Analytical Solution for the Sound Radiation Field of a Viscoelastically Supported Beam Traversed by a Moving Load

Sound radiation from a beam resting on a viscoelastic foundation is analytically studied when it is subjected to a moving load. The topic could cover a range of applications such as submerged floating tunnels, buried pipelines, and railway tracks. Galerkin's method is employed to obtain the transverse vibration of the beam. Based on the Rayleigh integral approach, acoustic pressure distribution around the beam is obtained in the time domain. In the second part of this paper, corresponding displacement and acoustic pressure are obtained by the use of the Rayleigh-Ritz approach in conjunction with the Laplace transform method and by the use of the Fourier transform, respectively. Durbin's numerical Laplace transform inversion scheme is eventually employed to obtain dynamic responses. A parametric study is then carried out and influences of the design parameters as well as the loading conditions on the acoustic pressure field are investigated

Dynamic response of a circular tunnel with imperfect surface interaction embedded in an elastic medium

The research work proposed here is part of a global project that aims at better characterizing a specific underground environment in the LSBB (Low Noise Inter-disciplinary Underground Science and Technology), situated in Rustrel, Vaucluse, France. The experimental environment under study is characterized by a system of galleries, several ones with a concrete layer. The first step of the methodology deals with setting up a forward problem to apprehend the geometry of the LSBB. \\In this paper, the 2D transient response of imperfect bonded circular lined pipeline lying in an elastic, homogeneous and infinite medium is studied. At first, the problem is solved in the frequency domain by using the wave function expansion method and imperfect interaction surface between elastic medium and tunnel is modeled as a linear spring. Wave propagation fields in tunnel and soil are expressed in terms of infinite series and stresses and displacements are given based on those series. By implying boundary conditions a linear equations system is obtained and the results of these equations lead to displacement and stress responses of the rock and tunnel.To solve the transient problem, the Laplace transform with respect to time is used which leads to system of linear equations in the Laplace domain. Durbin's numerical Laplace transform inversion method is employed to obtain dynamic responses. To exhibit a behavior of the responses, influences of the different parameters such as wall thickness of the tunnel is investigated. Hoop stresses and the displacements of the tunnel and rock are obtained due to acting load on the inner surface of the tunnel for selected parameters. In order to check the validity of the present work, we pay attention on the convergence of the results and also excellent agreement with previous result is achieved

Performance Portable Solid Mechanics via Matrix-Free pp-Multigrid

Finite element analysis of solid mechanics is a foundational tool of modern engineering, with low-order finite element methods and assembled sparse matrices representing the industry standard for implicit analysis. We use performance models and numerical experiments to demonstrate that high-order methods greatly reduce the costs to reach engineering tolerances while enabling effective use of GPUs. We demonstrate the reliability, efficiency, and scalability of matrix-free $p$-multigrid methods with algebraic multigrid coarse solvers through large deformation hyperelastic simulations of multiscale structures. We investigate accuracy, cost, and execution time on multi-node CPU and GPU systems for moderate to large models using AMD MI250X (OLCF Crusher), NVIDIA A100 (NERSC Perlmutter), and V100 (LLNL Lassen and OLCF Summit), resulting in order of magnitude efficiency improvements over a broad range of model properties and scales. We discuss efficient matrix-free representation of Jacobians and demonstrate how automatic differentiation enables rapid development of nonlinear material models without impacting debuggability and workflows targeting GPUs

Analytical Solution for the Sound Radiation Field of a Viscoelastically Supported Beam Traversed by a Moving Load

Sound radiation from a beam resting on a viscoelastic foundation is analytically studied when it is subjected to a moving load. The topic could cover a range of applications such as submerged floating tunnels, buried pipelines, and railway tracks. Galerkin’s method is employed to obtain the transverse vibration of the beam. Based on the Rayleigh integral approach, acoustic pressure distribution around the beam is obtained in the time domain. In the second part of this paper, corresponding displacement and acoustic pressure are obtained by the use of the Rayleigh-Ritz approach in conjunction with the Laplace transform method and by the use of the Fourier transform, respectively. Durbin’s numerical Laplace transform inversion scheme is eventually employed to obtain dynamic responses. A parametric study is then carried out and influences of the design parameters as well as the loading conditions on the acoustic pressure field are investigated