Prag Singhal - Academia.edu (original) (raw)

Papers by Prag Singhal

INTERNATIONAL SCIENTIFIC AND PRACTICAL CONFERENCE “TECHNOLOGY IN AGRICULTURE, ENERGY AND ECOLOGY” (TAEE2022)

The assignment problem is an important area in Mathematics that hasvarious applications in the fi... more The assignment problem is an important area in Mathematics that hasvarious applications in the fields of science and engineering. Graphs are commonly used for the conceptual representation of complex structures such as documents, text, and images. The matching of graphs also plays a vital role in solving assignment problems. In this paper, we attempt a model of strategy execution in parliamentary democracy as appointment between the prime mister and his/her cabinet minister is introduced. A brief discussion of some important variations of assignment problems such as Cabinet Reshuffle and Optimal Assignment problem also presented. Assignment algorithm is used in an optimal reshuffling of cabinet. The main motive of the Cabinet Reshuffle Assignment Model to assigned extreme numbers of posts to the ministers which they prefer. Kuhn-Munkres algorithm and optimal assignment problems have been examined with the help of working examples.

Journal of emerging technologies and innovative research, Jun 1, 2020

Trees outside forests (TOF) have crucial ecological and social-economic roles in rural and urban ... more Trees outside forests (TOF) have crucial ecological and social-economic roles in rural and urban contexts around the world. The present study aims to make a large-scale estimation framework to assess ecological diversity of Trees outside forests in some regions of Rajgarh district, Madhya Pradesh. Species have been identified following regional and local floras. GPS was used for registering geographical coordinates of the sampled plots. Systematic enumeration is provided for all the inventoried species. A total of 32 species of trees representing 19 families and 29 genera were recorded in the study area. Among them Eucalyptus tereticornis was the dominant (147), followed by Acacia nilotica (144 trees) and Azadirachta indica (129 trees). The Shanon-Wiener diversity index (H) for the transects was 1.96, Evenness (E) was 1.01and Simpson index (D) was 6.99. The study indicates the availability of higher level of species diversity in Rajgarh, Madhya Pradesh.

International Journal of Engineering and Applied Sciences, 2012

Differential Quadrature Method (DQM) is used to analyse free transverse vibrations of non-homogen... more Differential Quadrature Method (DQM) is used to analyse free transverse vibrations of non-homogeneous orthotropic rectangular plates of variable thickness. A new model to represent the non-homogeneity of the plate material has been taken which incorporates earlier models. Following Levy approach i.e the two parallel edges are simply supported, the fourthorder differential equation governing the motion of such plates of variable thickness has been solved for different combinations of clamped, simply-supported and free-edge boundary conditions. Effect of non- homogeneity together with other plate parameters such as orthotropy, aspect ratio and foundation modulus on the natural frequencies has been studied for the first three modes of vibration. Numerical results are presented to illustrate the method and demonstrate its efficiency. Normalized displacements are presented for specified plates for all the three boundary conditions.

Engineering Transactions, 2017

The objects of consideration are thin linearly elastic Kirchhoff-Love-type open circular cylindri... more The objects of consideration are thin linearly elastic Kirchhoff-Love-type open circular cylindrical shells having a functionally graded macrostructure and a tolerance-periodic microstructure in circumferential direction. The aim of this note is to formulate and discuss a new non-asymptotic averaged model for the analysis of selected dynamic problems for these shells. The proposed asymptotic-tolerance model equations have continuous and slowly varying coefficients depending also on a cell size. An important advantage of this model is that it makes it possible to study micro-dynamics of tolerance-periodic shells independently of their macro-dynamics.

Histoire urbaine, 2015

Distribution électronique Cairn.info pour Société française d'histoire urbaine. © Société françai... more Distribution électronique Cairn.info pour Société française d'histoire urbaine. © Société française d'histoire urbaine. Tous droits réservés pour tous pays. La reproduction ou représentation de cet article, notamment par photocopie, n'est autorisée que dans les limites des conditions générales d'utilisation du site ou, le cas échéant, des conditions générales de la licence souscrite par votre établissement. Toute autre reproduction ou représentation, en tout ou partie, sous quelque forme et de quelque manière que ce soit, est interdite sauf accord préalable et écrit de l'éditeur, en dehors des cas prévus par la législation en vigueur en France. Il est précisé que son stockage dans une base de données est également interdit.

Differential Quadrature Method (DQM) has been used to analyse free vibration of non-homogeneous o... more Differential Quadrature Method (DQM) has been used to analyse free vibration of non-homogeneous orthotropic rectangular plates of parabolically varying thickness resting on Winkler-type elastic foundation. The behaviour of non-homogeneity has been assumed due to exponential variation in Young's modulii and density in one direction. Three different combinations of clamped, simply supported and free edge conditions have been considered. Plots are given to show the effect of foundation parameter together with aspect ratio, taper constant, non-homogeneity parameter and density parameter on the natural frequencies for first three modes of vibration. Mode shapes have been computed for different values of plate parameters. A comparison of our results with those available in literature shows good agreement.

Vibrational behavior of orthotropic rectangular plates resting on Pasternak foundation having two... more Vibrational behavior of orthotropic rectangular plates resting on Pasternak foundation having two opposite edges(y = 0 and b) simply supported, with those edges subjected to linearly varying in-plane stresses σ y =-N 0 (1-γx/a) h, where h is the plate thickness and the other two edges (x = 0 and a) may be clamped or simply supported has been discussed on the basis of classical plate theory. By assuming the transverse displacement (w) to vary as sin(p Л y/b), the governing partial differential equation of motion is reduced to fourth order ordinary differential equation in x with variable coefficients. Chebyshev collocation method has been used to obtain the first three modes of vibration for two different combinations of clamped and simply supported boundary conditions: clamped at x = 0 and clamped or simply supported at the edge x = a. Effect of in-plane force together with elastic foundation and other plate parameters such as orthotropy, aspect ratio on the natural frequencies of v...

Vibrat ion characteristics of monoclinic rectangular plate of exponentially varying thickness res... more Vibrat ion characteristics of monoclinic rectangular plate of exponentially varying thickness resting on elastic foundation have been studied on the basis of classical plate theory. Following Lévy approach i.e. t wo parallel edges (y = 0 and b) are assumed to be simp ly-supported while the other two edges (x = 0 and a) may have either of three co mbinations C-C, C-S or C-F, where C, S and F stand for clamped, simp ly supported and free edge, respectively. Assuming the transverse displacement w to vary as sin (p y/b), the part ial differential equation wh ich governs the motion of equation is reduced to an ordinary differential equation in x with variab le coefficients. The resulting ordinary differential equation has been solved by Generalised Differential Quadrature Method (GDQM) for all the boundary conditions considered here. The effect of various plate parameters has been studied on the natural frequencies for the first three modes of vibration. Convergence studies have been car...

This paper presents a differential quadrature solution for analysis of transverse vibrations of n... more This paper presents a differential quadrature solution for analysis of transverse vibrations of non-homogeneous rectangular orthotropic plates of linearly varying thickness resting on Winkler foundation. Following Lévy approach i.e. two parallel edges are simply supported, the governing equation of motion has been solved for three different combinations of clamped, simply supported and free boundary conditions at the other two edges. Numerical results for first three natural frequencies for various values of parameters are presented in tables and graphs. The accuracy and convergence results are examined and verified.

International Journal Of Engineering & Applied Sciences

Differential Quadrature Method (DQM) is employed to obtain natural frequencies and mode shapes of... more Differential Quadrature Method (DQM) is employed to obtain natural frequencies and mode shapes of nonhomogeneous rectangular orthotropic plates of linearly varying thickness resting on two-parameter foundation (Pasternak). The analysis is based on classical plate theory. Numerical results are presented for various values of plate parameters for different boundary conditions. Convergence studies have been made to ensure accuracy of the results. A comparison of our results with those available in the literature shows the versatility and accuracy of DQM.

Engineering Solid Mechanics, 2016

This paper presents two parameter foundation models for free vibration analysis of nonhomogeneous... more This paper presents two parameter foundation models for free vibration analysis of nonhomogeneous orthotropic rectangular plate resting on elastic foundation whose concept is extensively used in engineering practice. Following Lévy approach i.e. the two parallel edges are simply supported, the fourth order differential equation governing the motion of such plates of non-linear varying thickness in one direction has been solved by using an efficient and rapid convergent numerical approximation technique that is called differential quadrature method (DQM). Appropriate boundary conditions accompany the differential quadrature method to transform the resulting differential equation into an eigenvalue problem. The effects of thickness variation, foundation parameters and other plate parameters with boundary conditions on frequency are examined. The numerical results show that the method converges significantly irrespective of parameters involved.

American Journal of Computational and Applied Mathematics, 2012

Vibrat ion characteristics of monoclinic rectangular plate of exponentially varying thickness res... more Vibrat ion characteristics of monoclinic rectangular plate of exponentially varying thickness resting on elastic foundation have been studied on the basis of classical plate theory. Following Lévy approach i.e. t wo parallel edges (y = 0 and b) are assumed to be simp ly-supported while the other two edges (x = 0 and a) may have either of three co mbinations CC , C-S or C-F, where C, S and F stand for clamped, simp ly supported and free edge, respectively. Assuming the transverse displacement w to vary as sin (p y/b), the part ial differential equation wh ich governs the motion of equation is reduced to an ordinary differential equation in x with variab le coefficients. The resulting ordinary differential equation has been solved by Generalised Differential Quadrature Method (GDQM) for all the boundary conditions considered here. The effect of various plate parameters has been studied on the natural frequencies for the first three modes of vibration. Convergence studies have been carried out for four decimal exactitude. Mode shapes for all the three plates have been presented. The efficiency of generalized differential quadrature method for the natural frequencies of vibrat ion of monoclin ic rectangular p lates has been examined.

INTERNATIONAL SCIENTIFIC AND PRACTICAL CONFERENCE “TECHNOLOGY IN AGRICULTURE, ENERGY AND ECOLOGY” (TAEE2022)

The assignment problem is an important area in Mathematics that hasvarious applications in the fi... more The assignment problem is an important area in Mathematics that hasvarious applications in the fields of science and engineering. Graphs are commonly used for the conceptual representation of complex structures such as documents, text, and images. The matching of graphs also plays a vital role in solving assignment problems. In this paper, we attempt a model of strategy execution in parliamentary democracy as appointment between the prime mister and his/her cabinet minister is introduced. A brief discussion of some important variations of assignment problems such as Cabinet Reshuffle and Optimal Assignment problem also presented. Assignment algorithm is used in an optimal reshuffling of cabinet. The main motive of the Cabinet Reshuffle Assignment Model to assigned extreme numbers of posts to the ministers which they prefer. Kuhn-Munkres algorithm and optimal assignment problems have been examined with the help of working examples.

Journal of emerging technologies and innovative research, Jun 1, 2020

Trees outside forests (TOF) have crucial ecological and social-economic roles in rural and urban ... more Trees outside forests (TOF) have crucial ecological and social-economic roles in rural and urban contexts around the world. The present study aims to make a large-scale estimation framework to assess ecological diversity of Trees outside forests in some regions of Rajgarh district, Madhya Pradesh. Species have been identified following regional and local floras. GPS was used for registering geographical coordinates of the sampled plots. Systematic enumeration is provided for all the inventoried species. A total of 32 species of trees representing 19 families and 29 genera were recorded in the study area. Among them Eucalyptus tereticornis was the dominant (147), followed by Acacia nilotica (144 trees) and Azadirachta indica (129 trees). The Shanon-Wiener diversity index (H) for the transects was 1.96, Evenness (E) was 1.01and Simpson index (D) was 6.99. The study indicates the availability of higher level of species diversity in Rajgarh, Madhya Pradesh.

International Journal of Engineering and Applied Sciences, 2012

Differential Quadrature Method (DQM) is used to analyse free transverse vibrations of non-homogen... more Differential Quadrature Method (DQM) is used to analyse free transverse vibrations of non-homogeneous orthotropic rectangular plates of variable thickness. A new model to represent the non-homogeneity of the plate material has been taken which incorporates earlier models. Following Levy approach i.e the two parallel edges are simply supported, the fourthorder differential equation governing the motion of such plates of variable thickness has been solved for different combinations of clamped, simply-supported and free-edge boundary conditions. Effect of non- homogeneity together with other plate parameters such as orthotropy, aspect ratio and foundation modulus on the natural frequencies has been studied for the first three modes of vibration. Numerical results are presented to illustrate the method and demonstrate its efficiency. Normalized displacements are presented for specified plates for all the three boundary conditions.

Engineering Transactions, 2017

The objects of consideration are thin linearly elastic Kirchhoff-Love-type open circular cylindri... more The objects of consideration are thin linearly elastic Kirchhoff-Love-type open circular cylindrical shells having a functionally graded macrostructure and a tolerance-periodic microstructure in circumferential direction. The aim of this note is to formulate and discuss a new non-asymptotic averaged model for the analysis of selected dynamic problems for these shells. The proposed asymptotic-tolerance model equations have continuous and slowly varying coefficients depending also on a cell size. An important advantage of this model is that it makes it possible to study micro-dynamics of tolerance-periodic shells independently of their macro-dynamics.

Histoire urbaine, 2015

Distribution électronique Cairn.info pour Société française d'histoire urbaine. © Société françai... more Distribution électronique Cairn.info pour Société française d'histoire urbaine. © Société française d'histoire urbaine. Tous droits réservés pour tous pays. La reproduction ou représentation de cet article, notamment par photocopie, n'est autorisée que dans les limites des conditions générales d'utilisation du site ou, le cas échéant, des conditions générales de la licence souscrite par votre établissement. Toute autre reproduction ou représentation, en tout ou partie, sous quelque forme et de quelque manière que ce soit, est interdite sauf accord préalable et écrit de l'éditeur, en dehors des cas prévus par la législation en vigueur en France. Il est précisé que son stockage dans une base de données est également interdit.

Differential Quadrature Method (DQM) has been used to analyse free vibration of non-homogeneous o... more Differential Quadrature Method (DQM) has been used to analyse free vibration of non-homogeneous orthotropic rectangular plates of parabolically varying thickness resting on Winkler-type elastic foundation. The behaviour of non-homogeneity has been assumed due to exponential variation in Young's modulii and density in one direction. Three different combinations of clamped, simply supported and free edge conditions have been considered. Plots are given to show the effect of foundation parameter together with aspect ratio, taper constant, non-homogeneity parameter and density parameter on the natural frequencies for first three modes of vibration. Mode shapes have been computed for different values of plate parameters. A comparison of our results with those available in literature shows good agreement.

Vibrational behavior of orthotropic rectangular plates resting on Pasternak foundation having two... more Vibrational behavior of orthotropic rectangular plates resting on Pasternak foundation having two opposite edges(y = 0 and b) simply supported, with those edges subjected to linearly varying in-plane stresses σ y =-N 0 (1-γx/a) h, where h is the plate thickness and the other two edges (x = 0 and a) may be clamped or simply supported has been discussed on the basis of classical plate theory. By assuming the transverse displacement (w) to vary as sin(p Л y/b), the governing partial differential equation of motion is reduced to fourth order ordinary differential equation in x with variable coefficients. Chebyshev collocation method has been used to obtain the first three modes of vibration for two different combinations of clamped and simply supported boundary conditions: clamped at x = 0 and clamped or simply supported at the edge x = a. Effect of in-plane force together with elastic foundation and other plate parameters such as orthotropy, aspect ratio on the natural frequencies of v...

Vibrat ion characteristics of monoclinic rectangular plate of exponentially varying thickness res... more Vibrat ion characteristics of monoclinic rectangular plate of exponentially varying thickness resting on elastic foundation have been studied on the basis of classical plate theory. Following Lévy approach i.e. t wo parallel edges (y = 0 and b) are assumed to be simp ly-supported while the other two edges (x = 0 and a) may have either of three co mbinations C-C, C-S or C-F, where C, S and F stand for clamped, simp ly supported and free edge, respectively. Assuming the transverse displacement w to vary as sin (p y/b), the part ial differential equation wh ich governs the motion of equation is reduced to an ordinary differential equation in x with variab le coefficients. The resulting ordinary differential equation has been solved by Generalised Differential Quadrature Method (GDQM) for all the boundary conditions considered here. The effect of various plate parameters has been studied on the natural frequencies for the first three modes of vibration. Convergence studies have been car...

This paper presents a differential quadrature solution for analysis of transverse vibrations of n... more This paper presents a differential quadrature solution for analysis of transverse vibrations of non-homogeneous rectangular orthotropic plates of linearly varying thickness resting on Winkler foundation. Following Lévy approach i.e. two parallel edges are simply supported, the governing equation of motion has been solved for three different combinations of clamped, simply supported and free boundary conditions at the other two edges. Numerical results for first three natural frequencies for various values of parameters are presented in tables and graphs. The accuracy and convergence results are examined and verified.

International Journal Of Engineering & Applied Sciences

Differential Quadrature Method (DQM) is employed to obtain natural frequencies and mode shapes of... more Differential Quadrature Method (DQM) is employed to obtain natural frequencies and mode shapes of nonhomogeneous rectangular orthotropic plates of linearly varying thickness resting on two-parameter foundation (Pasternak). The analysis is based on classical plate theory. Numerical results are presented for various values of plate parameters for different boundary conditions. Convergence studies have been made to ensure accuracy of the results. A comparison of our results with those available in the literature shows the versatility and accuracy of DQM.

Engineering Solid Mechanics, 2016

This paper presents two parameter foundation models for free vibration analysis of nonhomogeneous... more This paper presents two parameter foundation models for free vibration analysis of nonhomogeneous orthotropic rectangular plate resting on elastic foundation whose concept is extensively used in engineering practice. Following Lévy approach i.e. the two parallel edges are simply supported, the fourth order differential equation governing the motion of such plates of non-linear varying thickness in one direction has been solved by using an efficient and rapid convergent numerical approximation technique that is called differential quadrature method (DQM). Appropriate boundary conditions accompany the differential quadrature method to transform the resulting differential equation into an eigenvalue problem. The effects of thickness variation, foundation parameters and other plate parameters with boundary conditions on frequency are examined. The numerical results show that the method converges significantly irrespective of parameters involved.

American Journal of Computational and Applied Mathematics, 2012

Vibrat ion characteristics of monoclinic rectangular plate of exponentially varying thickness res... more Vibrat ion characteristics of monoclinic rectangular plate of exponentially varying thickness resting on elastic foundation have been studied on the basis of classical plate theory. Following Lévy approach i.e. t wo parallel edges (y = 0 and b) are assumed to be simp ly-supported while the other two edges (x = 0 and a) may have either of three co mbinations CC , C-S or C-F, where C, S and F stand for clamped, simp ly supported and free edge, respectively. Assuming the transverse displacement w to vary as sin (p y/b), the part ial differential equation wh ich governs the motion of equation is reduced to an ordinary differential equation in x with variab le coefficients. The resulting ordinary differential equation has been solved by Generalised Differential Quadrature Method (GDQM) for all the boundary conditions considered here. The effect of various plate parameters has been studied on the natural frequencies for the first three modes of vibration. Convergence studies have been carried out for four decimal exactitude. Mode shapes for all the three plates have been presented. The efficiency of generalized differential quadrature method for the natural frequencies of vibrat ion of monoclin ic rectangular p lates has been examined.