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Free vibration response of a joined shell system including cylindrical and spherical shells is analyzed in this research. It is assumed that the system of joined shell is made from a functionally graded material (FGM). Properties of the shells are assumed to be graded through the thickness. Both shells are unified in thickness. To capture the effects of through-the-thickness shear deformations and rotary inertias, first-order shear deformation theory of shells is used. The Donnell type of kinematic assumptions is adopted to establish the general equations of motion and the associated boundary and continuity conditions with the aid of Hamilton’s principle. The resulting system of equations is discretized using the semi-analytical generalized differential quadrature method. Considering the clamped and free boundary conditions for the end of the cylindrical shell and intersection continuity conditions, an eigenvalue problem is established to examine the vibration frequencies of the joined shell. After proving the efficiency and validity of the present method for the case of thin isotropic homogeneous joined shells, some parametric studies are carried out for the system of combined moderately thick cylindrical–spherical shell system. Novel results are provided for the case of FGM joined shells to explore the influence of power-law index and geometric properties.

The ultrasonic frequency radial vibration of an elastic thin spherical shell composed of isotropic materials is studied, the frequency equation of its vibration is deduced, and the equivalent circuit is obtained. The finite element software COMSOL is used to verify the obtained analytical theory, and the calculated results are basically consistent with the theoretical calculated values. The relevant conclusions provide references for the application of spherical shell structure in related fields.

The flange holes on large aluminum ball shells are processed on-site by industrial robots, and the flange holes need to ensure the hole position and axial accuracy requirements at the same time, but it is challenging to ensure that these two indexes meet the requirements at the same time due to the lower machining accuracy of the industrial robots. For this reason, the paper proposes a robot integrated error compensation method for hole position and axial deviation constraints. First, the robot machining path is generated, and the cutting allowance and hole inner wall measurement strategy are determined by running the machining path empty before machining. Integrated error compensation is then introduced and a new hole surface is constructed as a mirror surface under its conditions. The tool path is adjusted according to the mirror compensation principle to ensure consistency between the machined and target holes. The reconstructed target hole surface satisfies the integrated error constraints and realizes the balanced constraints of positional and axial tolerances, making full use of both tolerances. Finally, the method's effectiveness has been verified in a large-scale work. Experimental results show that hole position error is reduced from uncompensated (1.03, − 0.51) mm to compensated (0.25, − 0.005) mm, and axial error from uncompensated 22.32 mm to compensated 1.39 mm.

Multiplex detection of emerging pollutants is essential to improve quality control of water treatment plants, which requires portable systems capable of real-time monitoring. In this paper we describe a flexible, dual electrochemical sensing device that detects nonylphenol and paroxetine in tap water samples. The platform contains two voltammetric sensors, with different working electrodes that were either pretreated or functionalized. Each working electrode was judiciously tailored to cover the concentration range of interest for nonylphenol and paroxetine, and square wave voltammetry was used for detection. An electrochemical pretreatment with sulfuric acid on the printed electrode enabled a selective detection of nonylphenol in 1.0–10 × 10 –6  mol L –1 range with a limit of detection of 8.0 × 10 –7  mol L –1 . Paroxetine was detected in the same range with a limit of detection of 6.7 × 10 –7  mol L –1 using the printed electrode coated with a layer of carbon spherical shells. Simultaneous detection of the two analytes was achieved in tap water samples within 1 min, with no fouling and no interference effects. The long-term monitoring capability of the dual sensor was demonstrated in phosphate buffer for 45 days. This performance is statistically equivalent to that of high-performance liquid chromatography (HPLC) for water analysis. The dual-sensor platform is generic and may be extended to other water pollutants and clinical biomarkers in real-time monitoring of the environment and health conditions. Graphical abstract Silver pseudo-reference electrodes for paroxetine (REP) and nonylphenol (REN), working electrodes for paroxetine (WP) and nonylphenol (WN), and auxiliary electrode (AE). USP refers to the University of Sao Paulo. “Red” is reduced form and “Oxi” is oxidized form of analytes.

We present a hydrodynamic model for a thin spherical shell of active nematic liquid crystal with an arbitrary configuration of defects. The active flows generated by defects in the director lead to the formation of stable vortices, analogous to those seen in confined systems in flat geometries, which generate effective dynamics for four +1/2 defects that reproduces the tetrahedral to planar oscillations observed in experiments. As the activity is increased and two counterrotating vortices dominate the flow, the defects are drawn more tightly into pairs, rotating about antipodal points. We extend this situation to also describe the dynamics of other configurations of defects. For example, two +1 defects are found to attract or repel according to the local geometric character of the director field around them and the extensile or contractile nature of the material, while additional pairs of opposite charge defects can give rise to flow states containing more than two vortices. Finally, we describe the generic relationship between defects in the orientation and singular points of the flow, and suggest implications for the three-dimensional nature of the flow and deformation in the shape of the shell.

The present work fills a gap on the postbuckling behavior of multilayer functionally graded graphene platelet reinforced composite (FG-GPLRC) cylindrical and spherical shell panels resting on elastic foundations subjected to central pinching forces and pressure loadings. Based on a higher-order shear deformation theory and the von Kármán’s nonlinear strain–displacement relations, the governing equations of the FG-GPLRC cylindrical and spherical shell panels are established by the principle of virtual work. The non-uniform rational B-spline (NURBS) based isogeometric analysis (IGA), the modified arc-length method and the Newton’s iteration method are employed synthetically to obtain nonlinear load–deflection curves for the panels numerically. Several comparative examples are performed to test reliability and accuracy of IGA and arc-length method in present formulation and programming implementation. Parametric investigations are carried out to illustrate the effects of dispersion type of the graphene platelet (GPL), weight fraction of the GPL, thickness of the panel, radius of the panel and parameters of elastic foundation on the load–deflection curves of the FG-GPLRC shell panels. Some complex load–deflection curves of the FG-GPLRC cylindrical and spherical shell panels resting on elastic foundations may be useful for future references.

Can uncorrelated surrounding sound sources be used to generate extended diffuse sound fields? By definition, targets are a constant sound pressure level, a vanishing active sound intensity, and uncorrelated sound waves arriving isotropically from all directions. Are there ideal source layouts to synthesize a maximum diffuse sound field within? As methods, we employ numeric simulations and undertake a series of considerations based on uncorrelated source layouts at a finite radius. Statistically expected active sound intensity and sound energy density are insightful and highlight the relation of active sound intensity to potential theory. Correspondingly, both Gauß’ divergence and Newton’s spherical shell theorem apply, and they provide valuable insights. In a circular layout, uncorrelated elementary point-source fields decaying by 1/√r ideally compose an extended sound field of vanishing active sound intensity; in spherical layouts this is the case with a 1/r decay. None of the layouts synthesizes a perfectly constant sound energy density inside. Theory and simulation offer a broad basis for understanding the synthesis of diffuse sound fields with uncorrelated sources in the free sound field.

This paper employs the Higher-Order Shear and Normal Deformation Theory (HOSNDT) to a static analysis of spherical composite shells. By using a third-order parabolic variation of shear strains to account for transverse shear deformation effects, the theory does away with the necessity for shear correction factors and precisely captures deformation of the shell along the thickness. The concept of virtual work is used to systematically develop the governing equilibrium equations and associated boundary conditions. Under static transverse loads, the mathematical model is solved using Navier’s analytical method, which works well for simply supported doubly curved laminated shells. The solution provides non-dimensional displacements and stress components that allow for direct comparison with benchmark solutions. The validity and applicability of the developed theory are confirmed by the current numerical results, which show excellent agreement with the body of existing literature.

Dielectric elastomers (DEs) have attracted significant attention in many engineering fields due to their excellent deformation capabilities and mechanical properties. In this work, the nonlinear vibrations of the DE spherical shell characterized by the third-order Ogden model are investigated. The governing equation describing the radially symmetric motions of the shell is derived by the incompressibility constraint and the variational method. Through the qualitative and quantitative analyses, the nonlinear dynamical behaviors are discussed, along with the parameter analyses of the structural damping, pressure, direct current (DC) voltage and alternating current (AC) voltage. It is shown that with the increasing pressure and voltage, the vibrations transition from periodic vibrations to chaotic vibrations via the period-doubling bifurcation. Particularly, the self-similar structure of the system is found.

This paper deals with a new purely data-driven method, called the spatio-temporal Koopman decomposition, to approximate spatio-temporal data as a linear combination of (possibly growing or decaying exponentially) standing or traveling waves. The method combines (i) either standard singular value decomposition (SVD) or higher-order SVD and (ii) either standard dynamic mode decomposition (DMD) or an extension of this method by the authors, called higher-order DMD. In particular, for periodic or quasiperiodic attractors, the method gives the spatio-temporal pattern as a superposition of standing and/or traveling waves, which are identified in an efficient and robust way. Such superposition may give the whole pattern as a modulated, periodic or quasiperiodic, standing or traveling wave. The method is illustrated in some simple toy-model dynamics, and its performance is tested in the identification of standing and traveling waves in the Ginzburg–Landau equation and of azimuthal waves in a rotating spherical shell with thermal convection.