Skip Ribbon Commands
Skip to main content
Dr. Moniba Shams
Assistant Professor
Department of Mathematics

National University of Sciences and Technology (NUST)
Tel : +92 51 90855582


PhD Mathematics (Glasgow, UK)

Welcome! My background is applying mathematics to study wave propagation in elastic solids. I work with Surface and plane waves and my work can be found on my google scholar page for reference. Therefore, the research field is some times called as Elastodynamics or solid mechanics. I completed my PhD in the same field from University of Glasgow in 2011. My thesis can be found hereSince then I am affiliated with SNS-NUST. 

The phenomenon of wave propagation in solids has been an area of interest since it is applicable to many real life problems. For example, as mentioned in the book, the manufacturing of high frequency acoustic wave filters and transducers (used in everyday electronic device such as global positioning systems, cell phones, miniature motors, detectors, sensors, etc.), the health monitoring of of elastic structures (non-destructive evaluation in the automotive or aeronautic industry), the acoustic determination of elastic properties of solids (physics, medicine, engineering, etc.), ultrasonic imaging techniques (medicine, oil prospection, etc.), and so on. I would like to work with young researchers on new problems. The theories of linear and non-linear elasticity can be used in problems which involve fluid-solid interaction as well. ​


Research Area:

Solid Mechanics, Elastodynamics, Wave Propagation

Research Interests:

Study of wave properties in residually stressed materials is an saturated field of study in Elastodynamics. Materials are generally considered to be unstressed in their initial configuration. However, practically this is an assumption far from real. The presence of stress in the unloaded state of a material causes major changes in its properties and these changes are studied through the effect of this residual stress on the wave speed, its amplitude and various other parameters.

Research Students:

​Sr. ​Ph.d
​1 ​One student under supervision


​Sr. ​M.Phill
​1 ​Rashida Zafar (2019)
Title of MS dissertation: Hadamard-type fractional operators and their Mellin transform analysis.
​2 ​​​Sadaf Shaheen (2019)
Title of MS dissertation: Rayleigh Wave Propagation in Anisotropic Elastic Materials.
​3 ​Asad Ali (2019)
Title of MS dissertation: Reflection of quasi-P and quasi-SV waves at the surface of monoclinic medium.
​4 ​Attiya Imtiaz (2018)
Title of MS dissertation: Some formulas for Rayleigh wave speed.
​5 ​Ayesha Bibi (2017)
Title of MS dissertation: Effect of rotation on speed of surface waves in anisotropic materials.
​6 ​Noureen Tayyab (2017)
Title of MS dissertation: Surface waves in orthotropic elastic medium with voids.
​7 ​Naveed Iqbal (2014)
Title of MPhil Dissertation: Propagation of Waves in Initially-stressed Elastic Materials.
​8​ ​Mohammad Afzal Awan (2012)
Title of MPhil Dissertation: Rayleigh-lamb frequency spectrum for Isotropic materials.​

Research Publications:

  • Aziz,A.; Jamshed, W.; Ali, Y.; Shams, M.; Heat transfer and entropy analysis of Maxwell hybrid Nanofluid including effects of inclined magnetic field, Joule heating and thermal radiation, Discrete and continuous dynamical systems-series-s, To appear, 2019.
  • Shams, M.; Wave propagation in an incompressible hollow elastic cylinder with residual stress, Discrete and continuous dynamical systems-series-s, Accepted, 2019.
  • Shams, M.; Khalique, CM.; Aziz, T.; Plane Wave Reflection in a Compressible Half Space with Initial Stress, Open Physics, 17, 438-448, 2019.
  • E
  • jaz, K; Shams, M; Love waves in compressible elastic materials with a homogeneous initial stress, Mathematics and Mechanics of Solids, 24(8), 2576-2590, First published: 2018, Published: 2019.
  • Shams, M; Reflection of plane waves from the boundary of an initially stressed incompressible half-space, Mathematics and Mechanics of Solids, 24(2) 406-433, First published: 2017, Published: 2019.
  • Shams, M; Effect of initial stress on Love wave propagation at the boundary between a layer and a half-space, Wave Motion, 65, 92-104, 2016.
  • Shams, M; Ogden, RW; On Rayleigh-type surface waves in an initially stressed incompressible elastic solid, IMA Journal of Applied Mathematics, 79( 2), 360-376, 2014.
  • Hussain, T ; Awan, MA; Shams, M; Ahmad, F; Lamb Modes for an Isotropic Incompressible Plate, Mathematical Problems in Engineering,; 2013.
  • Shams, M; Destrade, M; Ogden, RW; Initial stresses in elastic solids: constitutive laws and acoustoelasticity, Wave Motion, 48, (7), 552-567, 2011.
  • Shams, M; Wave propagation in residually-stressed materials, 2010, University of Glasgow. (PhD Thesis).
  • Ahmad, F; Kiyani, N; Yousaf, F; Shams, M; Guided waves in a fluid-loaded transversely isotropic plate, Mathematical Problems in Engineering, 8(2) 151-159, 2002.

Current courses:

  • Mathematical Computing (MATLAB and Python) -4th Semester
  • Mathematical Modeling - 8th Semester (Maths and Phys)​

Already taught:

UG courses:

  • Calculus I (Single Variable Calculus)
  • Calculus II (Multi-variable Calculus)
  • Calculus III (Advanced Engineering Mathematics)
  • Linear Algebra with Applications using MATLAB
  • Ordinary Differential Equations
  • Discrete Mathematics and its Applications
  • Fundamentals of Mathematics (Basic Level Course for Bio-Bioinformatic)
  • Cryptography
  • Number Theory
  • Mathematical Modeling

PG Courses:

  • Computational Mathematics
  • Optimization Theory
  • Continuum Mechanics
  • Research Methodology
  • Differential Equations
  • Nonlinear Theory of Elasticity