derived mode shapes

USAGE SUMMARY

The phrase "derived mode shapes" is correct and usable in written English.
It can be used in contexts related to engineering, physics, or mathematics, particularly in discussions about vibration analysis or structural dynamics. Example: "The analysis revealed several derived mode shapes that indicate potential points of failure in the structure."

✓ Grammatically correct

Science

Human-verified examples from authoritative sources

Exact Expressions

3 human-written examples

Detailed characterizations of these modes from their derived mode shapes have been achieved for the typical case of triple-layered GSs, as well as general MLGSs.

Mechanical Systems and Signal Processing

Detailed characterizations of these modes from their derived mode shapes have been achieved for the typical case of an embedded triple-layered GSs, as well as general embedded MLGSs.

Computational Materials Science

Parametric study is also conducted on the derived mode shapes to systematically investigate the interference effect of the hyperbolic component near the boundaries and provide valuable guidelines for the sensor deployment in engineering applications.

Engineering Structures

Human-verified similar examples from authoritative sources

Similar Expressions

57 human-written examples

The analytical expressions derived for mode shapes, curvature shapes, natural frequencies and an improved strain energy based damage measure, are verified using experiments.

International Journal of Solids and Structures

Particularly, we derive the mode shape in order to yield a bounded inverse dynamics solution.

Applied Mathematical Modelling

In addition, two extended parameters initially named as power mode shape curvature and power flexibility are derived using power mode shapes.

Journal of Sound and Vibration

Consequently, the correct pairing of experimentally obtained and numerically derived natural frequencies and mode shapes is important.

Journal of Sound and Vibration

Explicit analytical expressions are derived for the vibrating mode shapes of a curved, bending-torsional-shearing coupled beam under clamped clamped boundary condition with the help of symbolic computing package Mathematica, and a process of searching is used to determine the natural frequencies.

Journal of Sound and Vibration

A general formulation is then derived for the mode shape, frequency response, and state-space representation of system.

Journal of Sound and Vibration

This paper derives the analytical vibration mode shapes of a continuous beam on rigid supports from the eigenvalue and eigenfunction analysis, thus eliminating the modelling errors from the assumed mode shapes.

Journal of Sound and Vibration

Exact expressions for natural frequencies and mode shapes are derived.

Journal of Sound and Vibration

Expert writing Tips

Best practice

When discussing complex systems, clearly specify the method used to obtain the "derived mode shapes". This provides context and enhances the reproducibility of your work.

Common error

Avoid assuming that "derived" automatically implies high accuracy. While derivation suggests a mathematical or systematic process, always validate the "derived mode shapes" with experimental data or simulations to ensure reliability.

Linguistic Context

The phrase "derived mode shapes" functions as a noun phrase that refers to specific patterns of vibration obtained through a process of calculation, analysis, or extraction. Ludwig AI indicates its correct usage in technical contexts.

Expression frequency: Common

Frequent in

Science

100%

Less common in

News & Media

0%

Formal & Business

0%

Ludwig's WRAP-UP

The phrase "derived mode shapes" is a grammatically sound and commonly used term in scientific and engineering contexts, as confirmed by Ludwig AI. It refers to vibrational patterns obtained through calculation or analysis. While "derived" implies a systematic process, validation with experimental data is crucial. Alternative phrases such as "calculated mode shapes" or "estimated mode shapes" can be used to add nuance. In writing, clearly specify the derivation method for clarity and reproducibility.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

calculated mode shapes

Emphasizes the computational aspect of obtaining the mode shapes.

estimated mode shapes

Highlights that the mode shapes are approximations or estimations.

determined mode shapes

Focuses on the process of finding or establishing the mode shapes.

obtained mode shapes

Indicates the mode shapes were acquired through a specific method.

extracted mode shapes

Suggests the mode shapes were isolated or pulled from a larger dataset.

predicted mode shapes

Highlights that the mode shapes are forecasts based on a model.

analytical mode shapes

Specifies that the mode shapes were found through analytical methods.

numerical mode shapes

Indicates the mode shapes are the result of numerical simulations.

theoretical mode shapes

Emphasizes the mode shapes are based on theoretical models.

simulated mode shapes

Highlights that the mode shapes come from a simulation.

FAQs

How are "derived mode shapes" used in structural analysis?

"Derived mode shapes" are used to understand how a structure vibrates at different frequencies, helping engineers identify potential weaknesses and optimize designs.

What is the difference between "derived mode shapes" and experimental mode shapes?

"Derived mode shapes" are obtained through analytical or numerical methods, while experimental mode shapes are measured directly from physical testing. They should ideally correlate, but differences can highlight modeling inaccuracies.

What are some alternatives to "derived mode shapes"?

You can use alternatives like "calculated mode shapes", "estimated mode shapes", or "obtained mode shapes" depending on the specific method used to determine the mode shapes.

How do I validate "derived mode shapes"?

You can validate "derived mode shapes" by comparing them with experimental results, performing convergence studies in numerical simulations, and checking for consistency with theoretical predictions.