Nonuniform Stiffness Distribution Research Articles

Dynamic Analysis of the Bolted Joint Structure with Interval Uncertainties

This paper investigates the dynamic influence of joint interfaces in bolted joint structures subjected to uncertain-but-bounded parameters. Firstly, applying the thin layer elements (TLE) represents the contact interfaces with nonuniform stiffness distribution. The stochastic model updating method is employed to identify the uncertain parameters of TLE. Secondly, the Legendre interval method (LIM) is applied to calculate the natural frequencies of bolted lap joints with uncertain parameters. By introducing the elastic modulus of TLE as interval vectors, relations between the natural frequencies and uncertain parameters could be analyzed using the LIM. Furthermore, the dependence of the dynamic response on TLE parameters can be established based on the modal superposition principle. Considering the influence of uncertain parameters, an uncertain acceleration frequency response surrogate function (UAFRSF) is proposed to predict the dynamic behavior and qualitatively analyze the parameter sensitivity of the bolted lap joints. The elastic modulus of TLE in different contact regions is selected as the interval variable. The acceleration frequency responses of the bolted lap joints under uncertain parameters are investigated. Compared with MCs simulations with 200 samples and Chebyshev interval method results, the effectiveness of the proposed method for solving the uncertain acceleration frequency response of bolted lap joints is verified. This research will provide theoretical support for improving the design of aero-engine joint structures.

Vibration analysis of cylindrical shell discontinuously coupled with annular plate with arbitrary boundary conditions

Discontinuously coupled cylindrical shell-plates or plate-like structures are common components of underwater vehicles, and their vibration characteristics change significantly due to modal coupling. The vibration of discontinuously coupled annular plate-cylindrical shell structures is analyzed based on the wave propagation method(WPM) and virtual spring(VS). Taking uniform annular plates and cylindrical shells as spectral elements, the displacement solutions are described by the trigonometric function and Bessel function respectively, and the vibration responses of the annular plate-cylindrical shell with arbitrary boundaries are obtained. Based on VS and weighted least square norm least square method(WLSNLSM), the discontinuous coupling between the annular plate and cylindrical shell is described as the non-uniform distribution of stiffness of virtual spring by continuity condition, and the dynamic stiffness matrices of continuously and discontinuously coupled structure can be obtained simultaneously. The reason for vibration characteristic change under discontinuous coupling is explained from the perspective of modal superposition. Finally, a finite element model is established to verify the accuracy of the proposed method. The influence of general discontinuous coupling on the dynamic behavior of shell structure is analyzed by numerical examples, which provides useful guidance for structural vibration analysis with discontinuous coupling.

Analysis of Concrete Pavement Slab resting on Non-uniform Elastic Foundation using the Finite Element Method

During the rigid pavement design, the concrete slab working on the base/subbase and subgrade is usually modeled as the slab on the elastic foundation. However, the non-uniform distribution of materials in the base or subgrade layers naturally exists in real conditions and should be considered. In this paper, a finite element method for calculating concrete pavement slabs on an elastic foundation with non-uniform stiffness distribution is developed. This study applies 4-node finite elements and Mindlin plate theory to formulate the finite element equations. The results predicted by the proposed approach are verified analytically. Calculation examples are conducted with the practical settings to investigate the influence of slab and foundation stiffness parameters on the slab displacement.

Effect of non-uniform stiffness distribution on the dynamics of inverted plates in a uniform flow

The stability of the inverted flexible plate with non-uniform stiffness distribution in a free stream is studied by numerical simulation and mathematical theory. In our study, the bending stiffness distribution is expressed as the function of the leading edge's bending stiffness K∗ and the polynomial of the plate's coordinate. Based on the former theoretical work on the stability of inverted plates with uniform stiffness distribution, we derive the upper limit value of K∗ at which the zero-deflection equilibrium loses its stability for the plate with non-uniform stiffness distribution. The critical K∗ derived from the mathematical theory agrees well with that obtained from the numerical simulation. An effective bending stiffness is defined, which can be used to unify the regimes of the motion modes between uniform plates and non-uniform plates. Moreover, three orders of mass ratio [O(10−2), O(10−1), and O(1)] are investigated, and the underlying mechanism for large amplitude flapping is clarified for the inverted plate with different mass ratios. An appropriate bending stiffness distribution can greatly improve the deformation of the plate. The findings shed some light on the energy harvesting of the inverted plate.

Modulation of magnetic anisotropy through self-assembled surface nanoclusters: Evolution of morphology and magnetism in Co–Pd alloy films

In this study, the self-assembly of surface nanoclusters on 10–20-nm-thick Co50Pd50 (Co–Pd) alloy thin films deposited on the Al2O3(0001) substrate was systematically investigated. The time-dependent evolution of the nanocluster size and magnetic properties was monitored using an atomic force microscope (AFM) and the magneto-optical Kerr effect. When the Co–Pd alloy films were stored in an ambient environment, small nanodots gradually gathered to form large nanoclusters. Approximately 30 days after growth, a nanocluster array formed with an average lateral size of 100±20nm and average height of 10±3nm. After 100 days, the average lateral size and average height had increased to 140±20 and 25±5nm, respectively. The AFM phase image exhibited a structured contrast on the nanocluster surface, indicating the nonuniform stiffness distribution of the nanoclusters. A microscopic Auger spectroscopy measurement suggested that in contrast to the Pd-rich signal in the flat area, the nanoclusters were cobalt- and oxygen-rich areas. Cross-sectional investigation through transmission electron microscopy coupled with energy dispersive spectroscopy showed that the nanoclusters were mostly composed of Co oxide. A uniform Pd-rich underlayer had been maintained underneath the self-assembled Co-oxide nanoclusters. With the formation of a Co-oxide nanocluster array and Pd-rich underlayer, the magnetic easy axis of the Co–Pd film gradually altered its direction from the pristine perpendicular to in-plane direction. Because of the change in the magnetic easy axis, the hydrogenation-induced spin-reorientation transition was suppressed with the evolution of the surface Co-oxide nanoclusters.

Effects of stiffness distribution and spanwise deformation on the dynamics of a ray-supported caudal fin

Using a fluid-structure interaction model, we study the effect of ray stiffness distribution on the deformation and performance of a caudal fin. By prescribing a simple swaying motion, our results show that through passive structural deformation alone it is possible to reproduce some complicated fin movements (e.g. the cup and ‘W’-shape deformations) observed in real fish. Moreover, it has been numerically shown that, compared with a fin with uniform ray stiffness, at the same (average) ray stiffness fins with nonuniform stiffness distribution may achieve further performance enhancement, e.g. increase in propulsion efficiency and decrease in lateral force generation. This is attributed to spanwise deformations caused by phase differences between different rays.

Effects of non-uniform stiffness on the swimming performance of a passively-flexing, fish-like foil model

Simple mechanical models emulating fish have been used recently to enable targeted study of individual factors contributing to swimming locomotion without the confounding complexity of the whole fish body. Yet, unlike these uniform models, the fish body is notable for its non-uniform material properties. In particular, flexural stiffness decreases along the fish’s anterior-posterior axis. To identify the role of non-uniform bending stiffness during fish-like propulsion, we studied four foil model configurations made by adhering layers of plastic sheets to produce discrete regions of high (5.5 × 10−5 Nm2) and low (1.9 × 10−5 Nm2) flexural stiffness of biologically-relevant magnitudes. This resulted in two uniform control foils and two foils with anterior regions of high stiffness and posterior regions of low stiffness. With a mechanical flapping foil controller, we measured forces and torques in three directions and quantified swimming performance under both heaving (no pitch) and constant 0° angle of attack programs. Foils self-propelled at Reynolds number 21 000–115 000 and Strouhal number ∼0.20–0.25, values characteristic of fish locomotion. Although previous models have emphasized uniform distributions and heaving motions, the combination of non-uniform stiffness distributions and 0° angle of attack pitching program was better able to reproduce the kinematics of freely-swimming fish. This combination was likewise crucial in maximizing swimming performance and resulted in high self-propelled speeds at low costs of transport and large thrust coefficients at relatively high efficiency. Because these metrics were not all maximized together, selection of the ‘best’ stiffness distribution will depend on actuation constraints and performance goals. These improved models enable more detailed, accurate analyses of fish-like swimming.

Tailoring the elastic postbuckling response of cylindrical shells: A route for exploiting instabilities in materials and mechanical systems

Postbuckling response, long considered mainly as a failure limit state is gaining increased interest for smart applications, such as energy harvesting, frequency tuning, sensing, actuation, etc. This letter explores the potential of cylindrical shells under axial compression, for which localized buckling events along with high-rate local deformations can be attained in their elastic postbuckling regime under smaller axial system deformation input, as a prototype for harnessing elastic instabilities. Three avenues are presented to tailor and control the elastic postbuckling response of axially-compressed shells: (1) by introducing seeded geometric imperfections (SGI); (2) by introducing non-uniform stiffness distributions (NSD); and (3) by providing lateral constraints and interactions (LCI). Prototyped cylindrical shells were fabricated through 3D printing and tested under loading–unloading cycles. Experimental results show that, with appropriate selection of geometry, material, and stiffness distribution, these three concepts offer significant advantages over uniform cylindrical shells for use of their notoriously unreliable elastic postbuckling response. This work provides new knowledge on the possibilities and means to design the cylindrical shells with controlled elastic postbuckling behavior and opens new avenues for using this structural form for applications in smart materials and structures.

Structural Integrity of Composite Columns Subject to Fire

This article investigates the thermal response of an axially restrained composite column, which is exposed to a heat flux due to fire. The heat damage, the charred layer formation and nonuniform transient temperature distribution in the column exposed to fire from one side are calculated by the thermal model developed by Gibson et al. [1]. For the thermal response analysis, the mechanical properties of the fire-damaged (charred) region are considered negligible, while the degradation of the elastic properties with temperature in the undamaged layer (especially near the glass transition temperature of the matrix) is accounted for using experimental data for the elastic moduli. Due to the nonuniform stiffness distribution through the thickness and the effect of the ensuing thermal moment, the structure behaves like an imperfect column, and responds by bending rather than buckling in the classical Euler (bifurcation) sense. Another important effect of the non-uniform temperature is that the neutral axis moves away from the centroid of the cross-section, resulting in an additional moment due to eccentric mechanical loading, which tends to bend the structure. The compressive behavior of a column subjected to simultaneous high intensity surface heating and axial compressive loading was investigated experimentally to verify the anticipated theoretical response. All specimens exhibited bending and subsequent catastrophic failure, even at compressive stresses well below these corresponding to the Euler load.

Sonoelastographic imaging of interference patterns for estimation of shear velocity distribution in biomaterials

The authors have recently demonstrated the shear wave interference patterns created by two coherent vibration sources imaged with the vibration sonoelastography technique. If the two sources vibrate at slightly different frequencies omega and omega+deltaomega, respectively, the interference patterns move at an apparent velocity of (deltaomega/2omega)upsilon(shear), where upsilon(shear) is the shear wave speed. We name the moving interference patterns "crawling waves." In this paper, we extend the techniques to inspect biomaterials with nonuniform stiffness distributions. A relationship between the local crawling wave speed and the local shear wave velocity is derived. In addition, a modified technique is proposed whereby only one shear wave source propagates shear waves into the medium at the frequency omega. The ultrasound probe is externally vibrated at the frequency omega-deltaomega. The resulting field estimated by the ultrasound (US) scanner is proven to be an exact representation of the propagating shear wave field. The authors name the apparent wave motion "holography waves." Real-time video sequences of both types of waves are acquired on various inhomogeneous elastic media. The distribution of the crawling/holographic wave speeds are estimated. The estimated wave speeds correlate with the stiffness distributions.

Snapping of Low Arches with Nonuniform Stiffness

Results in the form of critical load versus rise parameter are presented for two different types of symmetric stiffness distribution and three cross-sectional area to moment of inertia relations. Critical conditions are obtained through an approximate Ritz-type approach for both types of instability, limit point and unstable bifurcation. Exact solutions are obtained, whenever possible, which are used to provide a confidence factor for the approximate technique. Except for one special case, nonuniform stiffness geometries yield a stronger configuration than uniform stiffness geometries. In addition, for both nonuniform stiffness distributions considered, the more the stiffness is concentrated towards the center of the arch the stronger the arch.