Random Dynamic Response Research Articles

Effects of random variations of soil properties on site amplification of seismic ground motions

This paper investigates the effects of random variations of soil properties on site amplification of seismic waves. First, based on attenuation laws and the filtered Tajimi–Kanai spectrum, seismic motion at the base rock of a soil site is stochastically generated according to an assumed earthquake with a given magnitude and epicentral distance. Motions on the surface of this layered random soil site are calculated by nonlinear wave propagation methods, and by assuming the incoming seismic wave consisting of SH wave or combined P and SV waves. Soil properties, including shear modulus, damping ratio and mass density, as well as ground water level are considered as random in the numerical calculation. The Rosenblueth method is used to solve the random dynamic responses of the soil site. Parametric calculations are performed to investigate the effects of various parameters on site amplification of seismic waves. The mean and maximum ground motions on surface of the site are estimated. Numerical results indicate that the estimated surface motions differ substantially if the random variations of soil properties and soil saturation level are taken into consideration in the analysis.

Stochastic Structural Dynamics in Earthquake Engineering

1 - Stochasticity in Engineering Systems Basic Principles of Stochastic Structural Dynamics Classification of Problems Concluding Remarks Problems. 2 - Random Variable and Stochastic Processes Introductory Remarks The Concept of Probability Random Variables Transformations of Random Variables Some Useful Probability Distributions Stochastic Processes Non-stationary, Stationary and Ergodic Stochastic Processes Statistical Descriptors of Stationary-Ergodic Stochastic Processes Linear Transformations of Stationary-Ergodic Stochastic Processes Normal-Gaussian Stochastic Processes Envelopes and Extremes of Narrow Band Stochastic Processes Non-stationary Stochastic Processes Problem Classification Concluding Remarks Problems. 3 - Single DOF System Response to Random Input Introductory Remarks Description of the Problem The Single Degree-of-Freedom Oscillator Random Response of the Sdof System Solution in the Frequency Domain Design Aspects for Simple Frame Structures Under Random Loads Extreme Values of Random Dynamic Response Concluding Remarks Problems. 4 - Multiple DOF System Response to Random Input Introductory Remarks Principles of Stochastic Dynamic Analysis for Mdof Systems Two-dof Linear Oscillator Subjected to White-noise Excitation The Role of Cross-correlation of Load Components Principles of Stochastic Analysis of Continuous Dynamic Systems Concluding Remarks Problems. 5 - Nonlinear Oscillators under Stochastic Excitation Introductory Remarks Sources of Nonlinearity and Problem Classification Linear Oscillators Subjected to Non-normal Stationary Loading Nonlinear Oscillators Subjected to Normal Stationary Loading Concluding Remarks Problems. 6 - Response of Continuous Systems to Random Input Introductory Remarks Continuous Systems in Structural Dynamics Propagation of Seismically Induced Waves Perturbation Method for Random Continuous Media Numerical Simulation of Random Fields in Continuous Media Numerical Examples Concluding Remarks Problems. 7 - Random Field Simulations Introductory Remarks Monte-Carlo Simulations Numerical Realizations of Random Fields The Kanai-Tajimi and High-Pass Filters Response Spectra Concluding Remarks Problems. 8 - Numerical Methods in Stochastic Dynamics Introductory Remarks Classification of Numerical Methods Perturbation Method Stochastic Boundary Element Method Stochastic Finite Element Method Applications to Earthquake Engineering Numerical Examples Problems. 9 - Risk Analysis of Structures Introductory Remarks Some Basic Concepts in Reliability Risk Analysis Development of the Methodology Fragility Curves Concluding Remarks Problems. Appendix A - Basic Concepts in Structural Dynamics Appendix B - Solutions to Problems

TOPOLOGY OPTIMIZATION OF STRUCTURES UNDER DYNAMIC RESPONSE CONSTRAINTS

In recent years, the Evolutionary Structural Optimization (ESO) method has been developed into an effective tool for engineering design. However, no attempts have been made to incorporate random dynamic response constraints. The optimum design of structures with dynamic response constraints is of great importance, particularly in the aeronautical and automotive industries. This paper considers the extension and modification of the ESO method to control the structural random dynamic responses. The random dynamic theory is applied to build an expression of random dynamic response constraints considering engineering requirements. Based on the modal truncation method of eigenderivatives and some approximate process, a set of formulations for sensitivity numbers of mean square random dynamic responses is derived. The algorithm is implemented in optimization software. Several examples are provided to demonstrate the validity and effectiveness of the proposed method.

Nonlinear dynamic response of a nonuniform orthotropic circular plate under random excitation

In this paper, the random dynamic response of a nonuniform orthotropic circular plate has been investigated. This kind of problem has wide ranges of application in civil engineering, mechanical engineering and aerospace engineering. The dynamic von Karman's equation in conjunction with Galerkin technique has been applied to obtain the nonlinear dynamic response of a nonuniform orthotropic circular plate in terms of the deflection component. The above procedure yielded a nonlinear ordinary differential equation involving the deflection component, which can be solved by stochastic equivalent linearization technique. Finally, the statistical dynamic response of the nonlinear circular plate has been calculated and checked by Monte Carlo simulation, furthermore, the structural reliability analysis of the nonlinear circular plate has been performed on the basis of the statistical dynamic response of the plate.

Random dynamic response of a tethered buoyant platform production riser

A new normal mode spectral analysis method is presented for calculating r.m.s. riser deflections, bending stresses and lower ball joint angles. Forces on the riser consist of: (a) non-linear fluid drag taking account of the relative velocity due to tethered buoyant platform (TBP) motion, riser elastic deflection and wave induced fluid velocity, (b) wave induced fluid acceleration, (c) inertia forces due to TBP acceleration, and (d) buoyancy. The non-linear fluid drag forces are linearized using Tung and Wu's approximation based on the r.m.s. relative fluid velocity and current. A wide range of results is presented for risers in water depths up to 1000 m and it is observed that 6 normal modes are sufficient for calculating bending stresses. A static analysis is also presented for bending stresses due to wave and current induced drag forces and riser offset.