Flexural Analysis of Thick Isotropic Rectangular Plates Using Orthogonal Polynomial Displacement Functions

This paper analysed the flexural behaviour of SSSS thick isotropic rectangular plates under transverse load using the Ritz method. It is assumed that the line that is normal to the mid-surface of the plate before bending does not remain the same after bending and consequently a shear deformation function f (z) is introduced. A polynomial shear deformation function f (z) was derived for this research. The total potential energy which was established by combining the strain energy and external work was subjected to direct variation to determine the governing equations for the in – plane and out-plane displacement coefficients. Numerical results for the present study were obtained for the thick isotropic SSSS rectangular plates and comparison of the results of this research and previous work done in literature showed good convergence. However, It was also observed that the result obtained in this present study are significantly upper bound as compared with the results of other researchers who employed the higher order shear deformation theory (HSDT), first order shear deformation theory (FSDT) and classical plate theory (CPT) theories for the in – plane and out of plane displacements at span – depth ratio of 4. Also, at a span - depth ratio of and above, there was approximately no difference in the values obtained for the out of plane displacements and in-plane displacements between the CPT and the theory used in this study.

The CPR black hole with acceleration

Different deformations and modifications have been proposed in the Kerr black hole solution. In the so-called non-Kerr metric a deformation function was proposed. This approach has been generalized to include two different deformation functions to obtain the CPR black hole (Cardoso et al. in Phys Rev D 89:064007, 2014). In this letter we develop the accelerating version of this spacetime and study its thermodynamics.

Kinetic energy properties and weak equivalence principle in a space with generalized uncertainty principle

A space with deformed commutation relations for coordinates and momenta leading to generalized uncertainty principle (GUP) is studied. We show that GUP causes great violation of the weak equivalence principle for macroscopic bodies, violation of additivity property of the kinetic energy, dependence of the kinetic energy on composition, great corrections to the kinetic energy of macroscopic bodies. We find that all these problems can be solved in the case of arbitrary deformation function depending on momentum if parameter of deformation is proportional inversely to squared mass.

A completely deformed anisotropic class one solution for charged compact star: a gravitational decoupling approach

In this article, we have investigated a new completely deformed embedding class one solution for the compact star in the framework of charged anisotropic matter distribution. For determining of this new solution, we deformed both gravitational potentials as $$\nu ~\mapsto ~\xi +\alpha \, h(r)$$ν↦ξ+αh(r) and $$e^{-\lambda } \mapsto ~e^{-{\mu }} + \alpha \,f(r)$$e-λ↦e-μ+αf(r) by using Ovalle (Phys Lett B 788:213, 2019) approach. The gravitational deformation divides the original coupled system into two individual systems which are called the Einstein’s system and Maxwell-system (known as quasi-Einstein system), respectively. The Einstein’s system is solved by using embedding class one condition in the context of anisotropic matter distribution while the solution of Maxwell-system is determined by solving of corresponding conservation equation via assuming a well-defined ansatz for deformation function h(r). In this way, we obtain the expression for the electric field and another deformation function f(r). Moreover, we also discussed the physical validity of the solution for the coupled system by performing several physical tests. This investigation shows that the gravitational decoupling approach is a powerful methodology to generate a well-behaved solution for the compact object.

Minimally deformed anisotropic model of class one space-time by gravitational decoupling

In this article, we have presented a static anisotropic solution of stellar compact objects for self-gravitating system by using minimal geometric deformation techniques in the framework of embedding class one space-time. For solving of this coupling system, we deform this system into two separate system through the geometric deformation of radial components for the source function $$\lambda (r)$$λ(r) by mapping: $$e^{-\lambda (r)}\rightarrow e^{-\tilde{\lambda }(r)}+\beta \,g(r)$$e-λ(r)→e-λ~(r)+βg(r), where g(r) is deformation function. The first system corresponds to Einstein’s system which is solved by taking a particular generalized form for source function $$\tilde{\lambda }(r)$$λ~(r) while another system is solved by choosing well-behaved deformation function g(r). To test the physical viability of this solution, we find complete thermodynamical observable as pressure, density, velocity, and equilibrium condition via. TOV equation etc. In addition to the above, we have also obtained the moment of inertia (I), Kepler frequency (v), compression modulus ($$K_e$$Ke) and stability for this coupling system. The M–R curve has been presented for obtaining the maximum mass and corresponding radius of the compact objects.

COHERENT STATES FOR NONLINEAR TWO-BOSON REALIZATION OF THE ISOTROPIC OSCILLATOR ALGEBRA ON A SPHERE

In this paper, we generalize Schwinger realization of the 𝔰𝔲(2) algebra to construct a two-mode realization for deformed 𝔰𝔲(2) algebra on a sphere. We obtain a nonlinear (f-deformed) Schwinger realization with a deformation function corresponding to the curvature of sphere that in the flat limit tends to unity. With the use of this nonlinear two-mode algebra, we construct the associated two-mode coherent states (CSs) on the sphere and investigate their quantum entanglement. We also compare the quantum statistical properties of the two modes of the constructed CSs, including anticorrelation and antibunching effects. Particularly, the influence of the curvature of the physical space on the nonclassical properties of two modes is clarified.

Free Vibration of Elastic Timoshenko Beam on Fractional Derivative Winkler Viscoelastic Foundation

The fractional derivative Winkler viscoelastic foundation model is established by introducing the concept of fractional derivative. The control equations of free vibration of elastic Timoshenko beam on fractional derivative Winkler viscoelastic foundation are also built by considering the shear deformation and rotary inertia, and the control equations of elastic Timoshenko beam are decoupled by using the deformation function and considering the properties of fractional derivative, and the expressions of deflection and section corner of elastic Timoshenko beam on fractional derivative Winkler viscoelastic foundation are obtained. The influences of fractional derivative order and shear shape factor on the free vibration of elastic Timoshenko beam are discussed by numerical example.