Dynamic Scale Model Design for Hydrodynamic and Bending Similarity

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Solution Overview

Problem

Existing methods for designing underwater shaking table models of columnar marine structures fail to simultaneously achieve hydrodynamic force similarity and bending elastic force similarity, leading to significant sectional distortion, high counterweights, and difficulty in precise fabrication, especially under combined effects of earthquakes, waves, and currents.

Innovation Solution

A design method involving a three-step process: designing a scale model with structural density scale of 1 using bending elastic force-gravity similarity, adjusting dimensions for hydrodynamic force similarity, and fabricating using 3D printing technology, specifically employing selective laser melting (SLM) for complex shapes and wire arc additive manufacturing (WAAM) for simpler shapes.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Reliability

If the Morison equation and wave diffraction theory are used to adjust hydrodynamic force amplitude when structural density scale is not equal to 1, then hydrodynamic force similarity is improved, but the model requires heavy counterweights and experiences significant sectional dimension distortion

Engineering Contradiction:
Improvehydrodynamic force similarityVSAvoidmodel counterweight and sectional distortion
Core Design Contradiction:
ReliabilityVSDevice complexity

Solution Approach 1:

The patent performs preliminary action by setting the structural density scale equal to water density (Sρ=1) at the design stage, which prevents the need for heavy counterweights and sectional dimension distortion later. This preliminary parameter setting ensures that the structural mass scale naturally equals the water volume scale (Sm=SV), eliminating the need for corrective measures during model fabrication and testing

Inventive Principle:
Principle #10Preliminary action

2Reliability

If the structural density scale is set to 1 to achieve hydrodynamic force similarity, then the model and prototype can use the same material, but the conventional steel structure manufacturing methods (welding or bolting) become difficult to apply when members have complex geometries

Engineering Contradiction:
Improvematerial consistency between model and prototypeVSAvoidfabrication of complex geometry members
Core Design Contradiction:
ReliabilityVSEase of manufacture

Solution Approach 1:

The patent replaces the conventional mechanical manufacturing system (welding or bolting of steel members) with an additive manufacturing system. This substitution enables the fabrication of complex geometry members that would be difficult or impossible to manufacture using traditional mechanical methods, while maintaining material consistency between model and prototype through the use of the same steel material

Inventive Principle:
Principle #28Mechanics substitution (Replace mechanical system)

Applied Scientific Principles

This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.

Function Achieved in This Case

The method enables accurate prediction of prototype responses under seismic and combined load conditions with reduced sectional distortion and lower mass, allowing for precise fabrication without additional counterweights, thus improving the accuracy of underwater shaking table tests.

Implementation Method 1

employing selective laser melting (SLM) for complex shapes

Methodology Applied
Scientific EffectSelective Laser Melting: Selective Laser Sintering

Implementation Method 2

employing wire arc additive manufacturing (WAAM) for simpler shapes

Methodology Applied
Scientific EffectWire Arc Additive Manufacturing: Welding

Data Source

PatentUS12578705B2Method for dynamic scale model satisfying hydrodynamic force similarity and bending elastic force similarity
Publication Date: 2026.03.17 TIANJIN UNIV
  • US12578705B2 patent drawing
  • US12578705B2 patent drawing
  • US12578705B2 patent drawing

AI summary

Disclosed is a design method for a dynamic scale model satisfying hydrodynamic force similarity and bending elastic force similarity in the technical field of civil engineering. The design and fabrication method includes the following steps: step 1, designing a scale model satisfying structural dynamic similarity under pure seismic effects: designing a scale model A with a structural density scale Sρ of 1 using a bending elastic force-gravity similarity law; step 2, adjusting, based on the scale model A designed in step 1, a width of a water-facing surface and a width of a flow direction surface of the scale model according to a principle that a hydrodynamic force scale is consistent with an inertial force scale and the bending elastic force-gravity similarity law, to obtain a scale model B; step 3, fabricating the scale model B obtained in step 2 using 3D printing technology.