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<p>This <?tk 4?>work analyzes the analysis of simply supported orthotropic prestressed plates under distributed loads resting on variable Pasternak foundation. The fourth order partial equation which governs the problem, is reduced to coupled equations of second order differential equations and the variable separation technique is now applied. The coupled equation is evaluated by employing a variant of Struble’s procedure. The Heaviside function is used to provide a solution to the dynamical response of prestressed rectangle plates of various axes under effects of distributed loads. The findings demonstrate that the displacement of the simple support of the pre-stressed forces in <i>x</i> direction and <i>y</i> direction decrease for various values of the pre-stressed forces along <i>x</i> and <i>y</i> increase. The result also shows that the deflection of the orthotropic plate of simple supports is primarily influenced by the pre-stress along <i>x</i> axis than the pre-stress along <i>y</i> axis. Also, in moving mass solution and moving force solution, the pre-stressed force along <i>y</i> direction provides close results of pre-stressed rectangle plates of different axes with simple supports resting on bi-parametric foundational varyings. The evaluation of the closed-form solution demonstrates that the move of force solution is not restricted to the move of mass problem for a pre-stressed rectangle plate with varied axes and simple supports. This demonstrates that the critical speed has more effects on the move of the mass problem rather than the move of the force problem. The analysis of numerical results is done graphically. Furthermore, the pre-stressed force along both <i>x</i> and <i>y</i> axes of directions having specific values, the maximum absolute value of the move of the force solution is lower than the the maximum absolute value of the move for the mass solution. Because of this, in simple supports of a rectangle prestressed orthotropic plate, the moving mass solution is more dependable than the moving force solution.</p>

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Analysis of Simply Supported Orthotropic Pre-stressed Plates Under Distributed Loads Resting on Variable Pasternak Foundation

  • 期刊论文

  • 发表日期：

    2025年11月21日

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  • A. Akintomide,
  • T. O. Awodola

摘要

This work analyzes the analysis of simply supported orthotropic prestressed plates under distributed loads resting on variable Pasternak foundation. The fourth order partial equation which governs the problem, is reduced to coupled equations of second order differential equations and the variable separation technique is now applied. The coupled equation is evaluated by employing a variant of Struble’s procedure. The Heaviside function is used to provide a solution to the dynamical response of prestressed rectangle plates of various axes under effects of distributed loads. The findings demonstrate that the displacement of the simple support of the pre-stressed forces in x direction and y direction decrease for various values of the pre-stressed forces along x and y increase. The result also shows that the deflection of the orthotropic plate of simple supports is primarily influenced by the pre-stress along x axis than the pre-stress along y axis. Also, in moving mass solution and moving force solution, the pre-stressed force along y direction provides close results of pre-stressed rectangle plates of different axes with simple supports resting on bi-parametric foundational varyings. The evaluation of the closed-form solution demonstrates that the move of force solution is not restricted to the move of mass problem for a pre-stressed rectangle plate with varied axes and simple supports. This demonstrates that the critical speed has more effects on the move of the mass problem rather than the move of the force problem. The analysis of numerical results is done graphically. Furthermore, the pre-stressed force along both x and y axes of directions having specific values, the maximum absolute value of the move of the force solution is lower than the the maximum absolute value of the move for the mass solution. Because of this, in simple supports of a rectangle prestressed orthotropic plate, the moving mass solution is more dependable than the moving force solution.