• Structural Engineering and Mechanics
• /
• v.59 no.6
• /
• pp.1019-1035
• /
• 2016

This paper proposes a new foundation model called "Dynamic foundation model" for the dynamic analysis of plates on foundation subjected to a moving oscillator. This model includes a linear elastic spring, shear layer, viscous damping and the special effects of mass density parameters of foundation during vibration. By using finite element method and the principle of dynamic balance, the governing equation of motion of the plate travelled by the oscillator is derived and solved by the Newmark's time integration procedure. The accuracy of the algorithm is verified by comparing the numerical results with the other numerical results in the literature. Also, the effects of mass and damping ratio of system components, stiffness of suspension system, velocity of moving oscillator, and dynamic foundation parameters on dynamic responses are investigated. A very important role of these factors will be shown in the dynamic behavior of the plate.

• Coupled systems mechanics
• /
• v.12 no.1
• /
• pp.83-102
• /
• 2023

First introduced in 2016, the dynamic foundation model is an interesting topic in which the foundation is described close to reality by taking into account the influence of the foundation mass in the calculation of oscillation and is an important parameter that should be considered. In this paper, a follow-up investigation is conducted with the object of the Mindlin plate on a nonlinear dynamic foundation under moving loads. The base model includes nonlinear elastic springs, linear Pasternak parameters, viscous damping, and foundation mass. The problem is formulated by the finite element analysis and solved by the Newmark-β method. The displacement results at the center of the plate are analyzed and discussed with the change of various parameters including the nonlinear stiffness, the foundation mass, and the load velocity. The dynamic response of the plate sufficiently depends on the foundation mass.

• Structural Engineering and Mechanics
• /
• v.65 no.5
• /
• pp.505-511
• /
• 2018

Recently, a new foundation model called "Dynamic foundation model" was proposed for the dynamic analysis of structures on the foundation. This model includes a linear elastic spring, shear layer, viscous damping and the special effects of mass density parameter of foundation during vibration. However, the relationship of foundation property parameters with the experimental parameter of the influence of foundation mass also has not been established in previous research. Hence, the purpose of the paper presents a simple experimental model in order to establish relationships between foundation properties such as stiffness, depth of foundation and experimental parameter of the influence of foundation mass. The simple experimental model is described by a steel plate connected with solid rubber layer as a single degree of freedom system including an elastic spring connected with lumped mass. Based on natural circular frequencies of the experimental models determined from FFT analysis plots of the time history of acceleration data, the experimental parameter of the influence of foundation mass is obtained and the above relationships are also discussed.

• Steel and Composite Structures
• /
• v.37 no.1
• /
• pp.99-115
• /
• 2020

This article deals with the dynamic analysis in pad concrete foundation containing Silica nanoparticles (SiO₂) subject to seismic load. In order to control the foundation smartly, a piezoelectric layer covered the foundation. The weight of the building by a column on the foundation is assumed with an external force in the middle of the structure. The foundation is located in soil medium which is modeled by spring elements. The Mori-Tanaka law is utilized for calculating the equivalent mechanical characteristics of the concrete foundation. The Kevin-Voigt model is adopted to take into account the structural damping. The concrete structure is modeled by a thick plate and the governing equations are deduced using Hamilton's principle under the assumption of higher-order shear deformation theory (HSDT). The differential quadrature method (DQM) and the Newmark method are applied to obtain the seismic response. The effects of the applied voltage to the smart layer, agglomeration and volume percent of SiO₂ nanoparticles, damping of the structure, geometrical parameters and soil medium of the structure are assessed on the dynamic response. It has been demonstrated by the numerical results that by applying a negative voltage, the dynamic deflection is reduced significantly. Moreover, silica nanoparticles reduce the dynamic deflection of the concrete foundation.

• Structural Engineering and Mechanics
• /
• v.58 no.6
• /
• pp.1045-1075
• /
• 2016

Shallow footings are one of the most common types of foundations used to support mid-rise buildings in high risk seismic zones. Recent findings have revealed that the dynamic interaction between the soil, foundation, and the superstructure can influence the seismic response of the building during earthquakes. Accordingly, the properties of a foundation can alter the dynamic characteristics (natural frequency and damping) of the soil-foundation-structure system. In this paper the influence that shallow foundations have on the seismic response of a mid-rise moment resisting building is investigated. For this purpose, a fifteen storey moment resisting frame sitting on shallow footings with different sizes was simulated numerically using ABAQUS software. By adopting a direct calculation method, the numerical model can perform a fully nonlinear time history dynamic analysis to realistically simulate the dynamic behaviour of soil, foundation, and structure under seismic excitations. This three-dimensional numerical model accounts for the nonlinear behaviour of the soil medium and structural elements. Infinite boundary conditions were assigned to the numerical model to simulate free field boundaries, and appropriate contact elements capable of modelling sliding and separation between the foundation and soil elements are also considered. The influence of foundation size on the natural frequency of the system and structural response spectrum was also studied. The numerical results for cases of soil-foundation-structure systems with different sized foundations and fixed base conditions (excluding soil-foundation-structure interaction) in terms of lateral deformations, inter-storey drifts, rocking, and shear force distribution of the structure were then compared. Due to natural period lengthening, there was a significant reduction in the base shears when the size of the foundation was reduced. It was concluded that the size of a shallow foundation influences the dynamic characteristics and the seismic response of the building due to interaction between the soil, foundation, and structure, and therefore design engineer should carefully consider these parameters in order to ensure a safe and cost effective seismic design.

• Geomechanics and Engineering
• /
• v.23 no.6
• /
• pp.547-560
• /
• 2020

This paper studies the dynamic foundation-soil-foundation interaction for two square rigid foundations embedded in a viscoelastic soil layer. The vibrations come from only one rigid foundation placed in the soil layer and subjected to harmonic loads of translation, rocking, and torsion. The required dynamic response of rigid surface foundations constitutes the solution of the wave equations obtained by taking account of the conditions of interaction. The solution is formulated using the frequency domain Boundary Element Method (BEM) in conjunction with the Kausel-Peek Green's function for a layered stratum, with the aid of the Thin Layer Method (TLM), to study the dynamic interaction between adjacent foundations. This approach allows the establishment of a mathematical model that enables us to determine the dynamic displacements amplitude of adjacent foundations according to their different separations, the depth of the substratum, foundations masss, foundations embedded, and the frequencies of excitation. This paper attempts to introduce an approach based on a polynomial mathematical tool conducted from several results of numerical methods (BEM-TLM) so that practicing civil engineers can evaluation the dynamic foundations displacements more easy.

• Journal of Ocean Engineering and Technology
• /
• v.12 no.3 s.29
• /
• pp.19-30
• /
• 1998

In this paper, the dynamic analysis of a dolphin system for mooring a floating structure such as barge mounted plant is studied. The characteristics of the soil-pile system are simplified by a set of equivalent spring elements at the mudline. To evaluate the equivalent spring constants, the finite difference method is used. Since the characteristics of the soil-pile system are nonlinear in case of soft foundation, the nonlinear dynamic analysis technique is needed. The Newmark $beta$ method incorporating the modified Newton-Raphson method(initial stiffness method) is used. A numerical analysis is performed on two mooring dolphin systems on soft foundation and rock foundation. In case of the rock foundation, the characteristics are found to be nearly linear, so the linear dynamic analysis may be sufficient to consider the foundation effect. But in case of soft foundation, the non-linearity of the foundation appears to be very signigicant, so the nonlinear dynamic analysis si needed.

• Structural Engineering and Mechanics
• /
• v.54 no.4
• /
• pp.623-648
• /
• 2015

A numerical approach is presented for the analysis of the forced vibration of a rigid surface foundation with arbitrary shape. In the analysis, the foundation is discretized into a number of sub squaree-lements. The dynamic response within each sub-element is described by the Green's function, which is obtained by the Fourier-Bessel transform and Precise Integration Method (PIM). Incorporating the displacement boundary condition and force equilibrium of the foundation, it obtains a system of linear algebraic equation in terms of the contact forces within each sub-element. Solving the equation leads to the desired dynamic impedance functions of the foundation. Numerical results are obtained for foundation not only with simple geometrical configurations, such as rectangular and circular foundation, but also the case of irregularly shaped foundation. Several comparisons between the proposed approach and other methods are made. Very good agreement is reached. Also, parametric studies are carried out on the dynamic response of foundation. Addressed in this study are the effects of Poisson's ratio, material damping and contact condition of soil-foundation interface. Several conclusions are drawn the significance of the factors.

• Geomechanics and Engineering
• /
• v.34 no.6
• /
• pp.649-664
• /
• 2023

Structural inertial interaction is a representative the effect of dynamic soil-foundation-structure interaction (SFSI), which leads to a relative displacement between soil and foundation, period lengthening, and damping increasing phenomena. However, for a system with a significantly heavy foundation, the dynamic inertia of the foundation influences and interacts with the structural seismic response. The structure-to-foundation mass ratio (MR) quantifies the distribution of mass between the structure and foundation for a structure on a shallow foundation. Although both systems exhibit the same vertical factor of safety (FS_v), the MR and corresponding seismic responses attributed to the structure and foundation masses may differ. This study explored the influence of MR on the permanent deformation and seismic response of soil-foundation-structure system considering SFSI via numerical simulations. Given that numerous dimensionless parameters of SFSI described its influence on the structural seismic response, the parameters, except for MR and FS_v, were fixed for the sensitivity analysis. The results demonstrated that the foundation inertia of heavier foundations induced more settlement due to sliding behavior of heavily-loaded systems. Moreover, the structural inertia of heavier structures evidently exhibited foundation rocking behavior, which results in a more elongated natural period of the structure for lightly-loaded systems.

• Advances in aircraft and spacecraft science
• /
• v.3 no.4
• /
• pp.471-502
• /
• 2016

This paper presents the dynamic instability analysis of un-damped elastically supported piezoelectric functionally graded (FG) beams subjected to in-plane static and dynamic periodic thermomechanical loadings with uncertain system properties. The elastic foundation model is assumed as one parameter Pasternak foundation with Winkler cubic nonlinearity. The piezoelectric FG beam is subjected to non-uniform temperature distribution with temperature dependent material properties. The Young's modulus and Poison's ratio of ceramic, metal and piezoelectric, density of respective ceramic and metal, volume fraction exponent and foundation parameters are taken as uncertain system properties. The basic nonlinear formulation of the beam is based on higher order shear deformation theory (HSDT) with von-Karman strain kinematics. The governing deterministic static and dynamic random instability equation and regions is solved by Bolotin's approach with Newmark's time integration method combined with first order perturbation technique (FOPT). Typical numerical results in terms of the mean and standard deviation of dynamic instability analysis are presented to examine the effect of slenderness ratios, volume fraction exponents, foundation parameters, amplitude ratios, temperature increments and position of piezoelectric layers by changing the random system properties. The correctness of the present stochastic model is examined by comparing the results with direct Monte Caro simulation (MCS).