A Perturbation Approach for Lateral Excited Vibrations of a Beam-like Viscoelastic Microstructure Using the Nonlocal Theory

In this paper, we investigate the lateral vibration of fully clamped beam-like microstructures subjected to an external transverse harmonic excitation. Eringen’s nonlocal theory is applied, and the viscoelasticity of materials is considered. Hence, the small-scale effect and viscoelastic properties are adopted in the higher-order mathematical model. The classical stress and classical bending moments in mechanics of materials are unavailable when modeling a microstructure, and, accordingly, they are substituted for the corresponding effective nonlocal quantities proposed in the nonlocal stress theory. Owing to an axial elongation, the nonlinear partial differential equation that governs the lateral motion of beam-like viscoelastic microstructures is derived using a geometric, kinematical, and dynamic analysis. In the next step, the ordinary differential equations are obtained, and the time-dependent lateral displacement is determined via a perturbation method. The effects of external excitation amplitude on excited vibration are presented, and the relations between the nonlocal parameter, viscoelastic damping, detuning parameter, and the forced amplitude are discussed. Some dynamic phenomena in the excited vibration are revealed, and these have reference significance to the dynamic design and optimization of beam-like viscoelastic microstructures.

Stability of nanobeams and nanoplates with defects

The sensitivity of critical buckling load and critical stress concerning different geometrical and physical parameters of Euler-Bernoulli nanobeams with defects is studied. Eringen’s nonlocal theory of elasticity is used for the determination of critical buckling load for stepped nanobeams subjected to axial loads for different support conditions. An analytical approach to study the impact of discontinuities and boundary conditions on the critical buckling load and critical stress of nanobeams has been developed. Critical buckling loads of stepped nanobeams are defined under the condition that the nanoelements are weakened with stable crack-like defects. Simply supported, clamped and cantilever nanobeams with steps and cracks are investigated in this article. The presented results are compared with the other available results and are found to be in a close agreement.

Numerical Modeling on Crack Propagation Based on a Multi-Grid Bond-Based Dual-Horizon Peridynamics

Peridynamics (PD) is a novel nonlocal theory of continuum mechanics capable of describing crack formation and propagation without defining any fracture rules in advance. In this study, a multi-grid bond-based dual-horizon peridynamics (DH-PD) model is presented, which includes varying horizon sizes and can avoid spurious wave reflections. This model incorporates the volume correction, surface correction, and a technique of nonuniformity discretization to improve calculation accuracy and efficiency. Two benchmark problems are simulated to verify the reliability of the proposed model with the effect of the volume correction and surface correction on the computational accuracy confirmed. Two numerical examples, the fracture of an L-shaped concrete specimen and the mixed damage of a double-edged notched specimen, are simulated and analyzed. The simulation results are compared against experimental data, the numerical solution of a traditional PD model, and the output from a finite element model. The comparisons verify the calculation accuracy of the corrected DH-PD model and its advantages over some other models like the traditional PD model.

A 3D nano scale IGA for free vibration and buckling analyses of multi-directional FGM nanoshells

In this article, we explore a three-dimensional solid isogeometric analysis (3D-IGA) approach based on a nonlocal elasticity theory to investigate size effects on natural frequency and critical buckling load for multi-directional functionally graded (FG) nanoshells. The multi-directional FG material uses a power law rule with three power exponent indexes concerning three parametric coordinates. Nanoshell's geometries include the square plate, cylindrical and spherical panels with the side length considered in a nanoscale. Because 3D-IGA utilizes an approximation of NURBS basic functions to integrate from geometry modeling to discretized domain, it is the best promising candidate to fulfill a higher-order derivative requirement of the nonlocal theory on nanoshells. The numerical solutions are verified by those published in several pieces of literature to determine the current approach's accuracy and reliability. After a convergence solution is examined, a quartic NURBS basic function can yield ultra-converged and high-accurate results with a low computational cost. The findings show the size effect parameters which significantly impact the frequencies and the critical buckling factors of the multi-directional FG nanoshells. Generally, increases in the size effect parameters will cause declines in the frequencies and the critical buckling factors of the nanoshells.

Special features of short-duration processes in condensed media

The problem of the short-duration processes is considered on the base of the nonlocal theory of non-equilibrium transport, taking into account inertial effects. The system temporal evolution out of equilibrium connected to the dynamic structure transition described by the Speed-Gradient principle (SG-principle or SGP) developed in control theory and cybernetic physics. In the manuscript, we show that retardation of the system response to the short-duration loading due to inertial effects influences on the system evolution and can change its direction. The response to the shock loading of condensed matter is compared to quasi-stationary loading in a wide range of conditions. The short duration loading can lead the system into the structure unstable state and even give rise to self-organization of turbulent structures in the medium. The use of SGP for the modelling of such processes opens new possibilities to control them.