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We are examining the behavior of resonance frequencies and their response to variations of material parameters such as thicknesses, masses, and bulk velocities for certain Rayleigh–Lamb acoustic modes in a multilayered structure. The treatment is based on recent explicit analytic solutions that have allowed us to explore the entire parametric space using dimensionless ratios. This exploration has revealed a complex parametric dependence of the phase velocities and their mass loading response. Specifically, for the fundamental flexural modes in a bilayer, we have shown that both quantities change in a strongly non-monotonic way with thickness, density, or bulk velocity ratios. Even in the regime of thin coating, commonly encountered in acoustic sensing applications, we have found important differences from previously known results, e.g., that response to loading may switch its sign multiple times when the velocity of the deposited material is increased. We have also discovered that the fundamental dilatational modes can be highly effective in stabilizing resonant frequencies against even large variations of the thickness or mass of the exposed layer. This property is demonstrated in an explicit form by the derived expression for the mass coefficient of frequency for an arbitrary number of layers. [ABSTRACT FROM AUTHOR]

We are examining the behavior of resonance frequencies and their response to variations of material parameters such as thicknesses, masses, and bulk velocities for certain Rayleigh–Lamb acoustic modes in a multilayered structure. The treatment is based on recent explicit analytic solutions that have allowed us to explore the entire parametric space using dimensionless ratios. This exploration has revealed a complex parametric dependence of the phase velocities and their mass loading response. Specifically, for the fundamental flexural modes in a bilayer, we have shown that both quantities change in a strongly non-monotonic way with thickness, density, or bulk velocity ratios. Even in the regime of thin coating, commonly encountered in acoustic sensing applications, we have found important differences from previously known results, e.g., that response to loading may switch its sign multiple times when the velocity of the deposited material is increased. We have also discovered that the fundamental dilatational modes can be highly effective in stabilizing resonant frequencies against even large variations of the thickness or mass of the exposed layer. This property is demonstrated in an explicit form by the derived expression for the mass coefficient of frequency for an arbitrary number of layers.

This article explores the effects of two temperatures on the combined problem of wave propagation and thermomechanical loading in a homogeneous isotropic plate. The governing equations are converted to non-dimensional form, and the potential functions are introduced to simplify the problem. The plate's surfaces are assumed to be traction-free, rigidly fixed, thermally insulated and isothermal to study the wave propagation phenomenon. Secular equations in closed form and isolated mathematical conditions for symmetric and skew-symmetric wave mode propagation are derived. The phase velocity and attenuation coefficient are examined for the first problem. The results for uncoupled, coupled, Lord-Shulman (LS) and Green-Lindsay (GL) theories of thermoelasticity have been attained as special cases and agree with that in literature for one temperature theory. In the second part, thermo-mechanical loading has been considered to obtain the expressions of stress and displacement components, conductive and thermodynamic temperatures. The obtained analytical results are computed numerically as well as displayed graphically for copper material to demonstrate the impacts of two temperature theory and compared theoretically as well as numerically with one temperature Lord and Shulman theory. [ABSTRACT FROM AUTHOR]

We analyse veering of Rayleigh–Lamb waves propagating in a plane of elastic symmetry for a thin orthotropic plate. We demonstrate that veering results from interference of partial waves in a similar manner as it occurs in systems composed of one-dimensional (1D) structures, such as beams or strings. Indeed, in the neighbourhood of a veering point, the system may be approximated by a pair of interacting tout strings, whose wave speed is the geometric average of the phase and group velocity of the relevant partial wave at the veering point. This complementary pair of partial waves provides the coupling terms in a form compatible with a action–reaction principle. We prove that veering of symmetric waves near the longitudinal bulk wave speed repeats itself indefinitely with the same structure. However, the dispersion behaviour of Rayleigh–Lamb waves are richer than that of 1D systems, and this reflects also on the veering pattern. In fact, the interacting tout string model fails whenever the dispersion branch is not guided by either partial wave. This often occurs when neighbouring veering points interact and partial waves no longer provide guiding curves. [ABSTRACT FROM AUTHOR]

Perspective types of seismic barriers used to protect buildings and structures from the influence of Rayleigh, Rayleigh–Lamb, and Love acoustic surface waves, as well as head SP waves are considered. The barriers are based on multiple scattering elements and metamaterials. A comparison is made with traditional types of homogeneous seismic barriers made of elastic structural materials. [ABSTRACT FROM AUTHOR]

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]

Frequency equations are obtained for Rayleigh-Lamb wave propagation in a plate of micropolar elastic material with voids. The thickness of the plate is taken to be finite and the faces of the plate are assumed to be free from stresses. The frequency equations are obtained corresponding to symmetric and antisymmetric modes of vibrations of the plate, and some limiting cases of these equations are discussed. Numerical computations are made for a specific model to solve the frequency equations for symmetric and antisymmetric modes of propagation. It is found that both modes of vibrations are dispersive and the presence of voids has a negligible effect on these dispersion curves. However, the attenuation coefficient is found to be influenced by the presence of voids. The results of some earlier works are also deduced from the present formulation. [ABSTRACT FROM AUTHOR]

The present paper is aimed at studying the thermoelastic interaction in an infinite Kelvin-Voigt-type viscoelastic, thermally conducting plate. The upper and lower surfacesof the plate are subjected to stress-free, thermally insulated or isothermal conditions. The coupled dynamic thermoelasticity and generalized theories of thermoelasticity, namely, Lord and Shulman's, Green and Lindsay's, and Green and Nagdhi's are employed to understand the thermomechanical coupling and thermal and mechanical relaxation effects. Secular equations for the plate in closed from and isolated mathematical conditions for symmetric and skew-symmetric wave mode propagation in completely separate terms are derived. In the absence of mechanical relaxations (viscous effect), the results for generalized and coupled theories of thermoelasticity have been 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. The various forms and regions of Rayleigh-Lamb-type secular equation have been obtained and discussed in addition to Lame modes, decoupled shear horizontal (SH) modes, and thin-plate results. At short-wavelength limits, the secular equations for symmetric and skew-symmetric waves in a stress-free insulated and stress-free isothermal plate reduce to the Rayleigh surface wave frequency equation. The amplitudes of temperature and displacement components during symmetric and skew-symmetric motion of the plate have been computed and discussed. Finally, the numerical solution is carried out for copper material. The dispersion curves, and amplitudes of temperature change and displacements for symmetric and skew-symmetric wave modes are presented to illustrate and compare the theoretical results. [ABSTRACT FROM AUTHOR]

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]