Jove
Visualize
Contact Us

Related Concept Videos

Three-Dimensional Analysis of Strain01:29

Three-Dimensional Analysis of Strain

289
Three-dimensional strain analysis is crucial for understanding how materials deform under stress, particularly in elastic, homogeneous materials. This method employs principal stress axes to simplify complex stress states into more understandable forms. Subjected to stress, a small cubic element within a material either expands or contracts along these axes, transforming into a rectangular parallelepiped. This transformation effectively illustrates the material's deformation. The principal...
289
Fluid Pressure over Flat Plate of Variable Width01:02

Fluid Pressure over Flat Plate of Variable Width

1.8K
When a flat plate is submerged in a fluid, the fluid exerts pressure on the plate. This pressure can lead to many different phenomena, including drag and buoyancy. To understand the behavior of the fluid over a flat plate of variable width, it is essential to analyze the distribution of the pressure exerted.
The pressure distribution on the plate can be calculated by determining the force that acts on a differential area strip of the plate. Thus, the magnitude of the force is equal to the...
1.8K
Fluid Pressure over Curved Plate of Constant Width01:12

Fluid Pressure over Curved Plate of Constant Width

1.7K
When a curved plate of constant width is submerged in a liquid, the pressure acting normal to the plate varies continuously both in magnitude and direction. Calculating the magnitude and location of the resultant force at a point is often challenging for such cases. One of the methods to determine the resultant force and its location involves separately calculating the horizontal and vertical components of the resultant force. This complex calculation can be simplified by representing the...
1.7K
Transformation of Plane Stress01:18

Transformation of Plane Stress

383
Studying stress transformation is essential in understanding how stress components within a material, like a cube under plane stress, change with rotation. This change is analyzed by considering a prismatic element within the cube. As the element rotates, the stress components acting on it—both normal and shearing stresses—change in magnitude and orientation. This change is quantified using trigonometric functions of the rotation angle, relating the forces acting on the rotated element's...
383
Steady, Laminar Flow Between Parallel Plates01:17

Steady, Laminar Flow Between Parallel Plates

328
Understanding steady, laminar flow between parallel plates is essential for analyzing and designing flow in narrow rectangular channels, commonly found in various water conveyance and drainage systems. The Navier-Stokes equations govern fluid motion and are generally challenging to solve due to their nonlinearity. However, simplifications are possible in certain cases, like the steady laminar flow between parallel plates. For this scenario, we assume steady, incompressible, laminar flow.
328
Plastic Deformations of Members with a Single Plane of Symmetry01:21

Plastic Deformations of Members with a Single Plane of Symmetry

124
When a structural member undergoes plastic deformation due to bending, it is crucial to understand the position of the neutral axis and the stress distribution. This member, characterized by a single plane of symmetry, exhibits a uniform stress distribution, with negative stress above the neutral axis and positive stress below. Notably, the neutral axis does not align with the centroid of the cross-section. This misalignment is typical in cases where the cross-section is not rectangular or...
124

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Effects of a Digital Parent-Child Single-Session Growth Mindset Intervention on Adolescent Depression and Anxiety Symptoms: A Three-Arm Waitlist Randomized Controlled Trial.

European journal of investigation in health, psychology and education·2026
Same author

Spatiotemporal dynamics of leachate transport in compacted clay liners: Coupled effects of dynamic slip and microbial succession mediated by multiphase interfaces.

Environmental pollution (Barking, Essex : 1987)·2025
Same author

A Web-Based Single-Session Intervention of Growth Mindsets for Reducing Practicum-Related Anxiety Among Social Work and Counseling Trainees: A Pilot Randomized Controlled Trial.

Journal of evidence-based social work (2019)·2025
Same author

Efficacy of a Web-Based Integrated Growth Mindset Intervention on Reducing Anxiety Among Social Work and Counseling Practicum Trainees: Protocol for a 2-Arm Randomized Controlled Trial.

JMIR research protocols·2025
Same author

Using network analysis to identify central symptoms of depression and anxiety in different profiles of infertility patients.

BMC psychiatry·2025
Same author

Network analysis of stress and stigma symptoms and their associations with quality of life among Chinese female infertility patients.

BMC women's health·2024
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Experiment Video

Updated: Sep 10, 2025

Full-field Strain Measurements for Microstructurally Small Fatigue Crack Propagation Using Digital Image Correlation Method
07:37

Full-field Strain Measurements for Microstructurally Small Fatigue Crack Propagation Using Digital Image Correlation Method

Published on: January 16, 2019

9.8K

Dynamical Characterization of Plates Containing Plane Cracks with Functional Gradient Materials.

Gen Liu1, An Xi2,3, Yunchao Qi4

  • 1School of Advanced Manufacturing Technology, Guangdong Mechanical and Electrical Polytechnic, Guangzhou 510550, China.

Materials (Basel, Switzerland)
|August 28, 2025
PubMed
Summary

This study models functionally graded material (FGM) plates with cracks, revealing how crack length and material properties influence vibration frequencies and modes. Cracks alter vibration patterns and cause asymmetric displacements in FGM plates.

Keywords:
Ritz methodasymmetrical phenomenafunctionally graded material plateplanar crackvibration characteristics

More Related Videos

Finite Element Modeling for the Simulation of the Quasi-Static Compression of Corrugated Tapered Tubes
06:34

Finite Element Modeling for the Simulation of the Quasi-Static Compression of Corrugated Tapered Tubes

Published on: January 6, 2023

1.7K
A Method for Studying the Temperature Dependence of Dynamic Fracture and Fragmentation
09:12

A Method for Studying the Temperature Dependence of Dynamic Fracture and Fragmentation

Published on: June 28, 2015

8.7K

Related Experiment Videos

Last Updated: Sep 10, 2025

Full-field Strain Measurements for Microstructurally Small Fatigue Crack Propagation Using Digital Image Correlation Method
07:37

Full-field Strain Measurements for Microstructurally Small Fatigue Crack Propagation Using Digital Image Correlation Method

Published on: January 16, 2019

9.8K
Finite Element Modeling for the Simulation of the Quasi-Static Compression of Corrugated Tapered Tubes
06:34

Finite Element Modeling for the Simulation of the Quasi-Static Compression of Corrugated Tapered Tubes

Published on: January 6, 2023

1.7K
A Method for Studying the Temperature Dependence of Dynamic Fracture and Fragmentation
09:12

A Method for Studying the Temperature Dependence of Dynamic Fracture and Fragmentation

Published on: June 28, 2015

8.7K

Area of Science:

  • Solid Mechanics
  • Materials Science
  • Vibrational Analysis

Background:

  • Functionally Graded Materials (FGM) offer tunable properties by varying composition through thickness.
  • Cracks significantly impact structural integrity and dynamic behavior of materials.
  • Understanding vibration characteristics is crucial for predicting material performance and failure.

Purpose of the Study:

  • To develop a vibration model for functionally graded material (FGM) plates containing embedded planar cracks.
  • To analyze the influence of crack parameters and material gradient distribution on the vibrational characteristics of FGM plates.
  • To investigate the asymmetric displacement behavior induced by material gradients during vibration.

Main Methods:

  • Application of thin plate theory and von Kármán geometric nonlinear strain assumptions.
  • Derivation of kinetic and potential energies for different material regions.
  • Utilizing the Ritz method with displacement field trial functions to determine natural frequencies and modes.
  • Analysis of exponentially graded FGM plates with embedded planar cracks.

Main Results:

  • Natural frequencies decrease as crack length increases.
  • The presence of cracks modifies nodal line patterns and mode symmetry.
  • Relative displacement occurs between the upper and lower crack surfaces during free vibration.
  • Material gradient coefficients induce thickness-direction asymmetry and non-uniform displacements.

Conclusions:

  • Crack characteristics and material gradient coefficients are critical factors affecting FGM plate vibration.
  • Crack presence significantly alters the dynamic response and vibration modes.
  • Thickness-wise material asymmetry in FGM plates leads to complex displacement patterns, especially near cracks.