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Related Concept Videos

Residual Stresses in Circular Shafts01:10

Residual Stresses in Circular Shafts

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In materials that exhibit elastic and plastic behavior, known as elastoplastic materials, residual stresses can accumulate when these materials experience plastic deformation. This deformation arises from either high levels of shearing stress or significant strains. Residual stresses are internal stresses that persist within a material after removing the external force causing deformation. This phenomenon is demonstrated when observing the behavior of a shaft under torque; notably, the...
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Design of Transmission Shafts - Stress Analysis01:15

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Designing a transmission shaft requires a thorough understanding of the stresses induced by bending moments and torques, especially in systems where power is transferred through gears. These forces create force-couple systems at the centers of the shaft's cross-sections, leading to both transverse and torsional loading. Although shearing stresses from transverse loads are typically smaller than those from torques and are often overlooked, the significant normal stresses from these loads...
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Temperature Dependent Deformation01:12

Temperature Dependent Deformation

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In a nonhomogeneous rod made up of steel and brass, restrained at both ends and subjected to a temperature change, several steps are involved in calculating the stress and compressive load. Due to the problem's static indeterminacy, one end support is disconnected, allowing the rod to experience the temperature change freely. Next, an unknown force is applied at the free end, triggering deformations in the rod's steel and brass portions. These deformations are then calculated and added...
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Mechanical Systems01:22

Mechanical Systems

328
Mechanical systems are analogous to to electrical networks where springs and masses play similar roles to inductors and capacitors, respectively. A viscous damper in mechanical systems functions similarly to a resistor in electrical networks, dissipating energy. The forces acting on a mass in such systems include an applied force in the direction of motion, counteracted by forces from the spring, a viscous damper, and the mass's acceleration. This interplay of forces is mathematically...
328
Circular Shaft - Stresses in Linear Range01:13

Circular Shaft - Stresses in Linear Range

399
Consider a scenario where a circular shaft is subject to torque that remains within the boundaries of Hooke's Law, avoiding any permanent deformation. So, the formula for shearing strain is revisited. This formula is multiplied by the modulus of rigidity, and then Hooke's Law for the shearing stress and strain is applied. As a result, the equation for shearing stress in a shaft can be derived.
399
Thin-Walled Hollow Shafts01:15

Thin-Walled Hollow Shafts

277
In analyzing a thin-walled hollow shaft subjected to torsional loading, a segment with width dx is isolated for examination. Despite its equilibrium state, this segment faces torsional shearing forces at its ends. These forces are quantitatively described by the product of the longitudinal shearing stress on the segment's minor surface and the area of this surface, leading to the concept of shear flow. This shear flow is consistent throughout the structure, indicating a uniform distribution...
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Dynamic Stiffness Matrix Approach to Free Vibration Analysis of Functionally Graded Rotor Bearing System Subjected to

Bharath Obalareddy1, Prabhakar Sathujoda1, Roberto Citarella2

  • 1Department of Mechanical Engineering, Bennett University, Greater Noida 201310, India.

Materials (Basel, Switzerland)
|February 25, 2022
PubMed
Summary

This study applies the dynamic stiffness matrix (DSM) method to analyze functionally graded (FG) rotor bearing systems under temperature gradients. The novel DSM formulation accurately predicts natural and whirl frequencies for FG rotors.

Keywords:
Wittrick–William algorithmdynamic stiffness matrixfree vibrationfunctionally graded materialsnon-linear temperature distributionrotor bearing system

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Area of Science:

  • Mechanical Engineering
  • Vibrational Analysis
  • Materials Science

Background:

  • Functionally Graded (FG) materials offer tailored properties by varying composition across their structure.
  • Rotor bearing systems are critical in rotating machinery, and their vibration characteristics are essential for performance and safety.
  • Temperature gradients can significantly influence the mechanical behavior and vibrational response of rotor systems.

Purpose of the Study:

  • To introduce and apply the dynamic stiffness matrix (DSM) method for free vibration analysis of FG rotor bearing systems.
  • To investigate the impact of temperature gradients on the vibrational behavior of FG rotors.
  • To develop novel DSM formulations for Timoshenko FG rotor elements.

Main Methods:

  • Development of DSM formulations for Timoshenko FG rotor elements based on equilibrium conditions.
  • Assembly of global dynamic stiffness matrix by combining DSM of FG rotor elements, rigid disk, and linear bearings.
  • Computation of natural whirl frequencies using the Wittrick-William algorithm.

Main Results:

  • The dynamic stiffness matrix (DSM) method was successfully applied for the first time to FG rotor bearing systems with temperature gradients.
  • Novel DSM formulations for Timoshenko FG rotor elements were developed.
  • Computed natural and whirl frequencies were validated against existing literature, demonstrating the method's exactness.

Conclusions:

  • The DSM method provides an exact analytical solution for the free vibration analysis of FG rotor bearing systems.
  • The study highlights the applicability and accuracy of the DSM method for analyzing complex FG rotor dynamics under thermal loads.
  • This research establishes a foundation for further investigations into the vibrational behavior of FG rotors in various engineering applications.