Reflection of plane waves at the stress-free/rigid surface of a micro-mechanically modeled Piezo-electro-magnetic fiber-reinforced half-space

Singh, Sonam; Singh, Abhishek Kumar; Guha, Sayantan

doi:10.1080/17455030.2022.2083720

Cited by 9 publications

(5 citation statements)

References 45 publications

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“…Thus, from Eqs. ( 14)-( 18), we obtain 2(m 1 + m 2 ) + m 3 = m(say) equations in 2N + 2 unknowns which are to be determined by solving the system (19). The non-dimensionalization of the physical parameters is made using both the depths h 1 & h 2 .…”

Section: Numerical Resultsmentioning

confidence: 99%

“…Approximate solution of the 2N + 2 unknowns appearing in Eqs. ( 14)-( 18) can be obtained by the method of algebraic least-squares for which we consider infinite number of discretized points: (i) ŷ 1 , ŷ 2 , ŷ 3 , … on the barrier (0, d), (ii) ỹ 1 , ỹ 2 , ỹ 3 , … in the gap (d, h 2 ) and (iii) y ˇ1, y ˇ2, y ˇ3, … on the step (h 2 , h 1 ), which lead to an overdetermined system with infinite number of equations in the matrix form as (19) ,…”

Section: Methods Of Solutionmentioning

confidence: 99%

“…The study of water waves propagating over a permeable sea bottom was constructed using MMSE by Ni and Teng [18]. Singh et al [19] and Singh et al [20] studied the reflection of plane waves at the stress-free/rigid surface of a micro-mechanically modeled piezo-electro-magnetic fiber-reinforced composite half-space. A study on the headon collision between two solitary waves in a thin elastic plate floating on an inviscid fluid of finite depth was examined analytically by means of a singular perturbation method by Bhatti and Lu [21].…”

Section: Introductionmentioning

confidence: 99%

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Algebraic Method for Approximate Solution of Scattering of Surface Waves by Thin Vertical Barrier Over a Stepped Bottom Topography

Kumar

Goyal

Martha

2022

Contemporary Mathematics

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A study on interaction of surface water waves by thin vertical rigid barrier over a step type bottom topography is analysed. The associated mixed boundary value problem is solved using the eigenfunction expansion of the velocity potential. The resulting system of equations, avoiding the traditional approach of employing application of orthogonality relations, is solved using algebraic least squares method giving rise the numerical values of the reflection and transmission coefficients by the barrier over step. The energy balance relation for the given problem is derived and verified numerically ensuring the correctness of the present results. The present results are also compared with the data available in the literature for the validation purpose. The effect of step height, length of the barrier and angle of incidence on the reflection coefficient and the non-dimensional horizontal force on the barrier have been investigated through different plots. It is observed that barrier along with step works as an effective barrier to reflect more incident waves causing calm zone along the leeside.

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Section: Numerical Resultsmentioning

confidence: 99%

Section: Methods Of Solutionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Algebraic Method for Approximate Solution of Scattering of Surface Waves by Thin Vertical Barrier Over a Stepped Bottom Topography

Kumar

Goyal

Martha

2022

Contemporary Mathematics

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“…Abo-Dahab and Biswas [24] investigated the refraction and reflection of thermoelastic waves when the medium is under a magnetic field and initial stress at a solid-liquid interface. Guha and his coworker [25][26][27][28][29] delve into diverse facets of plane wave behavior within fiber-reinforced composite materials, explicitly emphasizing factors like initial stresses, fiber volume ratios, and interactions at material interfaces. These investigations provide valuable insights into how these composite materials respond to varying conditions, thereby advancing comprehension of their mechanical characteristics and the propagation of waves within them.…”

Section: T Tmentioning

confidence: 99%

Energy ratio response at the interface of elastic and dual-porous thermoelastic half-spaces

Kumar,

Gupta,

Pathania

et al. 2023

Phys. Scr.

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The present study delves into the intricate examination of energy distribution inherent in plane waves interfacing with an elastic half-space and a thermoelastic half-space characterized by a dual porosity framework. Employing the memory-dependent dual-phase-lag (DPL) hyperbolic two-temperature (H2T) thermoelastic paradigm, the investigation encompasses various incident wave types. The governing equations, rendered in a non-dimensional format, are meticulously addressed by applying the rigorous technique of eigenmode analysis. The intricate energy ratios are meticulously ascertained through the judicious imposition of boundary conditions and the discerning employment of reflection and transmission coefficients. Graphical representations have been exhibited, elucidating the effects of diverse parameters on distinct energy ratios within crystalline structures akin to magnesium materials. These parameters encompass but are not confined to the H2T paradigm, the absence of the two-temperature influence, the classical two-temperature approach, memory effects, and a spectrum of distinct kernel functions. The proposed model emanates cross-disciplinary utility, traversing the domains of seismology, acoustics, optics, materials science, structural engineering, and geophysics.

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“…Some works can be found in the literature dealing with crack propagation in media containing micro-scale properties, such as Singh et al [54], Singh et al [55], Singh et al [56], Yadav [57], etc. Some works on wave propagation aspects in fiber-reinforced composite media were done by Guha and Singh [58], Othmani et al [59], Singh et al [60], Singh et al [61], Singh et al [62], Singh et al [63], Singh et al [64], Guha and Singh [65], Guha and Singh [66], etc owing to the immense potential advantages of the considered composites compared to their monolithic counterparts. As mentioned earlier, some works such as Yildirim [67], Jin et al [68], etc, have explored vibration characteristics of micro-beams in sandwiched/layered piezo-electric/magnetic sheets with/ without the influence of external load.…”

Section: Introductionmentioning

confidence: 99%

Thermoelastic damping and frequency shift of different micro-scale piezoelectro-magneto-thermoelastic beams

Guha,

Singh,

Singh

2023

Phys. Scr.

Self Cite

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This work focuses on mathematically studying thermoelastic damping (TED) and frequency shift (FS) in micro-scale piezoelectro-magneto-thermoelastic (PEMT) composite beams composed of BaTiO3-CoFe2O4 combination. Pertaining to cutting-edge micro-technologies implemented in several engineering/scientific applications now-a-days, micro-scale doubly clamped (CC), doubly simply supported (SS), clamped-free (CF), and clamped-simply supported (CS) beams are extensively analyzed. The beams are modeled following the linear Euler–Bernoulli assumptions. The first two eigenvalues of all beams are numerically obtained using Newton-Raphson method. The closed-form expressions of TED and FS of all beams are derived analytically. The influences of Classical dynamical coupled (CL), Lord-Shulman (LS) & Green-Lindsay (GL) thermoelasticity theories, beam dimensions, BaTiO3 volume fraction (Ωf), and the first two modes M1 & M2) on the TED & FS are meticulously analyzed. Critical thickness (CrTh), critical length (CrLt), and TED (inverse Quality factor) of the beams are numerically obtained and studied. Among other key outcomes, the existence of a critical value of Ωf is established in the range Ωf∈ [ [0.5, 0.55], at which, the TED and FS display a drastic change in their natures. The outcomes of the present analysis may find immense potential uses in the design and development of PEMT composite micro-beams, and their applications in several areas such as supporting/stiffening other micro/nanostructures, construction works, sensitive sensing applications, etc.

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Reflection of plane waves at the stress-free/rigid surface of a micro-mechanically modeled Piezo-electro-magnetic fiber-reinforced half-space

Cited by 9 publications

References 45 publications

Algebraic Method for Approximate Solution of Scattering of Surface Waves by Thin Vertical Barrier Over a Stepped Bottom Topography

Algebraic Method for Approximate Solution of Scattering of Surface Waves by Thin Vertical Barrier Over a Stepped Bottom Topography

Energy ratio response at the interface of elastic and dual-porous thermoelastic half-spaces

Thermoelastic damping and frequency shift of different micro-scale piezoelectro-magneto-thermoelastic beams

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