Search results

This study aims to analyse the behaviour of plane waves within a nonlocal transversely isotropic visco-thermoelastic medium having variable thermal conductivity.

The concept of enunciation is used in the generalized theory of thermoelasticity in accordance with the Green–Lindsay and Eringen’s nonlocal elasticity models. The linear viscoelasticity model developed by Kelvin–Voigt is used to characterize the viscoelastic properties of transversely isotropic materials.

It has been noticed that three plane waves, which are coupled together, travel through the medium at three different speeds. The derivation of reflection coefficients and energy ratios for reflected waves is carried out by incorporating suitable boundary conditions. Numerical computations are performed for the amplitude ratios, phase speeds and energy partition and displayed in graphical form.

The outcomes of the numerical simulation demonstrate that the amplitude ratios are significantly influenced by variable thermal conductivity, nonlocal parameters and viscosity. It is further observed from the plots that the phase speeds in a transversely isotropic medium depend on the angle of incidence. In addition, it has been established that the energy is preserved during the reflection phenomenon.

The purpose of this paper is to depict the effect of thermal and diffusion phase-lags on plane waves propagating in thermoelastic diffusion medium with different material symmetry. A generalized form of mass diffusion equation is introduced instead of classical Fick's diffusion theory by using two diffusion phase-lags, one phase-lag of diffusing mass flux vector, represents the delayed time required for the diffusion of the mass flux and the other phase-lag of chemical potential, represents the delayed time required for the establishment of the potential gradient. The basic equations for the anisotropic thermoelastic diffusion medium in the context of dual-phase-lag heat transfer (DPLT) and dual-phase-lag diffusion (DPLD) models are presented. The governing equations for transversely isotropic and isotropic case are also reduced. The different characteristics of waves like phase velocity, attenuation coefficient, specific loss and penetration depth are computed numerically. Numerically computed results are depicted graphically for anisotropic, transversely isotropic and isotropic medium. The effect of diffusion and thermal phase-lags are shown on the different characteristic of waves. Some particular cases of result are also deduced from the present investigation.

The governing equations of thermoelastic diffusion are presented using DPLT model and a new model of DPLD. Effect of phase-lags of thermal and diffusion is presented on different characteristic of waves.

The effect of diffusion and thermal phase-lags on the different characteristic of waves is appreciable. Also the use of diffusion phase-lags in the equation of mass diffusion gives a more realistic model of thermoelastic diffusion media as it allows a delayed response between the relative mass flux vector and the potential gradient.

Introduction of a new model of DPLD in the equation of mass diffusion.

The purpose of study to this article is to analyze the Rayleigh wave propagation in an isotropic dry sandy thermoelastic half-space. Various wave characteristics, i.e wave velocity, penetration depth and temperature have been derived and represented graphically. The generalized secular equation and classical dispersion equation of Rayleigh wave is obtained in a compact form.

The present article deals with the propagation of Rayleigh surface wave in a homogeneous, dry sandy thermoelastic half-space. The dispersion equation for the proposed model is derived in closed form and computed analytically. The velocity of Rayleigh surface wave is discussed through graphs. Phase velocity and penetration depth of generated quasi P, quasi SH wave, and thermal mode wave is computed mathematically and analyzed graphically. To illustrate the analytical developments, some particular cases are deliberated, which agrees with the classical equation of Rayleigh waves.

The dispersion equation of Rayleigh waves in the presence of thermal conductivity for a dry sandy thermoelastic medium has been derived. The dry sandiness parameter plays an effective role in thermoelastic media, especially with respect to the reference temperature for η = 0.6,0.8,1. The significant difference in η changes a lot in thermal parameters that are obvious from graphs. The penetration depth and phase velocity for generated quasi-wave is deduced due to the propagation of Rayleigh wave. The generalized secular equation and classical dispersion equation of Rayleigh wave is obtained in a compact form.

Rayleigh surface wave propagation in dry sandy thermoelastic medium has not been attempted so far. In the present investigation, the propagation of Rayleigh waves in dry sandy thermoelastic half-space has been considered. This study will find its applications in the design of surface acoustic wave devices, earthquake engineering structural mechanics and damages in the characterization of materials.

The aim of this study is to investigate the effects of offset angle in wave soldering by using thermal fluid structure interaction modeling with experimental validation.

The authors used a thermal coupling approach that adopted mesh-based parallel code coupling interface between finite volume-and finite element-based software (ABAQUS). A 3D single pin-through-hole (PTH) connector with five offset angles (0 to 20°) on a printed circuit board (PCB) was built and meshed by using computational fluid dynamics preprocessing software called GAMBIT. An implicit volume of fluid technique with a second-order upwind scheme was also applied to track the flow front of solder material (Sn63Pb37) when passing through the solder pot during wave soldering. The structural solver and ABAQUS analyzed the temperature distribution, displacement and von Mises stress of the PTH connector. The predicted results were validated by the experimental solder profile.

The simulation revealed that the PTH offset angle had a significant effect on the filling of molten solder through the PCB. The 0° angle yielded the best filling profile, filling time, lowest displacement and thermal stress. The simulation result was similar to the experimental result.

This study provides a better understanding of the process control in wave soldering for PCB assembly.

This study provides fundamental guidelines and references for the thermal coupling method to address reliability issues during wave soldering. It also enhances understanding of capillary flow and PTH joint issues to achieve high reliability in PCB assembly industries.

The purpose of this paper is to study the propagation of inhomogeneous waves in a partially saturated poro-thermoelastic media through the examples of the free surface of such media..

The mathematical model evolved by Zhou et al. (2019) is solved through the Helmholtz decomposition theorem. The propagation velocities of bulk waves in partially saturated poro-thermoelastic media are derived by using the potential functions. The phase velocities and attenuation coefficients are expressed in terms of inhomogeneity angle. Reflection characteristics (phase shift, loci of vertical slowness, amplitude, energy) of elastic waves are investigated at the stress-free thermally insulated boundary of a considered medium. The boundary can be permeable or impermeable. The incident wave is portrayed with both attenuation and propagation directions (i.e. inhomogeneous wave). Numerical computations are executed by using MATLAB.

In this medium, the permanence of five inhomogeneous waves is found. Incidence of the inhomogeneous wave at the thermally insulated stress-free surface results in five reflected inhomogeneous waves in a partially saturated poro-thermoelastic media. The reflection coefficients and splitting of incident energy are obtained as a function of propagation direction, inhomogeneity angle, wave frequency and numerous thermophysical features of the partially saturated poro-thermoelastic media. The energy of distinct waves (incident wave, reflected waves) accompanying interference energies between distinct pairs of waves have been exhibited in the form of an energy matrix.

The sensitivity of propagation characteristics (velocity, attenuation, phase shift, loci of vertical slowness, energy) to numerous aspects of the physical model is analyzed graphically through a particular numerical example. The balance of energy is substantiated by virtue of the interaction energies at the thermally insulated stress-free surface (opened/sealed pores) of unsaturated poro-thermoelastic media through the bulk waves energy shares and interaction energy.

The purpose of this paper is to study the reflection of plane waves in thermoelastic medium with double porosity structure.

A two-dimensional model is considered of an isotropic thermoelastic half-space with double porosity. Thermoelasticity with one relaxation time given by Lord and Shulman (1967) has been used to study the problem. It is found that there exists four coupled longitudinal waves, namely, longitudinal wave (P), longitudinal thermal wave (T), longitudinal volume fractional wave corresponding to pores (PVI) and longitudinal volume fractional wave corresponding to fissures (PVII), in addition to an uncoupled transverse wave (SV).

The formulae for amplitude ratios of various reflected waves are obtained in closed form. It is found that these amplitude ratios are functions of angle of incidence. Effect of porosity and thermal relaxation time is shown graphically on the amplitude ratios with angle of incidence for a particular model.

Reflection of plane waves is of great practical importance. There are many organic and inorganic deposits beneath the earth surface. Wave propagation is the simplest and most economical technique to detect these. The model discussed in the present paper can provide useful information for experimental researchers working in the field of geophysics and earthquake engineering, along with seismologist working in the field of mining tremors and drilling into the crust of the earth.

The purpose of this paper is to investigate the decomposition behavior of binary mixtures of organic activators commonly used in the no-clean wave flux systems upon their exposure to thermal treatments simulating wave soldering temperatures. The binary blends of activators were studied at varying ratios between the components.

Differential scanning calorimetry and thermogravimetric analysis were used to study the characteristics of weak organic acid (WOA) mixtures degradation as a function of temperature. The amount of residue left on the surface after the heat treatments was estimated by gravimetric measurements as a function of binary mixture type, temperature and exposure time. Ion chromatography analysis was used for understanding the relative difference between decomposition of activators in binary blends. The aggressivity of the left residue was assessed using the acidity indication gel test, and effect on reliability was investigated by DC leakage current measurement performed under varying humidity and potential bias conditions.

The results show that the typical range of temperatures experienced by electronics during the wave soldering process is not sufficient for the removal of significant activator amounts. If the residues contain binary mixture of WOAs, the final ratio between the components, the residue level and the corrosive effects depend on the relative decomposition behavior of individual components. Among the WOA investigated under the conventional wave soldering temperature, the evaporation and removal of succinic acid is more dominant compared to adipic and glutaric acids.

The findings are attributed to the chemistry of WOAs typically used as flux activators for wave soldering purposes. The results show the importance of controlling the WOA content and ratio between activating components in a flux formulation in relation to its tendencies for evaporation during soldering and the impact of its residues on electronics reliability.

The results show that the significant levels of flux residues can only be removed at significantly higher temperatures and longer exposure times compared to the conventional temperature range used for the wave soldering process. The potential corrosion issues related to insufficient flux residues removal will be determined by the residue amount, its composition and ratio between organic components. The proper time of thermal treatment and careful choice of fluxing formulation could ensure more climatically reliable product.

Increased use of surface mount ceramic capacitors in wave solder applications has resulted in a number of field failures due to migration of microcracks through the capacitor. Cracks are initiated in board assembly by a number of processes including excessive forces of assembly equipment, board warpage and/or deflection, rework temperatures, and wave solder profiles. Thermal shock from wave solder contributes approximately 20–25% of the failures. The majority of capacitor manufacturers recommend no greater than 100°C delta between pre‐heat and wave solder temperature during processing. This can be difficult to achieve when processing a range of board sizes. A delta of 120°C allows for different size boards without using a custom thermal profile for each. This study shows no increased failure rate for X7R 1206 capacitors between the two process deltas of 100°C and 120°C. The suggested delta of 100°C is based on a 15000 psi tensile strength of the dielectric and is conservative. The temperature profile may be extended to include the more versatile 120° delta without compromising the reliability of the component.

This paper aims to study the impact of pyro-electricity, moisture and temperature diffusivity on the energy distribution of plane waves at the free surface of an orthotropic piezo-hygro-thermo-elastic medium.

This study presents the novel creation of governing equations for an anisotropic piezothermoelastic medium with moisture impact, which is a significant contribution of this paper.

In addition to providing numerical data for the amplitude ratios and energy ratios of reflected waves, this study identifies five different kinds of coupled reflected plane waves, namely, quasi-longitudinal P wave, quasi-thermal wave, quasi-transverse wave, quasi-moisture wave and electric potential wave.

The graphical analysis examines the impact of various factors, such as the angle of incidence, moisture and temperature diffusivity, pyro-electricity and frequency, on energy distribution.

This paper's results significantly impact the development of more efficient piezoelectric materials and their applications in geophysics.

The authors of the submitted document initiated and produced it collectively, with equal contributions from all members.

This paper aims to study the energy ratios of plane waves on an interface of nonlocal thermoelastic halfspace (NTS) and nonlocal orthotropic piezothermoelastic half-space (NOPS).

The memory-dependent derivatives (MDDs) approach with a hyperbolic two-temperature (HTT), three-phase lag theory is used here to study how the energy ratios change at the interface with the angle of incidence.

Plane waves that travel through NTS and hit the interface as a longitudinal wave, a thermal wave, or a transversal wave send four waves into the NOPS medium and three waves back into the NTS medium. The amplitude ratios of the different waves that are reflected and transmitted are used to calculate the energy ratios of the waves. It is observed that these ratios are affected by the HTT, nonlocal and MDD parameters.

The energy ratios correspond to four distinct models; nonlocal HTT with memory, nonlocal HTT without memory, local HTT with memory and nonlocal classical-two-temperature with memory concerning the angle of incidence from 0 degree to 90 degree.

This model applies to several fields, including earthquake engineering, soil dynamics, high-energy particle physics, nuclear fusion, aeronautics and other fields where nonlocality, MDD and conductive temperature play an important role.

The authors produced the submitted document entirely on their initiative, with equal contributions from all of them.