I want to know, how modal analysis helps in structural design problem?

Thank you Sir.

It is only important for structures subject to vibration (e.g. Earthquake). Modal analysis determines all the possible unforced free vibration natural mode shapes and their associated frequencies of the concerned structure without any damping . These data helps later when performing forced vibration (e.g. spectrum analysis).

Well modal analysis is very useful, actually by using orthogonality of modes, our coupled equations of motion of a N degrees of freedom system change to N decoupled equations that you can deal with them separately and this advantage is very useful and simplify our computations.

1. After creating a huge FE model, Finite Element Engineer usually run Normal mode analysis to ensure whether the model is properly constrained or not.If it is not properly constrained you can see the rigid body motion in that direction.

2. Normal Mode analysis is useful for extracting Mode shape( Eigen Vector) and their corresponding natural frequency value( Eigen Value). For a continuous system there are infinite number natural frequencies. Mode Shape describe the pattern in which the system will deform when exited at resonant frequency.

I hope this link will help you more

http://beta.machinedesign.com/medical/how-reduce-regulatory-delays-formalizing-design-control-processes?utm_test=redirect&utm_referrer=

Hi

The resonance peak tells you that you get more response at a particular frequency for a given level of excitation but does not fully explain why this is so. For this you need modes.

Simply put, when you have well separated resonance peaks, the deflection pattern at resonance is very close to the mode shape. However, when you have multiple resonances - the shapes mix and it is hard to tell one from the other. You may have also double resonance to handle.

The difference between resonance and natural frequency is that the latter is the frequency at which a system vibrates as soon as it is left free. The mode shape is then the shape at which free vibration occurs.

Also, both from a troubleshooting and numerical point of view - modes simplify life as they reduce the problem. A mode is a single degree of freedom (dof), N modes are N dofs.

So, it does make lots of sense to understand these frequencies and shapes.

And here is a link to how far you can push Experimental Modal Analysis and modal summation.

https://www.researchgate.net/post/how_to_calculate_modal_density_and_modal_overlap_factor

Here is a link to easy to read material intended for self study on various topics, e.g. modal analysis

http://qringtech.com/learnmore/recommended-reading/

Some ramblings of mine on modelling, measurement, model QA, automation and optimization is found here. http://qringtech.com/learnmore/why-simulate-measure-correlate-automate/

Sincerely

Claes

Hi

Modal analysis is the study of the dynamic properties of structures under vibrational excitation.

Modal analysis is the field of measuring and analyzing the dynamic response of structures and or fluids during excitation. Examples would include measuring the vibration of a car's body when it is attached to an electromagnetic shaker, analysis of unforced vibration response of vehicle suspension or the noise pattern in a room when excited by a loudspeaker. Modern day modal analysis systems are composed of 1)sensors such as transducers (typically accelerometers, load cells), or non contact via a Laser vibrometer, or stereophotogrammetric cameras 2) data acquisition system and an analog-to-digital converter front end (to digitize analog instrumentation signals) and 3) host PC (personal computer) to view the data and analyze it.

At final a best way to verify elastic model is the modal analysis.

Modal Analysis help you identify, measure, or analyze the dynamic response of structure or machine parameters under excitation.

Modal analysis gives you the information regarding the different modes of vibration; i.e. different shape that can be taken up by the structure during vibration. This shape during different modes are called mode shape and all mode shapes have their corresponding natural frequency. 

Modal analysis gives the natural frequencies and modes of a component (say here cantilever beam) which are its shapes in which it vibrates when excited by some external force. A continuous beam can have infinite no of modes, the lower of which are of practical interest. Modal analysis tells you about the modes which should be avoided while designing a component to avoid larger responses for known excitation forces

Dear Raju Das,

after 15 years of modal testing and calculation I feel now I have the answer for your question I had myself for so long! best answers today are:

1) Modal Model is one of the most fascinating theory in engineering for many fields: vibration, electronics, optics and more. has a lot of mathematical and computational advantage, so if your problem can use modal analysis, you are simply lucky, but you have to study all the theory and make practice.

2) experimental modal analysis is a powerful tool to validate your FEM or analytical vibration model and with today instrument is very easy.

Yes, Carlo is true

Additionally, by modal analyses, you will be able to evaluate and monitor the evolution or decreasing trends of the mechanical dynamic characteristics i.e. modulus of elasticity and shear modulus, internal friction, mechanical impedance and .... non-destructively, through the time, after probable corrosion or deterioration. 

Then you will be able to judge the health of the structural members.

Simply - the modal shape can be assumed to be the deflected shape under vibration actions.

What the designer needs to know is tolerability of the actions and the resilience of the structure under such actions. For serviceability the designer also wants to know that functionality is maintained and the user finds the range comfortable and safe.

From the practical point of view, it should provide you with Natural Frequencies and Mode Shapes. The former you can use as input in a, say, harmonic response analysis. The latter will help you identify the way a structure/system will vibrate and decide on, say, their dynamic design.

Each structure depending on its distribution of mass and stiffnes, will have a diferent  and unique behaviour during vibration. Any structure has an infinite degrees of freedom, but normally we choose only the more significative for modeling. The modal analysis will give you the natural frequency of vibration of your structure and the shape of deflection during vibration. Really the structure will vibrate as a combination of all it shapes modes, but the predominant normally is the first. Modal analysis is the base for all other analyis like Response Spectrum and Time History

Modal analysis provide you with information about the natural frequency and mode shapes of any structure if is excited and then left free. It gives idea how it will respond to any excitation at any particular frequency if the excitation frequency is near to any of its natural modes.

 In brief, modal analysis helps one determine the natural frequencies (frequencies of free vibration) and mode shapes (the shapes of deformation of the structure). This is useful because for a structure to be safe the excitation frequencies should not match the natural frequencies.

The modal analysis gives you the natural frequencies, mode shapes and additionally, mode participation factors. The maximum vibration occurs at the natural frequencies which we generally try to minimise. Hence it tells us at which frequencies the system is vulnerable to vibration. If we perform modal analysis and find that the natural frequencies are within the range of excitation frequencies, we generally ( though not always) try to modify the structure so as to shift the natural frequencies out of the range of excitation frequencies. Modeshapes tell us how the structure tends to deform at the specific natural frequencies. The modeshapes tell us which regions would experience high stresses if the deformed shape is similar to the modeshape. This is useful because we generally do not want the weld regions to be the region of high stress as it can affect the fatigue life of the structure. Further, the mode participation factors tell us which modes would be excited the most. The effective masses tell us which modes have to be included in the given dynamic ( frequency response or transient dynamic) simulations. Hope this helps.

Also, look at it from this angle:

Output from Modal Analysis becomes input for more advanced, Harmonic Response analysis, etc.

Long story short:

The combination of natural frequency, damping and mode shape gives you the UNIQUE signature of the studied physical system.

In mechanical or structural design, you need to reduce the resulted vibration response. The obtained response will show relatively high peaks at natural frequencies. Then your role as an engineer is to reduce the excitation or to fit the design (by changing stiffness,mass, damping if possible) for shifting the natural frequencies away from your system operating frequency

to fit the design (by changing stiffness,mass, damping if possible) you need to see how the mode shape looks like at that natural frequency.

The information can give me the heath of the beam at current state.

The modal frequencies and mode shape obtained from Modal analysis tells that the particular component will have higher response when a certain dynamic load is applied to it at those natural frequencies. the mode shapes are the shapes or ways in which that component will bend when applied dynamic loads of varying frequencies. The response at those exciting frequencies will depend on the components damping characteristics.

In the modal analysis, we determine the natural frequency, mode shapes and mode participation factors. The modal analysis enables the design to prevent resonant vibration or to vibrate at a specific frequency and provides engineers with an idea of how the design will respond to different dynamic load types.

Article Modal analysis of functionally graded piezoelectric material plates

These frequencies' values would reveal the resonance state, in which the structure vibrates with extremely large amplitudes, which is exceedingly detrimental to our structures. This scenario arises when the external frequency—which might be an earthquake or wind frequency—coincides with one of the inherent frequencies of the building. And the mode shape is the structure's corresponding shape at that time. Every naturally occurring frequency has a corresponding mode shape. The contour of the mode reveals the distorted forms of the structure during resonance. Assuming you already know the values of these frequencies, you may build the structure so that its frequencies do not fall inside the range of external frequencies. You have the choice of altering the stiffness, damping, characteristics, or mass value. You may save the structure from the most lethal calamities this way.

A modal analysis will give the damping of the modes through the mode fitting process. The damping is necessary input to a model, if you plan to model the beam e.g. in FEA or SEA.