On Wave Propagation in Thermoplastic Media

1966 ◽  
Vol 33 (3) ◽  
pp. 514-520 ◽  
Author(s):  
A. D. Fine ◽  
H. Kraus
Keyword(s):  
Wave Propagation ◽  
Closed Form ◽  
Wave Front ◽  
Dynamic Behavior ◽  
Static Analysis ◽  
Equations Of Motion ◽  
Normal Velocity ◽  
Wave Fronts ◽  
Closed Form Solutions ◽  
Infinite Region

The dynamic behavior of a medium, according to the uncoupled thermoplastic theory, is presented and is compared to the behavior that would be obtained from an uncoupled quasi-static analysis. Since the inertia terms are retained in the equations of motion, wave fronts (or surfaces of discontinuity) are produced in the medium. The normal velocity of the wave front separating the elastic and plastic regions is determined. General closed-form solutions of the displacement (according to both the dynamic and the quasi-static approaches) are obtained; their unique forms are found for the semi-infinite region, and an illustrative numerical example is then presented.

Evaluating Large Aboveground Storage Tanks Subject to Seismic Loading: Part I — Closed-Form Solutions and Equivalent Static Analysis

2018 ◽  
Author(s):  
Phillip E. Prueter ◽  
Seetha Ramudu Kummari
Keyword(s):  
Closed Form ◽  
Static Analysis ◽  
Storage Tank ◽  
Fluid Structure Interaction ◽  
Seismic Loading ◽  
Storage Tanks ◽  
Design Standards ◽  
Closed Form Solutions ◽  
Structure Interaction ◽  
Explicit Dynamic

Evaluating the dynamic response of large, aboveground storage tanks exposed to seismic loading is multifaceted. There are foundation-structure and fluid-structure interaction effects that can influence the overall tank behavior and likely failure modes. Additionally, local stresses at anchor bolt support chair attachments and the shell-to-floor junction can be difficult to quantify without detailed finite element analysis (FEA). Often times, performing explicit dynamic analysis with liquid sloshing effects can be time consuming, expensive, and even impractical. The intent of this paper is to summarize simplified analysis techniques that can be leveraged to evaluate aboveground storage tanks subject to seismic loading. Closed-form calculations to establish a recommended design for a tank, including seismic considerations, are available in storage tank design standards, including API 650 [1] (Appendix E). Seismic design standards have evolved significantly in recent years. Furthermore, for many vintage, in-service storage tanks, explicit seismic considerations were not incorporated into the original design. In Part I of this study, these design equations and other closed-form solutions are used to evaluate the structural integrity of a large, in-service, mechanically-anchored storage tank. The design equations in API 650 [1] are used to form the basis of simplified, equivalent static analysis, where seismic loads are applied to a three-dimensional FEA model via equivalent lateral body forces. These practical results are then compared to explicit dynamic seismic behavior of the same tank with fluid-structure interaction effects considered (in Part II of this study [2]). These comparisons offer insight into the appropriateness of using simplified hand-calculations and equivalent static analysis (and their relative conservatism) in lieu of more rigorous explicit dynamic and fluid sloshing simulations.

Active-Passive Hybrid Constrained Layer for Structural Damping Augmentation

2000 ◽  
Vol 122 (3) ◽  
pp. 254-262 ◽  
Author(s):  
Yanning Liu ◽  
K. W. Wang
Keyword(s):  
Closed Form ◽  
Viscoelastic Material ◽  
Closed Loop ◽  
Equations Of Motion ◽  
Generic Model ◽  
Structural Damping ◽  
Active Materials ◽  
Closed Form Solutions ◽  
Fail Safe ◽  
Active Constrained Layer

A new surface-damping concept with an active-passive hybrid constraining layer (HCL) is proposed to improve the damping performance of traditional active constrained layer (ACL) systems. Instead of using a pure piezoelectric constraining layer, passive and active materials are used together to constrain the viscoelastic material layer. A generic model of the HCL treatment is presented. Nondimensional equations of motion and boundary and connecting conditions are derived. The closed-form solutions to the equations are developed and analyzed. Tabletop tests are also performed to verify the feasibility of the new damping concept. It is shown that by properly selecting a passive constraining material and assigning appropriate lengths for the active and passive constraining parts, HCL can outperform a system with a pure active PZT coversheet, both in terms of its fail-safe ability and closed-loop damping performance. [S0739-3717(00)01503-8]

Liquid Container Filling and Charging

1976 ◽  
Vol 98 (2) ◽  
pp. 730-732
Author(s):  
R. H. Nunn ◽  
E. J. Gibson
Keyword(s):  
Closed Form ◽  
Dynamic Behavior ◽  
Analytical Model ◽  
Experimental Results ◽  
Simple Analytical Model ◽  
Liquid Slug ◽  
Analytical Formulation ◽  
Closed Form Solutions

A simple analytical model has been developed to describe the dynamic behavior of a liquid slug as it is rapidly and suddenly rammed into a receiving chamber. Useful closed-form solutions are obtained from approximate versions of the governing relationships. Experimental results indicate the essential correctness of the analytical formulation.

Design of the Ball Screw Mechanism for Optimal Efficiency

1989 ◽  
Author(s):  
M.-C. Lin ◽  
S. A. Velinsky ◽  
B. Ravani
Keyword(s):  
Closed Form ◽  
Static Analysis ◽  
Load Capacity ◽  
Equations Of Motion ◽  
Closed Form Solution ◽  
Form Solution ◽  
Ball Screw ◽  
Exact Theory ◽  
Screw Mechanism ◽  
Extensive Computation

Abstract This paper develops theories for evaluating the efficiency of the ball screw mechanism and additionally, for designing this mechanism. Initially, a quasi-static analysis, which is similar to that of the early work in this area, is employed to evaluate efficiency. Dynamic forces, which are neglected by the quasi-static analysis, will have an effect on efficiency. Thus, an exact theory based on the simultaneous solution of both the Newton-Euler equations of motion and the relevant kinematic equations is employed to determine mechanism efficiency, as well as the steady-state motion of all components within the ball screw. However, the development of design methods based on this exact theory is difficult due to the extensive computation necessary and thus, an approximate closed-form representation, that still accounts for the ball screw dynamics, is derived. The validity of this closed-form solution is proven and it is then used in developing an optimum design methodology for the ball screw mechanism based on efficiency. Additionally, the self-braking condition is examined, as are load capacity considerations.

scholarly journals Verification Assessment of Piston Boundary Conditions for Lagrangian Simulation of Compressible Flow Similarity Solutions

2015 ◽  
Vol 1 (2) ◽  
Author(s):  
Scott D. Ramsey ◽  
Philip R. Ivancic ◽  
Jennifer F. Lilieholm
Keyword(s):  
Shock Wave ◽  
Wave Propagation ◽  
Boundary Conditions ◽  
Closed Form ◽  
Compressible Flow ◽  
Similarity Solutions ◽  
Test Problems ◽  
Closed Form Solutions ◽  
Self Similar ◽  
Temporal Extent

This work is concerned with the use of similarity solutions of the compressible flow equations as benchmarks or verification test problems for finite-volume compressible flow simulation software. In practice, this effort can be complicated by the infinite spatial/temporal extent of many candidate solutions or “test problems.” Methods can be devised with the intention of ameliorating this inconsistency with the finite nature of computational simulation; the exact strategy will depend on the code and problem archetypes under investigation. For example, self-similar shock wave propagation can be represented in Lagrangian compressible flow simulations as rigid boundary-driven flow, even if no such “piston” is present in the counterpart mathematical similarity solution. The purpose of this work is to investigate in detail the methodology of representing self-similar shock wave propagation as a piston-driven flow in the context of various test problems featuring simple closed-form solutions of infinite spatial/temporal extent. The closed-form solutions allow for the derivation of similarly closed-form piston boundary conditions (BCs) for use in Lagrangian compressible flow solvers. The consequences of utilizing these BCs (as opposed to directly initializing the self-similar solution in a computational spatial grid) are investigated in terms of common code verification analysis metrics (e.g., shock strength/position errors and global convergence rates).

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