In this paper, natural frequencies and dynamic response of thick beams made of saturated porous materials resting on viscoelastic foundation are investigated for the first time. The beam is modeled using higher-order beam theory. Kelvin-voight model is used to model the viscoelastic foundation. Distribution of porosity along the thickness is considered in two different patterns, which are symmetric nonlinear and nonlinear asymmetric distributions. The relationship between stress and strain is based on the Biot constitutive law. Lagrange equations are used to express the motion equations. Finite element and Newark methods are used to solve the governing equations. The effect of different boundary conditions and various parameters such as porosity and Skempton coefficients, slenderness ratio as well as stiffness and damping coefficients of viscoelastic foundation on natural frequency and transient response of beam have been studied. Results show that in a drained condition, beam has smallest fundamental frequency and by increasing the Skempton coefficient, the fundamental frequency of the beam increases. Manuscript profile

in this study, static, dynamic and natural frequency responses of the functionally graded saturated porous plate have been investigated. Two types of distributions including symmetric nonlinear distribution of porosity and asymmetric nonlinear distribution of porosity in the thickness direction of the plate have been considered. First-order shear deformation theory (FSDT) and Lagrange method are used to model the problem. Finite element and Newmark direct integration methods are used to solve the governing motion equations in time and space domains, and then the effect of different parameters such as porosity and Skempton coefficients, and two different types of porosity distribution, length to thickness ratio and boundary conditions on static and time responses, and natural frequencies of functionally graded saturated porous plate have been investigated. Results show that by increasing the Skempton coefficient will always reduce the displacement and amplitude of vibration . Also, increasing the porosity coefficient will increase the displacement Manuscript profile