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Recently, symbolic regression (SR) has demonstrated its efficiency for discovering basic governing relations in physical systems. A major impact can be potentially achieved by coupling symbolic regression with asymptotic methodology. The main advantage of asymptotic approach involves the robust approximation to the sought for solution bringing a clear idea of the effect of problem parameters. However, the analytic derivation of the asymptotic series is often highly nontrivial especially, when the exact solution is not available. In this paper, we adapt SR methodology to discover asymptotic series. As an illustration we consider three problem in mechanics, including two-mass collision, viscoelastic behavior of a Kelvin–Voigt solid and propagation of Rayleigh–Lamb waves. The training data is generated from the explicit exact solutions of these problems. The obtained SR results are compared to the benchmark asymptotic expansions of the above mentioned exact solutions. Both convergent and divergent asymptotic series are considered. A good agreement between SR expansions and exact analytical results is observed. It is demonstrated that the proposed approach can be used to identify material parameters, e.g. Poisson's ratio, and has high prospects for utilizing experimental and numerical data. • Robust framework for asymptotic expansions in mechanics using symbolic regression. • Discovery of symbolic regression expansions from very few data points. • High accuracy of symbolic regression expansions vs. associated benchmark expansions. [ABSTRACT FROM AUTHOR]

We analyze variation of the Rayleigh-Lamb (RL) vibration spectrum of a free isotropic layer on parameters motivated by a previously unnoticed anomaly of its dependence on constituent materials, when some RL modes would reduce their propagation speed in a medium with higher bulk velocities. We explore the spectrum in more detail by following the arguments of parametric scaling and find the location of its anomalous non-monotonic dependence on bulk velocity at finite wavelengths for the S 1 and A 2 modes. These modes are well known for the anomaly of their dispersion that has recently attracted much interest related to the phenomenon of negative refraction. We demonstrate that the parametric and dispersion anomalies occupy adjacent areas on the spectral surfaces in the wavenumber-parameter space. We argue that such close connection may be found in other waveguides and can present interest for acoustic technologies as well as for quantum applications of anomalous scattering and transport by RL phonons. • Resonance frequencies of Rayleigh-Lamb acoustic waves in a thin layer may depend non-monotonically on materials velocities. • The S1 and A2 modes could reduce their propagation speed in a medium with higher bulk velocities. • Parametric and dispersion anomalies of the S1 and A2 modes are located in adjacent regions of the frequency-wavenumber space. • Connection between the two anomalies presents interest for acoustic technologies, quantum scattering and transport by phonons. [ABSTRACT FROM AUTHOR]

Abstract: The present paper is aimed at studying the effects of rotation on the thermoelastic interaction in an infinite Kelvin–Voigt-type viscoelastic, thermally conducting plate rotating about the normal to its faces with uniform angular velocity. This facilitates the decoupling of anti-plane/in-plane motion which is not possible, in general. The upper and lower surfaces of the plate are subjected to stress-free, thermally insulated or isothermal conditions. The formulation is applied according to three theories of the generalized thermoelasticity: Lord-Shulman with one relaxation time, Green–Lindsay with two relaxation times, as well as the coupled theory. Secular equations are derived for the plate in closed form isolated mathematical conditions for symmetric and skew-symmetric wave mode propagation in completely separate terms. In the absence of mechanical relaxations (Rotation and viscous effects), the results for generalized and couple theories of thermoelasticity were obtained as particular cases from the derived secular equations. In the absence of thermomechanical coupling, the analysis for a viscoelastic plate can be deduced from the present one. Finally the numerical solution is carried out for copper material. The function iteration numerical scheme is used to solve the complex secular equations, in order to obtain phase velocity and attenuation coefficients of propagating wave mode. The dispersion curves and attenuation coefficients profiles so obtained for symmetric and skew-symmetric wave modes are presented graphically to illustrate and compare the theoretical results in the presence and absence of rotation. The study may be useful in the construction and design of gyroscopes and rotation sensors as well as in the application in diverse fields. [Copyright &y& Elsevier]

Several beam and plate models have been recently developed in the literature to accommodate for size-dependence. These are usually obtained starting from a generalized continuum theory (such as the couple-stress, strain-gradient or non-local theory or their modifications) and then deducing the governing equations through Hamilton's principle and ingenuous kinematical assumptions. This approach, originated by Kirchhoff, usually fails to reproduce the dispersion features of the equivalent 3D theory. Besides, it produces a variety of models, in dependence of the different assumptions, such as Kirchhoff's or Mindlin's. In contrast, in this paper we adopt asymptotic reduction: moving from the couple-stress linear theory of elasticity with micro-inertia, we deduce new models for elongation and flexural deformation of microstructured plates. The resulting models are consistent, in the sense that they reproduce the dispersion features of the corresponding 3D body. Also, models are unique, for they may only differ by the order of the approximation. We find that microstructure especially affects inertia terms, which can be hardly captured by a-priori kinematical assumptions. For static flexural deformations, our results match those already obtained assuming plane cross-sections within the modified couple-stress theory. In fact, we show that couple-stress, reduced couple-stress and strain gradient theories all lead to equivalent results. Higher order models are also given, that describe the near first-cut-off behaviour and account for thickness deformations in the spirit of Timoshenko. [ABSTRACT FROM AUTHOR]