Sharif Digital Repository

An exact solution is established pertaining to the problem of undamped free vibration of a thin circular plate resting on a Winkler foundation with variable subgrade modulus. The solution is performed by applying the infinite power series method. Moreover, the solution procedure is demonstrated through an illustrative example, wherein the general frequency equation is derived for two different boundary conditions. The correctness of the solution is also verified using results available in the literature. Finally, it is shown that the proposed method of solution is directly applicable to the more-general problem of circular plates on a variable-modulus Pasternak-type foundation  

The underground and buried oil and gas pipelines are continuously in contact with earthen soils on the outer surface and compressible fluids on the inner surface. Most these earthen soils can be appropriately represented by a model named Pasternak. Similarly, undersea oil and gas pipelines and tubes of heat exchangers remain in contact with fluids on both sides and also rockets and missiles filled with solid and liquid fuels and shallow shells supported on soft and light filaments in space vehicles, boilers and storage tanks on floor grid work in ships can also be considered as thin circular cylindrical shells on a Pasternak foundation. The basic aim of the presented study is investigation... 

In this paper, a new analytical approach is proposed for free vibration and buckling analysis of a rectangular Mindlin plate resting on the Winkler–Pasternak foundation of varying stiffness. According to Mindlin theory, there are three independent governing differential equations. Thus, three Fourier series expansions along with auxiliary polynomial functions are employed to represent the plate's deflection and rotation angle functions. The process of making a set of equations is then completed satisfying the corresponding equilibrium equations and boundary conditions. The proposed method incorporates general elastic supports for all plate's edges, and subsequently can deal with all possible... 

In this paper, the generalized differential quadrature (GDQ) method is used to study free vibration of moderately thick rectangular plate partially resting on Pasternak foundation. The foundation is considered to support the plate either completely or partially. The governing equations which consist of a system of partial differential equations (PDEs) are obtained based on the first-order shear deformation theory. Various combinations of simply supported, clamped and free boundary conditions are considered. Application of the GDQ method to the governing PDEs resulted in a system of algebraic equations. Solution of this system with accordance to the considered boundary conditions leads to an... 

In the last decade, extensive attention is devoted to intelligibly designed materials of macro/micro-structures containing the fluid flow. In this study, intelligent control and vibrational stability of cantilevered fluid conveying macro/micro-tubes utilizing axially functionally graded (AFG) materials are considered. The governing equation of motion of the system is derived based on modified couple stress theory and then is discretized using Galerkin method. A detailed investigation is carried out to elaborate the influence of various parameters such as material properties, axial compressive load, and Pasternak foundation on the dynamical behavior of the system, all of which are influential... 

In the last decade, extensive attention is devoted to intelligibly designed materials of macro/micro-structures containing the fluid flow. In this study, intelligent control and vibrational stability of cantilevered fluid conveying macro/micro-tubes utilizing axially functionally graded (AFG) materials are considered. The governing equation of motion of the system is derived based on modified couple stress theory and then is discretized using Galerkin method. A detailed investigation is carried out to elaborate the influence of various parameters such as material properties, axial compressive load, and Pasternak foundation on the dynamical behavior of the system, all of which are influential... 

In this paper, the vibration of a moderately thick plate to a moving mass is investigated. Pasternak foundation with a variable subgrade modulus is considered to tackle the shortcomings of Winkler model, and an analytical-numerical solution is proposed based on the eigenfunction expansion method. Parametric studies by using both CPT (Classical Plate Theory) and FSDT (First-Order Shear Deformation Plate Theory) are carried out, and, the differences between them are also highlighted. The obtained results reveal that utilizing FSDT without considering the rotary inertia leads to a smaller deflection in comparison with CPT pertaining to a thin plate, while it demonstrates a greater response for... 

Dynamic response of infinite beams supported by random viscoelastic Pasternak foundation subjected to harmonic moving loads is studied. Vertical stiffness in the support is assumed to follow a stochastic homogeneous field consisting of a small random variation around a deterministic mean value. By employing the first order perturbation theory and calculating appropriate Green's functions, the variance of the deflection and bending moment are obtained analytically in integral forms. To simulate the induced uncertainty, two practical cases of cosine and exponential covariance are utilized. A frequency analysis is performed and influences of the correlation length of the stiffness variation on...