This study investigates the two-dimensional vibrational response of a poroelastic medium subjected to both an

initial static stress state and an external magnetic field. The theoretical formulation is based on Biot’s theory of

poroelasticity and incorporates electromagnetic effects through Maxwell’s equations, enabling a fully coupled

description of solid deformation, pore-fluid pressure, and magnetoelastic interactions.

The governing equations account for mechanical pre-stress, fluid solid coupling, magnetic body forces, and

are relevant to applications in geomechanics, seismo-electromagnetic phenomena, and the development of

magneto-sensitive porous materials.

Keywords: Poroelasticity; Biot theory; Magnetoelasticity; Initial stress; Two-dimensional wave propagation;

Coupled field modelling; Pore-fluid interaction; Magnetic body forces; Compressional and shear waves; Elastic

porous media.

Poroelastic solids consist of a deformable porous skeleton permeated by fluid, and their mechanical behaviour

depends on the interaction between solid deformation and fluid movement. Biot’s theory offers an established

foundation for describing such media, predicting the existence of two compressional waves fast and slow and a

shear wave, each influenced by factors such as porosity, permeability, and the strength of solid–fluid coupling.

media, modifying wave velocities, deformation patterns, and dynamic stability.

Therefore, incorporating initial stress into vibration analysis yields a more realistic representation of natural and

engineered systems. Another influential factor is the presence of a magnetic field, especially in porous media

containing electrically conductive fluids or magnetic particles.

Magnetoelastic coupling arising from the interaction of mechanical deformation with electromagnetic fields

governed by Maxwell’s equations—introduces additional forces that can stiffen or soften the medium. Magnetic

fields can alter wave speeds, control attenuation, and enable tunable properties, making them relevant in sensors,

non-destructive assessment, and magneto-sensitive composite structures.

Although poroelasticity, initial stress, and magnetoelasticity have each been studied independently, the combined

influence of these factors on two-dimensional vibrations has received limited attention. In reality, many systems

Willson [3] examined the behavior of magnetoelastic plane waves, while Narain [4] analyzed torsional

magnetoelastic waves in an initially stressed bar. Mahmoud [5] explored how magnetic fields and initial stress

influence wave propagation in bone.

Pandey and Sharma [6] studied shear wave behavior in a dissipative magneto-poroelastic isotropic medium, and

Singh and S. Singh [7] investigated shear wave propagation in a magneto-poroelastic layer enclosed between

two media. The combined influence of initial stress and rotation on magnetoelastic waves in an isotropic half-

space was reported by Abd-Alla [8], who also examined magnetic field and initial stress effects in poroelastic

materials [9].

Lopatnikov [10] developed a thermodynamically consistent formulation for magneto-poroelastic materials,

while Dorfmann and Ogden [11] provided insight into nonlinear interactions in magnetoelastic systems.

field within a generalized thermoelastic framework. Magneto-thermo-poroelastic wave behavior in fluid-filled

porous materials under initial stress was investigated by Sahu and Acharya [16].

Al-Bazaz and Othman [17] explored temperature-dependent magneto-poroelastic wave characteristics in media

with pre-existing stress. Plane wave propagation under magnetic fields and initial stress, based on Biot’s theory,

and was discussed by Singh and Tripathi [18].

El-Sayed and Abd-Alla [19] studied wave propagation in a magneto-poroelastic half-space with uniform initial

stress, while Pandey and Gupta [20] analyzed the impact of magnetic fields and prestress on wave dispersion in

porous elastic structures. The effect of magnetic fields on transversely isotropic poroelastic materials was

presented by Manjula and Sree Lakshmi [21], and Manjula Ramagiri [22] investigated wave motion in magneto-

thermoelastic solids in the presence of static stress.

in porous media and have direct relevance to seismic wave modelling, geomechanics, and the design of magneto-

responsive smart materials.

Consider an isotropic poroelastic solid in cartesian coordinate system

. Let

and

the solid and fluid displacements. The governing equations are taken from [23], with initial stress and magnetic

field, fluid pressures are given in [1, 3].

(1)

In eq. (1)

are the stresses,

is the fluid pressure.

are the mass coefficients.

having electrical conductivity are [24]

are the electric intensity, electric current density, primary magnetic field, magnetic

permeability, perturbed magnetic field over the constant primary magnetic field. Solving

of equ. (2) and then

put the value of

(4)

In eq. (4),

is the initial stress,

is the poisson ratio,

in [1]

(6)

In eq. (6)

decomposed in the following form.

(7)

Substituting eq. (7) in eq. (6) we get the following equations

Where

and the wavenumber for different angles0

Figures 1–5 illustrate the variation of frequency with wavenumber for Material-I under a fixed static stress level

(ST-5), considering different propagation angles, initial stress values, and magnetic field strengths. From these

figures, it is evident that an increase in initial stress, magnetic field intensity, or wavenumber leads to a

corresponding rise in frequency. Similarly, Figures 6–10 present the frequency–wavenumber behavior for

Material-II under the same static stress condition

(ST-5). These plots show a trend comparable to Material-I, where higher initial stress, stronger magnetic fields,

and larger wavenumbers result in higher frequencies. In the limiting case where both magnetic field and initial

Fig:7 Variation of frequency with wavenumber for Material-II at