1,721,733 research outputs found
Path Integral approach via Laplace’s method of integration for nonstationary response of nonlinear systems
Full text linkIn this paper the nonstationary response of a class of nonlinear systems subject to broad-band stochastic excitations is examined. A version of the Path Integral (PI) approach is developed for determining the evolution of the response probability density function (PDF). Specifically, the PI approach, utilized for evaluating the response PDF in short time steps based on the Chapman–Kolmogorov equation, is here employed in conjunction with the Laplace’s method of integration. In this manner, an approximate analytical solution of the integral involved in this equation is obtained, thus circumventing the repetitive integrations generally required in the conventional numerical implementation of the procedure. Further, the method is extended to nonlinear oscillators, approximately modeling the amplitude of the system response as a one-dimensional Markovian process. Various nonlinear systems are considered in the numerical applications, including Duffing and Van der Pol oscillators. Appropriate comparisons with Monte Carlo simulation data are presented, demonstrating the efficiency and accuracy of the proposed approach
Efficient path integral approach via analytical asymptotic expansion for nonlinear systems under Gaussian white noise
Full text linkIn this paper an efficient formulation of the Path integral (PI) approach is developed for determining the response probability density functions (PDFs) and first-passage statistics of nonlinear oscillators subject to stationary and time-modulated external Gaussian white noise excitations. Specifically, the evolution of the response PDF is obtained in short time steps, by using a discrete version of the Chapman-Kolmogorov equation and assuming a Gaussian form for the conditional response PDF. Next, the technique involves proceeding to treating the problem via an analytical asymptotic expansion procedure, namely the Laplace’s method of integration. In this manner, the repetitive double integrals involved in the standard implementation of the PI approach are evaluated in a closed form, while the response and first-passage PDFs are obtained by mundane step-by-step application of the derived approximate analytical expression. It is shown that the herein proposed formulation can drastically decrease the associated computational cost by several orders of magnitude, as compared to both the standard PI technique and Monte Carlo solution (MCS) approach. A number of nonlinear oscillators are considered in the numerical examples. Notably, for these systems both response PDFs and first-passage probabilities are presented, whereas comparisons with pertinent MCS data demonstrate the efficiency and accuracy of the technique
Development and validation of effective computational strategies for the study of metal-nitroxide systems
No full textDevelopment and validation of effective computational strategies for the study of metal-nitroxide systems
No full textLine element-less method (LEM) for arbitrarily shaped nonlocal nanoplates: exact and approximate analytical solutions
Full text linkThis paper presents an innovative procedure for the analysis of nonlocal plates with arbitrary shape and various boundary conditions. In this regard, the Eringen’s nonlocal model is used to capture small length scale effects. The proposed procedure, referred to as Line ElementLess Method (LEM), is a completely meshfree approach requiring the evaluations of simple line integrals along the plate boundary parametric equation. Further, the deflection function is represented by a series expansion is terms of harmonic polynomials whose coefficients are found by performing variations of appropriately introduced functionals, leading to a linear system of algebraic. Notably, the proposed procedure yields approximate analytical solutions for general shapes and boundary conditions, and even exact solutions for some plate geometries
Development and validation of effective computational strategies for the study of metal-nitroxide systems
No full textResponse of nonlinear oscillators with fractional derivative elements under evolutionary stochastic excitations: A Path Integral approach based on Laplace's method of integration
No full textIn this paper, an approximate analytical technique is developed for determining the non-stationary response amplitude probability density function (PDF) of nonlinear/hysteretic oscillators endowed with fractional element and subjected to evolutionary excitations. This is achieved by a novel formulation of the Path Integral (PI) approach. Specifically, a stochastic averaging/linearization treatment of the original fractional order governing equation of motion yields a first-order stochastic differential equation (SDE) for the oscillator response amplitude. Associated with this first-order SDE is the Chapman–Kolmogorov (CK) equation governing the evolution in time of the non-stationary response amplitude PDF. Next, the PI technique is employed, which is based on a discretized version of the CK equation solved in short time steps. This is done relying on the Laplace’s method of integration which yields an approximate analytical solution of the integral involved in the CK equation. In this manner, the repetitive integrations generally required in the classical numerical implementation of the procedure are avoided. Thus, the non-stationary response amplitude PDF is approximately determined in closed-form in a computationally efficient manner. Notably, the technique can also account for arbitrary excitation evolutionary power spectrum forms, even of the non-separable kind. Applications to oscillators with Van der Pol and Duffing type nonlinear restoring force models, and Preisach hysteretic models, are presented. Appropriate comparisons with Monte Carlo simulation data are shown, demonstrating the efficiency and accuracy of the proposed approac
An enhanced indirect modal identification procedure for bridges based on the dynamic response of moving vehicles
No full textIndirect dynamic structural identification, referred to as Vehicle Scanning Method (VSM), pertains to the estimation of bridge modal parameters by using data recorded from sensors directly mounted on a moving vehicle. This procedure has recently gained increasing attention due to its low cost and simple implementation. Nevertheless, the non-stationary and complex nature of the vehicle–bridge interaction phenomenon poses some limitations to the applicability of the method, especially in terms of accuracy. In this regard, in this paper, an enhanced procedure for the dynamic identification of bridges modal parameters based on the VSM is introduced, taking into account the effects of vehicle/bridge damping and road pavement roughness. Specifically, based on the Variational Mode Decomposition (VMD) method, the relevant Intrinsic Mode Functions (IMFs) and corresponding modal frequencies are determined from the recorded signal. Further, the Natural Excitation Technique (NExT) is adopted in conjunction with a noise-robust area ratio-based approach, for modal damping ratios estimation. Finally, mode shapes are evaluated by properly correcting the instantaneous amplitudes of each IMF considering the influence of the corresponding estimated modal damping ratio. Several numerical simulations are presented to show the validity of the proposed procedure and comparisons with the classical Hilbert Spectrum-based identification approach are employed to assess its reliability and improved accuracy
Dynamic response of beams excited by moving oscillators: Approximate analytical solutions for general boundary conditions
Full text linkIn this paper, the dynamic response of an Euler-Bernoulli beam with general boundary conditions (BCs) and subject to a moving oscillator is examined. Notably, novel approximate closed-form expressions are determined for the vertical responses of both the beam and the moving oscillator, specifically considering the effect of damping in these systems, commonly omitted in standard approaches in the literature. In this regard, a modal superposition procedure is adopted and combined with an appropriate expansion-based approach of the dynamic response of the system, which naturally arises considering the oscillator-beam mass ratio to be reasonably small. Further, general boundary conditions are treated exploiting the use of a suitable set of orthogonal polynomial functions as beam mode shapes. In this manner, novel direct expressions for the response of the system are derived, in which the mode shapes coefficients explicitly appear. This leads to a straightforward application of the proposed solution, irrespective of the chosen BCs. Several numerical examples are presented to assess the reliability and accuracy of the proposed approach, considering different cases of beam BCs, and moving oscillator's parameters. Results are validated by comparison with the data of finite element analyses, and numerical solutions of the complete system of governing equations
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