This study presents an analytical investigation of the forced radial vibration and vibration isolation of elastic metacomposite spherical bodies with embedded heavy hard spheres as local resonators. An effective medium formulation is employed to derive closed-form solutions for both solid and hollow spherical bodies under various boundary conditions, including traction- and displacement-driven excitations. The presence of local resonators gives rise to a frequency-dependent effective mass density, which becomes negative within a finite frequency range known as the bandgap. It is shown that, when the excitation frequency lies within this bandgap, the governing wavenumber becomes purely imaginary, leading to evanescent wave behavior and exponential attenuation of both displacement and stress fields. As a result, the vibrational response is strongly confined near the excitation boundary, demonstrating pronounced vibration isolation. A series of illustrative examples is presented for solid spheres, hollow spheres, and spherical cavities in infinite media. The results reveal that, outside the bandgap, the vibrational mode is characterized by oscillatory behavior, while within the bandgap, vibrational mode is effectively suppressed in the domain far away from the excitation boundary. Moreover, the attenuation of the vibrational mode is found to be more significant when the excitation frequency is near the lower bound of the bandgap. These findings highlight the potential of metacomposite spherical structures as efficient vibration isolation devices in engineering applications.
Rolling-element bearings exhibit strongly nonlinear dynamic behaviour due to radial internal clearance, intermittent Hertzian contact, eccentricity, damping, and raceway imperfections. This study addresses the inverse identification of radial internal clearance in a nonlinear 2-DOF rolling-bearing system governed by intermittent contact. A physics-informed neural formulation is employed to reconstruct the two-dimensional bearing response and simultaneously estimate the unknown clearance by embedding the governing equations of motion directly into the training loss. A SIREN architecture with sinusoidal activation functions is used to represent the oscillatory displacement response and its time derivatives. The framework is assessed using limited and noisy displacement observations generated from 4th-order Runge–Kutta solutions for different clearance values and operating conditions, with noise levels of 1% , 5% , and 10% . The method accurately reconstructs both transient and steady-state responses. The clearance-normalized vector reconstruction error ranges from 0.085% to 0.162% , while the maximum relative error in radial internal clearance identification remains below 0.012% . No systematic deterioration in reconstruction or identification accuracy is observed with increasing noise under the considered conditions. These results establish a physics-informed computational framework for identifying radial internal clearance from nonlinear bearing dynamics. Although the present validation is based on model-generated observations, the formulation provides a basis for subsequent assessment using experimental bearing data.
Friction on coated surfaces is a factor affecting coating durability, so its reliable prediction is of practical importance. This study presents an asperity-based numerical model, built on single-asperity elastic–elastoplastic–plastic contact mechanics combined with a dislocation-slip friction law, for estimating the friction coefficient of coated surfaces under dry sliding conditions. The model combines surface roughness (Ra), the mechanical properties of the coating and substrate, the applied normal force, and the coating thickness to evaluate the contact area and deformation state of individual asperities at the microscopic scale; subsequently, the frictional forces generated by the interacting asperities are summed, and the coefficient of friction is calculated as the ratio of the total friction force to the applied load. The model was evaluated against ball-on-disk dry sliding tests on tungsten carbide (WC)-coated ST37 steel samples of three coating thicknesses and three roughness levels. The predicted friction coefficients agree with the measured values with an average deviation of about 10
We propose a variational continuum model for mechanically biased adhesion of cell plaques, describing their interactions with a substrate exhibiting spatial gradients in stiffness (durotaxis), viscosity (viscotaxis), or both. The adhesion plaque is modelled as an elasto-active bar whose internal remodelling strain evolves in response to mechanical cues, while the substrate is represented as a spatially inhomogeneous viscoelastic solid of the Standard Linear Solid type. The mechanosensitive resistance to remodelling is assumed to depend nonlinearly on the interface force between the plaque and the substrate, governed by a linear elastic law. This coupling drives an inhomogeneous spatial response to mechanical gradients, thereby inducing a bias in cell active remodelling towards mechanically favourable regions of the substrate, as shown by numerical simulations. The model captures adhesive bias towards stiffer regions in the durotaxis case, and towards more viscous regions in the viscotaxis case. We also consider scenarios in which these gradients compete, showing the interplay of characteristic parameters in determining the direction of active bias. Comparisons with experiments show qualitative agreement, suggesting the proposed framework offers a plausible continuum alternative to clutch-based models.
The paper constructs and analyzes a generalized s-sub-step implicit method for nonlinear dynamics. The proposed methods are designed to achieve identical second-order accuracy, unconditional stability, no overshoots, and self-starting features. In addition, identical effective mass matrices are achieved for each algorithm to embed optimal spectral characteristics, namely maximum numerical dissipation but minimum period elongation errors. Further, the proposed methods are optimized to reduce numerical low-frequency dissipation when maintaining minimum period elongation errors and controllable numerical high-frequency dissipation. Unlike the published algorithms, this paper imposes a set of dissipative parameters ρ ^∞ _j to control numerical dissipation in each sub-step. The amount of dissipation in the sub-steps does not influence spectral features of the entire method but transforms an integration scheme used in the corresponding sub-step. Spectral analysis and numerical examples are carried out to illustrate the superiority of the proposed methods. In particular, the optimized methods significantly outperform the traditional implicit algorithms with respect to the low-frequency accuracy when ensuring the same computational cost.
