Virtual Validation Aids in the Design of Earthquake-Resilient Buildings

Shake Tables Are Precision Seismic Simulators That Save Lives

According to the British Geological Survey, massive earthquakes with a magnitude of 7 or higher occur an average of 15 times a year. But their effects, as witnessed in the deadly tremors that hit Turkey and Syria in 2023, can be devastating.

While earthquakes cannot be prevented or predicted, structural engineers can design buildings to withstand the violent shaking that causes damage and collapse. Earthquake-resilient design includes the physical testing of building models and subscale structures by subjecting them to the same displacements, velocities, and forces acting on them when the ground beneath them moves back and forth. Shake table testing helps structural engineers design buildings that don’t collapse in an earthquake, or if the buildings are damaged, it makes them safe enough so people can be rescued.

The shake tables used for such tests are large steel weldments that weigh as much as 1,000 metric tons and take millions of dollars to build and operate. They are powered by hydraulic actuators, which are fed pressurized oil using hydraulic pumps and accumulators.

Shake table testing helps structural engineers design buildings that don’t collapse in an earthquake, or if the buildings are damaged, it makes them safe enough so people can be rescued.

A physical model of a shake table, with arrows superimposed over the shake table plate showing that the table can move in three dimensions and a model of a lab with a shake table testing a small structure.

CAD models of a shake table and test laboratory. (Image credit: MTS Systems)

MTS Systems, a manufacturer of mechanical test and simulation equipment, makes many of the shake tables installed around the world today. The company designs and builds shake tables for seismic testing and to test automotive and aerospace components for durability, performance, and vibration transmissibility. 

An inaccurate table design can cost the company millions of dollars. Mechanical engineers at MTS who design shake tables, as well as the company’s customers who use these tables, must be able to predict whether a table can accurately replicate an earthquake’s forces.

Testing the impact of a seismic event on a physical-scale model of a colonial-era church. (Images credit: Universidad Mariano Gálvez de Guatemala, courtesy of MTS Systems)

For this, they rely on a unique tool called the Degree of Freedom System Analysis Tool (DOFSAT). Built by senior MTS staff engineer Bradford Thoen using MATLAB® and Simulink®, DOFSAT helps MTS mechanical engineers validate their shake table design. Once the table is built and installed in the customer’s lab, it enables him to design his test to determine key factors such as how big he can make his physical model, whether the earthquake is within the motion and force limits of the table, how long a test can last before pressurized oil runs out, and the fewest number of hydraulic pumps needed. “This improves the accuracy and reduces the operational costs of testing,” says Thoen.

Shaking Up Seismic Simulator Design

MTS shake tables range in size from 1.5-by-1.5 meter, 2-ton tables that move along one axis for testing subscale models all the way up to 16-by-20 meter, 1,000-ton tables with six degrees of freedom for testing full-scale building models.

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MTS seismic simulators. (Video credit: MTS Systems)

"We use Simulink, MATLAB, and Signal Processing Toolbox to model the inverse dynamics of the shake table system."

Bradford Thoen, senior MTS staff engineer

MTS’ custom-designed tables apply real-world earthquake conditions to a range of test structures. Customers provide test specifications such as earthquake test waveforms and the test specimen’s mass, moment of inertia, and center of gravity. MTS mechanical engineers use this input to design a system they predict will meet those specifications. The system comprises a table weldment, actuators, servo valves, swivels, hydraulic pumps, and hydraulic accumulation. Often there is a shortfall somewhere in the design, and several design iterations are required.

“For example, a customer will give us some earthquake records and say they want to test for this earthquake on a specimen that weighs 800 tons,” says Thoen. “They want to operate the tables at full capacity to get every last drop of performance out of these very complex and expensive systems by putting the biggest, heaviest possible specimen on the table and operating on it at maximum force levels. Maximizing specimen size mitigates test inaccuracy inherent in scaling down the size of a model structure.”

The engineers start with a design that provides estimated force, displacement, or velocity. Then they use the DOFSAT tool to validate their design and ensure that it meets the customer’s requirements. Using the tool, the table designers confirm that a test can produce the largest required seismic forces and that the system has enough pressurized oil to run tests for a certain length time of time.

“We use Simulink, MATLAB, and Signal Processing Toolbox™ to model the inverse dynamics of the shake table system,” says Thoen. 

A forward model calculates actuator and table motion and force created as servo valves open up to allow pressurized oil into the actuator. An inverse model, by contrast, takes the desired table motion and calculates the servo valve openings needed to create the required actuator motion and force. 

A MATLAB app manages the Simulink model. Once MTS engineers enter the table design parameters into a spreadsheet, the model predicts what servo valve openings are required. A valve opening of over 100% means the test is not realizable, and the model helps the engineers understand why.

Screenshot of the DOF System Analysis user interface.

The DOF System Analysis Tool. (Image credit: MTS Systems)

They can then tweak their design and do multiple iterations quickly until their table design recreates the desired seismic event.

Making DOFSAT More Accessible

Although Thoen created the DOFSAT tool almost 15 years ago, using it required a MATLAB license. To make the DOFSAT tool more accessible to customers and design teams, Thoen’s team, in partnership with MathWorks, used Simulink Compiler™ to compile the model into an easily deployable, executable file.

“Using Simulink Compiler and teaming with MathWorks to create a deployable application was a game changer for us. We’re now able to distribute the tool easily to mechanical engineers and customers throughout the world.”

Bradford Thoen, senior MTS staff engineer

“Using Simulink Compiler and teaming with MathWorks to create a deployable application was a game changer for us,” says Thoen. “We’re now able to distribute the tool easily to mechanical engineers and customers throughout the world.”

MTS has made the standalone app available for download through its software center, and users around the world use it for a range of civil engineering applications. For instance, MTS collaborated with a team at the College of Civil Engineering at Tongji University in China to design a one-of-a-kind shaking table system for seismic testing of large-scale models of complex structures such as the 62-kilometer-long Taizhou Bridge and a tunnel that connects Mainland China with Hong Kong. The system features two 70-ton shake tables and two 30-ton shake tables that can be arranged in different configurations within two adjacent trenches, and their motion can be synchronized to accurately simulate seismic waves.

Seismic testing of a scale model of a long suspension bridge. The shake tables are positioned under each of the bridges’ vertical support structures.

A multiple-shake table system designed for testing large-scale models of complex structures, such as this expansion bridge model. (Image credit: Tongji University, China, courtesy of MTS Systems)

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The Model 354 LG MAST System. (Video credit: MTS Systems)

The DOFSAT app also finds use in projects beyond civil engineering. MTS engineers use it extensively to design multiaxial simulation table (MAST) systems for the automotive and aerospace market. Car companies use MAST systems to test ground vehicle and aircraft components under severe vibrational conditions.

An MTS team recently designed a MAST system with 12 actuators to conduct fatigue testing on very large electric vehicle (EV) battery packs. EV batteries provide power but are also load-bearing structural components. “These batteries are really heavy, and they experience a lot of vibration,” says Thoen. “Automakers want to ensure that the battery is robust and stays intact when the cars are driven on rough roads.”

Thoen continually updates the DOFSAT app. He recently added the ability to predict swivel joint angles. Both ends of the hydraulic actuators have mechanical swivel joints that allow the actuator to conform to the motion of the table. These swivels have rotation limits. The DOFSAT app predicts the azimuth, elevation, and skew angles that each swivel will experience during an earthquake test, allowing MTS design engineers to verify that their choice of swivel rotation limits is adequate.

“The MathWorks team worked with us to make changes and updates to the executables,” says Thoen. “Working with MathWorks has been invaluable in making DOFSAT accessible around the world.”

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