In this study, the liquid sloshing in a cylindrical tank considering soil–structure interaction a... more In this study, the liquid sloshing in a cylindrical tank considering soil–structure interaction and undergoing horizontal excitation is investigated analytically. Multiple rigid annular baffles are positioned on the rigid wall to mitigate the liquid sloshing. Firstly, combined with the subdomain partition method for sloshing, the complex liquid domain is partitioned into simple subdomains with the single condition for boundary. Based on continuity conditions of velocity and pressure as well as the linear sloshing equation for free surface, the exact solution for convective velocity potential is derived with high accuracy. By yielding the similar hydrodynamic shear and moment as those of the original system, a mechanical model is developed to describe continuous sloshing, and parameters of the model are given in detail. Then, by means of the least squares approach, the Chebyshev polynomials are utilized to fit impedances for the circular surface foundation. A lumped parameter model i...
A direct approach is used to derive the exact solution for the free vibration of thin rectangular... more A direct approach is used to derive the exact solution for the free vibration of thin rectangular plates with discrete sprung masses attached. The plate is simply supported along two opposite edges and elastically supported along the two other edges. The elastic support can represent a range of boundary conditions from free to clamped supports. Considering only the compatibility of the internal forces between the plate and the sprung masses, the equations of the coupled vibration of the plate-spring-mass system are derived. The exact expressions for mode and frequency equations of the coupled vibration of the plate and sprung masses are determined. The solutions converge steadily and monotonically to exact values. The correctness and accuracy of the solutions are demonstrated through comparison with published results. A parametric study is undertaken focusing on the plate with one or two sprung masses. The results can be used as a benchmark for further investigation.The solution pro...
This paper studies the stress and displacement distributions of transversely isotropic rectangula... more This paper studies the stress and displacement distributions of transversely isotropic rectangular plates with continuously varying thickness and simply supported at four edges. On the basis of three-dimensional elasticity theory, the general expressions for the displacements and stresses of the plate under static loads, which exactly satisfy the governing differential equations and the edge conditions of the plate, are analytically derived. The unknown coefficients in the solutions are approximately determined by using the double Fourier sinusoidal series expansions to the upper surface and lower surface conditions of the plate. Convergence and comparison studies demonstrate the correctness and effectiveness of the proposed method.
The phenomenon of earthquake-induced structural pounding was extensively studied by some research... more The phenomenon of earthquake-induced structural pounding was extensively studied by some researchers using different models for the impact force. The aim of this paper is to provide a new formula of impact stiffness in the linear viscoelastic contact model, based on the assumption that the maximum impact deformation from the distributed mass model should be equal to that from the equivalent lumped mass model. The correctness and accuracy of the proposed formula have been confirmed by comparing the pounding simulation using the present formula of impact stiffness with those using the existing formulae.
This paper studies the parameter effect of side retainers on seismic response of bridges with fle... more This paper studies the parameter effect of side retainers on seismic response of bridges with flexible rubber bearings. The pounding effect between girder and side retainers is analyzed by the nonlinear time-history analysis. The pounding and sliding of bearings are simulated by the nonlinear contact elements. Comparative analysis of seismic performance of bridge with/without retainers is carried out. Furthermore, the seismic performances of ordinary retainers and new retainers are compared. Finally, the effect of side retainer parameters on seismic response of bridge is analyzed. The results indicate that the sliding of elastomeric pad bearing should be considered in seismic design. It is shown that the retainers can effectively restrain the relative displacement between girder and piers, and the new type of retainers can greatly reduce the pounding force. It is also proved that both stiffness and gap of the retainer have significant influences on the pounding force.
In this work, analytical solution of simply supported sandwich arches considering permeation effe... more In this work, analytical solution of simply supported sandwich arches considering permeation effect of adhesives is presented. The permeation layer is described by the functionally graded material, exponentially graded in the radial direction. The stresses and deformations of each layer are based on the two-dimensional (2D) elasticity theory in the polar coordinate. The governing equations of the arch are solved by the layer-wise method, which turns the differential equations with variable coefficients into constant coefficients. The solution can be obtained efficiently by means of the recursive matrix method, especially for the arch with many layers. The present solution agrees well with the finite element solution with a fine mesh, while the finite element method is time consuming in mesh division and calculation. The one-dimensional (1D) solution based on the Euler–Bernoulli theory is close to the present one; however, the error increases as the arch becomes thick. The effect of ...
An analytical solution of stresses and deformations for two-layer Timoshenko beams glued by a vis... more An analytical solution of stresses and deformations for two-layer Timoshenko beams glued by a viscoelastic interlayer under uniform transverse load is presented. The standard linear solid model is employed to simulate the viscoelastic characteristics of the interlayer, in which the memory effect of strains is considered. The mechanical behavior of each layer is described by the first-order shear deformation theory (FSDT). By means of the principle of minimum potential energy, a group of equations for displacements and rotation angles are derived out. The final solution is obtained by conducting the Laplace transform and the inversion of Laplace transform to the equation group. Numerical comparison shows that the present solutions and the finite element results are in good agreement. It is shown that the present results are more accurate than those obtained from the Euler-Bernoulli beam theory, especially for thick beams. And the present solutions can accurately describe the variatio...
Nonlinear response of liquid partially filled in a rigid cylindrical container with a rigid annul... more Nonlinear response of liquid partially filled in a rigid cylindrical container with a rigid annular baffle subjected to lateral excitation is studied. A semianalytical approach is presented to determine the natural frequencies and modes of the liquid sloshing. Introducing the generalized time-dependent coordinates, the surface wave height and the velocity potential are expressed in terms of the natural modes of liquid sloshing. Based on the Bateman–Luke variational principle, the infinite-dimensional modal system is given by the variational procedure. The infinite-dimensional modal system is reduced by using the Moiseev asymptotic relations. The resultant hydrodynamic force and moment of the liquid pressure acting on the container mainly depend on the position vector of the mass center of the liquid. Expanding the integral about the weighted position coordinates into the Taylor series about the surface wave height at the unperturbed free surface gives the formula of the position vec...
In this study, the liquid sloshing in a cylindrical tank considering soil–structure interaction a... more In this study, the liquid sloshing in a cylindrical tank considering soil–structure interaction and undergoing horizontal excitation is investigated analytically. Multiple rigid annular baffles are positioned on the rigid wall to mitigate the liquid sloshing. Firstly, combined with the subdomain partition method for sloshing, the complex liquid domain is partitioned into simple subdomains with the single condition for boundary. Based on continuity conditions of velocity and pressure as well as the linear sloshing equation for free surface, the exact solution for convective velocity potential is derived with high accuracy. By yielding the similar hydrodynamic shear and moment as those of the original system, a mechanical model is developed to describe continuous sloshing, and parameters of the model are given in detail. Then, by means of the least squares approach, the Chebyshev polynomials are utilized to fit impedances for the circular surface foundation. A lumped parameter model i...
A direct approach is used to derive the exact solution for the free vibration of thin rectangular... more A direct approach is used to derive the exact solution for the free vibration of thin rectangular plates with discrete sprung masses attached. The plate is simply supported along two opposite edges and elastically supported along the two other edges. The elastic support can represent a range of boundary conditions from free to clamped supports. Considering only the compatibility of the internal forces between the plate and the sprung masses, the equations of the coupled vibration of the plate-spring-mass system are derived. The exact expressions for mode and frequency equations of the coupled vibration of the plate and sprung masses are determined. The solutions converge steadily and monotonically to exact values. The correctness and accuracy of the solutions are demonstrated through comparison with published results. A parametric study is undertaken focusing on the plate with one or two sprung masses. The results can be used as a benchmark for further investigation.The solution pro...
This paper studies the stress and displacement distributions of transversely isotropic rectangula... more This paper studies the stress and displacement distributions of transversely isotropic rectangular plates with continuously varying thickness and simply supported at four edges. On the basis of three-dimensional elasticity theory, the general expressions for the displacements and stresses of the plate under static loads, which exactly satisfy the governing differential equations and the edge conditions of the plate, are analytically derived. The unknown coefficients in the solutions are approximately determined by using the double Fourier sinusoidal series expansions to the upper surface and lower surface conditions of the plate. Convergence and comparison studies demonstrate the correctness and effectiveness of the proposed method.
The phenomenon of earthquake-induced structural pounding was extensively studied by some research... more The phenomenon of earthquake-induced structural pounding was extensively studied by some researchers using different models for the impact force. The aim of this paper is to provide a new formula of impact stiffness in the linear viscoelastic contact model, based on the assumption that the maximum impact deformation from the distributed mass model should be equal to that from the equivalent lumped mass model. The correctness and accuracy of the proposed formula have been confirmed by comparing the pounding simulation using the present formula of impact stiffness with those using the existing formulae.
This paper studies the parameter effect of side retainers on seismic response of bridges with fle... more This paper studies the parameter effect of side retainers on seismic response of bridges with flexible rubber bearings. The pounding effect between girder and side retainers is analyzed by the nonlinear time-history analysis. The pounding and sliding of bearings are simulated by the nonlinear contact elements. Comparative analysis of seismic performance of bridge with/without retainers is carried out. Furthermore, the seismic performances of ordinary retainers and new retainers are compared. Finally, the effect of side retainer parameters on seismic response of bridge is analyzed. The results indicate that the sliding of elastomeric pad bearing should be considered in seismic design. It is shown that the retainers can effectively restrain the relative displacement between girder and piers, and the new type of retainers can greatly reduce the pounding force. It is also proved that both stiffness and gap of the retainer have significant influences on the pounding force.
In this work, analytical solution of simply supported sandwich arches considering permeation effe... more In this work, analytical solution of simply supported sandwich arches considering permeation effect of adhesives is presented. The permeation layer is described by the functionally graded material, exponentially graded in the radial direction. The stresses and deformations of each layer are based on the two-dimensional (2D) elasticity theory in the polar coordinate. The governing equations of the arch are solved by the layer-wise method, which turns the differential equations with variable coefficients into constant coefficients. The solution can be obtained efficiently by means of the recursive matrix method, especially for the arch with many layers. The present solution agrees well with the finite element solution with a fine mesh, while the finite element method is time consuming in mesh division and calculation. The one-dimensional (1D) solution based on the Euler–Bernoulli theory is close to the present one; however, the error increases as the arch becomes thick. The effect of ...
An analytical solution of stresses and deformations for two-layer Timoshenko beams glued by a vis... more An analytical solution of stresses and deformations for two-layer Timoshenko beams glued by a viscoelastic interlayer under uniform transverse load is presented. The standard linear solid model is employed to simulate the viscoelastic characteristics of the interlayer, in which the memory effect of strains is considered. The mechanical behavior of each layer is described by the first-order shear deformation theory (FSDT). By means of the principle of minimum potential energy, a group of equations for displacements and rotation angles are derived out. The final solution is obtained by conducting the Laplace transform and the inversion of Laplace transform to the equation group. Numerical comparison shows that the present solutions and the finite element results are in good agreement. It is shown that the present results are more accurate than those obtained from the Euler-Bernoulli beam theory, especially for thick beams. And the present solutions can accurately describe the variatio...
Nonlinear response of liquid partially filled in a rigid cylindrical container with a rigid annul... more Nonlinear response of liquid partially filled in a rigid cylindrical container with a rigid annular baffle subjected to lateral excitation is studied. A semianalytical approach is presented to determine the natural frequencies and modes of the liquid sloshing. Introducing the generalized time-dependent coordinates, the surface wave height and the velocity potential are expressed in terms of the natural modes of liquid sloshing. Based on the Bateman–Luke variational principle, the infinite-dimensional modal system is given by the variational procedure. The infinite-dimensional modal system is reduced by using the Moiseev asymptotic relations. The resultant hydrodynamic force and moment of the liquid pressure acting on the container mainly depend on the position vector of the mass center of the liquid. Expanding the integral about the weighted position coordinates into the Taylor series about the surface wave height at the unperturbed free surface gives the formula of the position vec...
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