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Indeterminate Structure

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Indeterminate structures refer to structures where internal forces and reactions cannot be determined using only the equations of static equilibrium.  Indeterminate structures have more unknown forces and reaction forces than equations of static equilibrium that can be used to determine them. Indeterminate structures are often used in engineering to create complex, efficient, and aesthetically pleasing structures. There are various types of indeterminate structures used in engineering and...
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When designing or analyzing a structural member, it is important to consider the internal loadings developed within the member. These internal loadings include normal force, shear force, and bending moment. Engineers can ensure that the structural member can support the applied external forces by calculating these internal loadings.
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A close look at earthquakes provides evidence for the conditions appropriate for resonance, standing waves, and constructive and destructive interference. A building may vibrate for several seconds with a driving frequency matching the building's natural frequency of vibration; this produces a resonance that results in one building collapsing while the neighboring buildings do not. Often, buildings of a certain height are devastated, while other taller buildings remain intact. This...
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In mechanical engineering, the stability of systems under various forces is critical for designing durable and efficient structures. One fundamental way to explore these concepts is by analyzing systems like two rods connected at a pivot point, O, with a torsional spring of spring constant k at the pivot point. This system is similar in appearance to a scissor jack used to change tires on a car. In this case, the arms of the linkage (equivalent to the rods in this system) are entirely vertical,...
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Deformation of a Beam under Transverse Loading01:15

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Understanding beam deflection, particularly for indeterminate beams with overhanging segments and multiple concentrated loads, is crucial for ensuring structural integrity and functionality. The process begins with constructing an accurate free-body diagram, which helps identify the forces and moments acting on the beam. This diagram is vital for visualizing how bending moments vary along the beam's length, influencing its curvature.
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When a rigid body is hanging freely from a fixed pivot point and is displaced, it oscillates similar to a simple pendulum and is known as a physical pendulum. The period and angular frequency of a physical pendulum are obtained by using the small-angle approximation and drawing parallels with a spring-mass system. The small-angle approximation (sinθ=θ) is valid up to about 14°.
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Simulation of Human-induced Vibrations Based on the Characterized In-field Pedestrian Behavior
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Physics-informed deep learning for structural vibration identification and its application on a benchmark structure.

Minte Zhang1, Tong Guo1, Guodong Zhang1

  • 1School of Civil Engineering, Southeast University, Nanjing 210096, People's Republic of China.

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
|November 19, 2023
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Summary
This summary is machine-generated.

This study introduces a novel physics-informed deep learning (PIDL) framework for structural vibration identification. PIDL integrates deep learning with structural dynamics, improving accuracy in identifying excitations and parameters for civil structure monitoring.

Keywords:
explicit time-domain methodgenerative deep learningphysics-informed deep learningstructural health monitoringstructural vibration identification

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Area of Science:

  • Civil Engineering
  • Machine Learning
  • Structural Dynamics

Background:

  • Structural vibration identification is crucial for civil engineering, relying on sensor data.
  • Predicting responses at unmonituted locations with limited data is challenging.
  • Current deep learning methods struggle to incorporate physics laws into vibration analysis.

Purpose of the Study:

  • To present a novel physics-informed deep learning (PIDL) framework for structural vibration identification.
  • To combine deep generative networks with structural dynamics knowledge.
  • To improve the accuracy and reliability of vibration analysis in civil structures.

Main Methods:

  • Developed a PIDL framework integrating a convolutional neural network and a physics-informed variational autoencoder.
  • Utilized explicit time-domain (ETD) analysis with generated unit impulse response (UIR) signals.
  • Incorporated an ETD method-aided convolution function into the loss function for UIR signal alignment.

Main Results:

  • The PIDL framework effectively extracts physics-related dynamics features.
  • Accurate identification of excitation signals and latent physics parameters was achieved across various damage patterns.
  • Demonstrated improved accuracy and reliability compared to conventional deep learning methods.

Conclusions:

  • The PIDL framework successfully integrates structural dynamics knowledge into deep learning for vibration analysis.
  • The study highlights the potential of PIDL in civil structure monitoring and health assessment.
  • This research advances structural vibration identification by incorporating physics-informed machine learning.