scholarly journals Flexural dynamic response of monopile foundations under linear wave loads

2020 ◽  
Vol 4 (1) ◽  
pp. 44-50
Author(s):  
Theofanis Giotis ◽  
◽  
Dimitrios Pavlou ◽  
Keyword(s):  
Dynamic Response ◽  
Laplace Transform ◽  
Linear Wave ◽  
Wave Loads ◽  
Cylindrical Structures ◽  
Double Laplace Transform ◽  
Static Solutions ◽  
The Laplace Transform ◽  
Analytical Result ◽  
The One

An analytical solution for the dynamic response of submerged slender circular cylindrical structures subjected to linear wave loads is presented. A double Laplace transform with respect to temporal and spatial variables is applied both to motion equation and boundary conditions. The dynamic deflection of the beam is obtained by inversion of the Laplace transform. The latter with respect to spatial variable is obtained analytically, while the one concerning the temporal variable is numerically calculated using Durbin numerical scheme. Results in the case of a representative example for a monopile foundation subjected to Airy waves are presented and discussed, and the analytical result is compared against numerical dynamic and static solutions.

scholarly journals The Integral of the Supremum Process of Brownian Motion

2009 ◽  
Vol 46 (2) ◽  
pp. 593-600 ◽  
Author(s):  
Svante Janson ◽  
Niclas Petersson
Keyword(s):  
Brownian Motion ◽  
Laplace Transform ◽  
Explicit Formula ◽  
Local Time ◽  
Time Interval ◽  
Standard Brownian Motion ◽  
Excursion Theory ◽  
Double Laplace Transform ◽  
The Laplace Transform ◽  
Supremum Process

In this paper we study the integral of the supremum process of standard Brownian motion. We present an explicit formula for the moments of the integral (or area)(T) covered by the process in the time interval [0,T]. The Laplace transform of(T) follows as a consequence. The main proof involves a double Laplace transform of(T) and is based on excursion theory and local time for Brownian motion.

scholarly journals The Regularity of the Laplace Transform

2019 ◽  
pp. 5-11
Author(s):  
Andrey Pavlov
Keyword(s):  
Laplace Transform ◽  
Double Laplace Transform ◽  
The Laplace Transform

The paper proves the regularity of the double Laplace transform in the neighborhood of zero. The class of the transform of Laplace from the transform of Fourier is considered from the functions without a regularity in null.

Effects of Impact on the Behavior of a Flexible Multiple Disk Clutch and Brake

1987 ◽  
Vol 109 (4) ◽  
pp. 416-421 ◽  
Author(s):  
Kosuke Nagaya
Keyword(s):  
Dynamic Response ◽  
Laplace Transform ◽  
Dynamic Behavior ◽  
Circular Plate ◽  
Static Load ◽  
Equation Of Motion ◽  
Dynamic Loads ◽  
The Laplace Transform ◽  
The Impact

This paper discusses the dynamic behavior of a flexible multiple disk clutch subjected to dynamic loads. The expressions for obtaining the dynamic response and the transmission torque of the clutch have been derived from the equation of motion of a circular plate by applying the Laplace transform procedure. The results for the clutch subjected to a static load have also been obtained. The comparison between both static and dynamic results has been made to clarify the effect of the impact of the load on the behavior of the clutch.

scholarly journals Three-Dimensional Semianalytical Solutions for Piezoelectric Laminates Subjected to Underwater Shocks

2020 ◽  
Vol 2020 ◽  
pp. 1-20
Author(s):  
Xu Liang ◽  
Wenbin Lu ◽  
Ronghua Zhu ◽  
Changpeng Ye ◽  
Guohua Liu
Keyword(s):  
Dynamic Response ◽  
Boundary Conditions ◽  
Laplace Transform ◽  
Electric Potential ◽  
Differential Quadrature Method ◽  
Three Dimensional ◽  
Laminated Plates ◽  
Inversion Method ◽  
Variation Principle ◽  
The Laplace Transform

In this study, a piezoelectric laminate is analyzed by applying the Laplace transform and its numerical inversion, Fourier transform, differential quadrature method (DQM), and state space method. Based on the modified variation principle for the piezoelectric laminate, the fundamental equations for dynamic problems are derived. The solutions for the displacement, stress, electric potential, and dielectric displacement are obtained using the proposed method. Durbin’s inversion method for the Laplace transform is adopted. Four boundary conditions are discussed through the DQM. The proposed method is validated by comparing the results with those of the finite element method (FEM). Moreover, this semianalytical method is further extended to describe the dynamic response of piezoelectric laminated plates subjected to underwater shocks by introducing Taylor’s fluid-structure interaction algorithm. Both air-backed and water-backed laminated plates are investigated, and the effect of the fluid is examined. In the time domain, the electric potential and displacements of sample points are calculated under four boundary conditions. The present method is shown to be accurate and can be a useful method to calculate the dynamic response of underwater laminated sensors.

Double Laplace Transform Computing Dynamic Response of the Large Thickness to Span Ratio Beam

2013 ◽  
Vol 834-836 ◽  
pp. 1333-1336
Author(s):  
Wei Zhang
Keyword(s):  
Dynamic Response ◽  
Laplace Transform ◽  
Response Curve ◽  
Sandwich Beam ◽  
Beam Deflection ◽  
Deep Beam ◽  
Torsion Beam ◽  
Beam Dynamic ◽  
Double Laplace Transform ◽  
Beam Bending

In this paper, use double Laplace transform, in the image space deep beam deflection and corner of analytic is obtained,Then use the numerical inversion of Laplace transform ,time domain dynamic response curve is calculated. Also apply to the combined effects of sandwich beam bending and torsion beam dynamic response calculation.

scholarly journals The Laplace transform on a class of Boehmians

1992 ◽  
Vol 46 (2) ◽  
pp. 347-352 ◽  
Author(s):  
Dennis Nemzer
Keyword(s):  
Laplace Transform ◽  
Inversion Formula ◽  
Proper Subspace ◽  
Basic Properties ◽  
The Laplace Transform ◽  
Abelian Theorem ◽  
The One

The one-sided Laplace transform is defined on a space of generalised functions called transformable Boehmians. The space of one-sided Laplace transformable distributions is shown to be a proper subspace of transformable Boehmians. Some basic properties of the Laplace transform are investigated. An inversion formula and an Abelian theorem of the final type are obtained.

scholarly journals The Integral of the Supremum Process of Brownian Motion

2009 ◽  
Vol 46 (02) ◽  
pp. 593-600
Author(s):  
Svante Janson ◽  
Niclas Petersson
Keyword(s):  
Brownian Motion ◽  
Laplace Transform ◽  
Explicit Formula ◽  
Local Time ◽  
Time Interval ◽  
Standard Brownian Motion ◽  
Excursion Theory ◽  
Double Laplace Transform ◽  
The Laplace Transform ◽  
Supremum Process

In this paper we study the integral of the supremum process of standard Brownian motion. We present an explicit formula for the moments of the integral (or area)(T) covered by the process in the time interval [0,T]. The Laplace transform of(T) follows as a consequence. The main proof involves a double Laplace transform of(T) and is based on excursion theory and local time for Brownian motion.

Dynamic Response of a Floating Cylinder Subjected to Coupled Wave and Wind Loading

2012 ◽  
Author(s):  
H. Yu ◽  
N. Srivastava
Keyword(s):  
Dynamic Response ◽  
Wind Wave ◽  
Finite Depth ◽  
Offshore Structures ◽  
Wind Loading ◽  
Linear Wave ◽  
Large Radius ◽  
Wave Loads ◽  
Offshore Structure ◽  
Radiation Theory

The broad objective of the research presented herein is to analyze dynamical interactions in offshore structures under combined wind and wave loads for enhanced power delivery and reliability of hybrid wind-wave generation systems. As an offshore structure representative, a model for an inclined floating cylinder at finite depth is developed employing linear wave theory coupled with wind-induced effects. Although detailed wave models have often been incorporated while studying the dynamics of such cylinders, wind-induced effects have been mostly modeled as an axial drag term that affects the drift of the structure along the wind direction. In this article, the effects of not only wind-induced drag, but also lift and oscillations on the structure (i.e. the floating inclined cylinder) are studied. Further, the effects of vortex shedding are considered. Cross-flow principle is used to calculate the wind loads on the cylinder. Assuming small wave steepness and a large radius of cylinder (in comparison to the wavelength), linear wave diffraction and radiation theory coupled with wind-induced effects is employed to analyze the dynamic response of the inclined floating cylinder. Numerical results on the dynamic response of an inclined floating cylinder subjected to coupled wind-wave loading system are presented and discussed while highlighting the increasing relevance of such modeling strategies for hybrid wind-wave power generation systems and their control.

Some fluctuation identities for Lévy processes with jumps of the same sign

2004 ◽  
Vol 41 (04) ◽  
pp. 1191-1198 ◽  
Author(s):  
Xiaowen Zhou
Keyword(s):  
Laplace Transform ◽  
Lévy Process ◽  
Joint Distribution ◽  
Lévy Processes ◽  
Levy Processes ◽  
Levy Process ◽  
Exit Problem ◽  
The Laplace Transform ◽  
The One

We consider a two-sided exit problem for a Lévy process with no positive jumps. The Laplace transform of the time when the process first exits an interval from above is obtained. It is expressed in terms of another Laplace transform for the one-sided exit problem. Applications of this result are discussed. In particular, a new expression for the solution to the two-sided exit problem is obtained. The joint distribution of the minimum and the maximum values of such a Lévy process is also studied.

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