for mechanical waves. Spatial periodicity provides one mechanism for the emergence of bandgaps in periodic composite materials such as lattice materials, phononic crystals, and acoustic metamaterials. Coupling a propagating wave in a periodic medium with a local resonator provides an alternate mechanism for band-gap emergence. This study examines these two band-gap formation mechanisms using a receptance coupling technique. The receptance coupling technique yields closed-form expressions for the location of bandgaps and their width. Numerical simulations of Blochwaves are presented for the Bragg and sub-Bragg bandgaps and compared with the bounding frequency predictions given by the receptance analysis of the unitcell dynamics. It is observed that the introduction of periodic local resonators narrows Bragg bandgaps above the local resonant bandgap. Introduction of two fold periodicity is shown to widen the Bragg bandgap, thus expanding the design space. The generality of the receptance technique presented here allows straightforward extension to higher dimensional systems with multiple degrees of freedom coupling. Implication of this study for nano-electro-mechanical systems (NEMS) based filters will be discussed.

Vascular stents are expanded in blood vessels with lumens larger than their cardiac counterparts. Extreme radial expansion significantly reduces the expanded length of some designs, resulting in insufficient lesion coverage and inaccurate placement. It is hypothesized that expansion mechanisms of a balloon-expandable stent, driven by plastic hinges, are controlled by the cell topology. This hypothesis is first tested for stent expansion using kinematic and kinetic analyses, followed by more detailed finite element (FE) calculations. Three balloon-expandable stent designs are laser micro-machined for experimental verification of the length–diameter relations predicted by the analytical and FE models. It is found that stent designs with positive, negative, or zero foreshortening over expansion phase can be designed by tailoring unit cell geometries and hence obtain desired length–diameter and pressure–diameter characteristics.

A systematic study on the influence of the cell geometry of a cardiovascular stent on its radial compliance and longitudinal strain is presented. Eight stent cell geometries—based on common lattice cells—are compared using finite element analysis. It is found that, for a given strut thickness, the radial compliance depends on the shape of the cell and is intimately connected with the longitudinal strain through effective Poisson’s ratio, which depends on the cell geometry. It is demonstrated experimentally that a hybrid stent containing both positive and negative Poisson’s ratio cell lattice geometries exhibited very low values of longitudinal strain. This study indicates that cell geometries may be tailored to minimize longitudinal stresses imposed by the stent onto the artery wall.

A single image Optical Diffraction based profiling method is proposed employing a double micro-cantilever(MC) structure achieving deflection resolutions of 1nm and surface stress changes of 50µN/m in a typical MC based sensor.

A simple and easy-to-implement algorithm to identify a generalized proportional viscous damping matrix is developed in this work. The chief advantage of the proposed technique is that only a single drive-point frequency response function (FRF) measurement is needed. Such FRFs are routinely measured using the standard techniques of an experimental modal analysis, such as impulse test. The practical utility of the proposed identification scheme is illustrated on three representative structures: (1) a free-free beam in flexural vibration, (2) a quasiperiodic three-cantilever structure made by inserting slots in a plate in out-of-plane flexural vibration, and (3) a point-coupled-beam system. The finite element method is used to obtain the mass and stiffness matrices for each system, and the damping matrix is fitted to a measured variation of the damping (modal damping factors) with the natural frequency of vibration. The fitted viscous damping matrix does accommodate for any smooth variation of damping with frequency, as opposed to the conventional proportional damping matrix. It is concluded that a more generalized viscous damping matrix, allowing for a smooth variation of damping as a function of frequency, can be accommodated within the framework of standard finite element modeling and vibration analysis of linear systems.

Dynamic response of lattice structures in linear and nonlinear regime is investigated. In the linear regime, connections between vibration and buckling are revisited in the context of plane wave propagation. The power of wave technique in picking up the correct bifurcation mode and the associated critical load is illustrated. The stability of spatially localised structures arising from homoclinics is examined in the nonlinear regime. Simple analytical results will be presented and illustrated using numerical examples.

Rayleigh quotients in the context of linear, nonconservative vibrating systems with viscous and nonviscous dissipative forces are studied in this paper. Of particular interest is the stationarity property of Rayleigh-like quotients for dissipative systems. Stationarity properties are examined based on the perturbation theory. It is shown that Rayleigh quotients with stationary properties exist for systems with proportional viscous and nonviscous damping forces. It is also shown that the stationarity property of Rayleigh quotients in the case of nonproportional damping (viscous and nonviscous) is conditional upon the diagonal dominance of the modal damping matrix.

This paper presents structural analysis methods to model morphing, achieved via buckling of struts in multi-element structural components. An exact element theory and an energy-based variational approach are used to deduce a closed-form relationship between actuator force and displacement, by firstly assuming an ideal actuator. Subsequently, the flexibility of the actuator is incorporated via a lumped parameter model to account for actuator-structure interaction. The single element actuation concept is extended to multielement frame architecture to produce displacements of an example aircraft tail section, by actuating one or two elements of the assembly. Hybrid actuation, combining large force with large displacement actuators is also introduced, whereby large shape changes can be achieved with optimum demand on the actuators. It is concluded that exact element theory has significant potential in deducing closed-form relationship between the actuator forces and structural displacements. The energy approach, based on the trial function to represent the displacements, is shown to be approximate, but sufficient. These closed-form relationships can be readily used in optimisation routines to achieve an optimal structure to produce structural shape changes.

Amorphous siliconlike films with hydrophobic functionalities have been deposited by plasma-enhanced chemical-vapor deposition on carbon-fiber-reinforced polymer (CFRP) unidirectional laminates used for micromechanical applications where high strength-to-weight and high stiffness-to-weight ratios are required. To improve long-term geometrical stability in ultrahigh-precision machine structures, hydrophobic CFRP materials are desirable. Three layers have been grown with different plasma-process parameters from a mixture of hexamethyldisiloxane, O2, and Ar. Chemical composition, water contact angle, surface energy, morphology, and tribological properties have been evaluated to choose the one that best fulfills hydrophobicity, wear, and scratch resistance. Wear tests have also been carried out on CFRP laminates coated with a polyurethane layer to compare the wear performance of the above specimens with that of a conventional hydrophobic coating. Scanning electron microscope images show a very good adhesion of the films to the composite substrate because the failure of the film and of the substrate (such as fiber failure) take place simultaneously.

Plane wave propagation in infinite two-dimensional periodic lattices is investigated using Floquet-Bloch principles. Frequency bandgaps and spatial filtering phenomena are examined in four representative planar lattice topologies: hexagonal honeycomb, Kagome lattice, triangular honeycomb, and the square honeycomb. These topologies exhibit dramatic differences in their long-wavelength deformation properties. Long-wavelength asymptotes to the dispersion curves based on homogenization theory are in good agreement with the numerical results for each of the four lattices. The slenderness ratio of the constituent beams of the lattice (or relative density) has a significant influence on the band structure. The techniques developed in this work can be used to design lattices with a desired band structure. The observed spatial filtering effects due to anisotropy at high frequencies (short wavelengths) of wave propagation are consistent with the lattice symmetries.

A systematic molecular dynamics simulation study is performed to assess the effects of temperature and free edges on the ultimate tensile strength and Young's modulus of a single-layer graphene sheet. It is observed that graphene sheets at higher temperatures fail at lower strains, due to the high kinetic energy of atoms. A numerical model, based on kinetic analysis, is used to predict the ultimate strength of the graphene under various temperatures and strain rates. As the width of a graphene reduces, the excess edge energy associated with free edge atoms induces an initial strain on the relaxed configuration of the sheets. This initial strain has a greater influence on the Young's modulus of the zigzag sheet compared with that of the armchair sheets. The simulations reveal that the carbon–carbon bond length and amplitude of intrinsic ripples of the graphene increases with temperature. The initial out-of-plane displacement of carbon atoms is necessary to simulate the physical behaviour of a graphene when the Nose–Hoover or Berendsen thermostat is used.

Identification of damping matrices from measured frequency response functions is a difficult and error‐prone procedure. In practice, the assumption of proportional damping is frequently made without physical justification. Several researchers have suggested identification algorithms for the full damping matrix. A critical review is presented of algorithms which work in the frequency domain. Some novel approaches are included: one new algorithm is based on matrix perturbation theory, while others are hybrid combinations of earlier methods. The sensitivity of the algorithms to measurement noise and other commonly encountered difficulties in realistic measurements is addressed. Representative results from a simulation study comparing all the methods will be presented, leading to recommendations for the choice of identification algorithms in practice.

Damping identification in structural vibration from measured frequency response functions is a difficult task. Several methods have been proposed in the literature to identify the damping matrix. Some employ modal parameters such as natural frequencies, damping factors, and mode shapes, while others work directly from the frequency response function matrix. In practice, in the presence of noise and incompleteness of data, it is hard to guess how well any of these methods will perform. This paper reports a systematic simulation study to test the relative benefits/disadvantages of a wide range of approaches, existing and novel. Representative model systems have been chosen to test performance under various conditions of measurement noise, system complexity, damping type, modal overlap factor, and modal truncation. A very wide range of results is summarized by computing various norms of performance for all the methods studied. Recommendations are made for the best methods to extract reliable damping information from practical measurements.

Electro-rheological (ER) fluids are a class of smart materials exhibiting significant reversible changes in their rheological and hence mechanical properties under the influence of an applied electric field. Efforts are in progress to embed ER fluids in various structural elements to mitigate vibration problems. The present work is an experimental investigation of the behaviour of a sandwich beam with ER fluid acting as the core material. A starch–silicone-oil-based ER fluid is used in the present study. Significant improvements in the damping properties are achieved in experiments and the damping contributions by viscous and non-viscous forces are estimated by force-state mapping (FSM) technique. With the increase in electric field across the ER fluid from 0 to 2 kV, an increase of 25–50% in equivalent viscous damping is observed. It is observed that as concentration of starch is increased, the ER effect grows stronger but eventually is overcome by applied stresses.

The elastic moduli of single layer graphene sheet (SLGS) have been a subject of intensive research in recent years. Calculations of these effective properties range from molecular dynamic simulations to use of structural mechanical models. On the basis of mathematical models and calculation methods, several different results have been obtained and these are available in the literature. Existing mechanical models employ Euler-Bernoulli beams rigidly jointed to the lattice atoms. In this paper we propose truss-type analytical models and an approach based on cellular material mechanics theory to describe the in-plane linear elastic properties of the single layer graphene sheets. In the cellular material model, the C-C bonds are represented by equivalent mechanical beams having full stretching, hinging, bending and deep shear beam deformation mechanisms. Closed form expressions for Young's modulus, the shear modulus and Poisson's ratio for the graphene sheets are derived in terms of the equivalent mechanical C-C bond properties. The models presented provide not only quantitative information about the mechanical properties of SLGS, but also insight into the equivalent mechanical deformation mechanisms when the SLGS undergoes small strain uniaxial and pure shear loading. The analytical and numerical results from finite element simulations show good agreement with existing numerical values in the open literature. A peculiar marked auxetic behaviour for the C-C bonds is identified for single graphene sheets under pure shear loading.