Different Modes of Combination in Response Spectrum by SolidWorks Simulation

The response spectrum method is used to compute inertial response, estimates of response quantities developed for each mode, each direction of excitation and each input, if multiple inputs are considered. The total response is then formed by summing over all modal component, spatial component and excitation component responses. It estimate the structural response to short, nondeterministic, transient dynamic events. Examples of such events are earthquakes and shocks. Since the exact time history of the load is not known, it is difficult to perform a time-dependent analysis.

It is a widely used procedure for performing elastic dynamic seismic analysis, represents the set of the maximum acceleration, velocity or displacement responses of a family of single-degree-of-freedom (SDOF) damped oscillators. 

Fig: 1

For a given time period of system, maximum response is picked. This process is continued for all range of possible time periods of SDOF system. Final plot with system time period on x-axis and response quantity on y-axis is the required response spectra pertaining to specified damping ratio and input ground motion as acceleration, velocity or displacement response.

Factor Influencing Response Spectra:

1. Damping in the system

2. Time period of the system

3. Energy release mechanism

Errors in Evaluation of Response Spectrum:

Truncation Error: - In general, a truncation error exists in numerical methods for

integrating differential equations.

Rounding the Time Record: - For earthquake records digitized at irregular time intervals, the integration technique proposed in this report requires rounding of the time record and the attendant error depends on the way the rounding is done. For round-off to 0.005 sec, the average error in spectrum values is expected.

Error Due to Discretization: - In any numerical method of computing the spectra, the

response is obtained at a set of discrete points. Since spectral values represent

maximum values of response parameters which may not occur at these discrete points,

discretization introduces an error which gives spectrum values lower than the true

values.

Multi degree of freedom (MDOF) systems are usually analyzed using Modal Analysis. A

typical MDOF system with ‘n’ degree of freedom. The system when subjected to ground motion undergoes deformations in number of possible ways. These deformed shapes are known as modes of vibration or mode shapes.

In SolidWorks Simulation, we can predict the Displacement, Maximum Stress Induced and frequency with respective mode shapes of the system. with response as acceleration, velocity or displacement input to the system, with irrespective of the system type, the system can be 

Regular or Irregular as shown in Fig:2 & Fig:3.

  Fig:2(irregular Structure)

Fig:3(Regular) 

Regular Structure:

The design shall be approximately symmetrical in plan with respect to two orthogonal axis with flowing assumptions:

1. Location of joints with equal spacing in the design.

2. No horizontal or vertical irregularity of the structure

3. No change in material or shape of the structure cross section.

Irregular Structure:

If the design does not follow any assumptions of the regular system, becomes irregular structure. Most of the mechanical designs are Irregular in nature, as there may be material changes to the main members to improve the strength of the design.

There are different methods that are used for combining the response of each direction of system the methods for MDOF system are as follows:

1. Square root of sum of squares (SRSS) Method

2. Absolute Sum (ABSSUM) Method

3. Complete quadratic combination (CQC) Method

4. Naval Research Laboratory (NRL)

Square root of sum of squares (SRSS) Method:

The maximum response is obtained by square root of sum of square of response in each mode of vibration, the effect is calculated for each individual Frequency of the system with the defined response at different directions, these responses are summed up and an averaged.

Limitation of SRSS:

· There is a poor estimator of peak responses when applied to systems with closely spaced natural periods.

· Significant errors are caused when working with Irregular system.

Absolute Sum Method:

The peak responses of all the modes are added algebraically, assuming that all modal peaks occur at same time. The maximum response is given by:

Complete quadratic combination (CQC) Method:

The previously illustrated errors which are inherent in absolute sum or the SRSS method are rectified with CQC, The maximum response from all the modes is calculated as:

r_max is the maximum response

r_i, r_j are maximum responses in the i^th and j^th modes

α_ij is Cross Modal Coefficient

ξ is Modal  Damping Ratio, β is Frequency Ratio [ ]

Naval Research Laboratory (NRL) Method:

The Naval Research Laboratory (NRL) method to combine the peak responses from all mode shapes into overall displacements and stresses. It is modification of the SRSS Method, takes the absolute value of the response for the mode that exhibits the largest response and adds it to the SRSS response of the remaining modes the maximum response from all the modes is calculated as:

Where {u_j}_max represents the mode with the largest response among all modal responses.

All the above methods discussed are available in SolidWorks Simulation, according to the structure type and the user requirement, we can define the mode combination method as shown in the Fig: 4.

Fig: 4

We had discussed the different mode combination techniques in Response Spectrum, and the purpose of the different techniques and also the model equations of the techniques with their limitations.

THANK YOU FOR READING!

What is Pores Medium & How to Simulate it in SOLIDWORKS Flow Simulation?

Material which contain Pores are called Porous material, the weight of the porous material is less when compared to the solid material. The porosity of the material is defined by the Porous size the is formed in the material, there are different techniques for manufacturing these type of material depending on the size of the porous void that to be formed.

There are wide range of applications like catalysis, chemical separations, tissue engineering and exhaust manifold. In the exhaust manifold the harm full chemicals are removed by using porous material.

There are different types of Porous material according to direction of flow

1. Isotropic

2. Non Isotropic(Unidirectional, Axisymmetric, Orthotropic)

There will be change in the pressure, velocity and direction of flow changes according to the porous medium, by using Solidworks flow simulation can simulate the flow.

Steps for creating the Porous medium in Flow study:

1. Create the wizard by defining the Flow type, units, types of Fluid.

2. If the porous is not showing in the tree then Right click on project(1) options appear as shown in the Fig:1, click customize tree

3. The options appear as shown in Fig:2, click on the Porous Medium to get activated.

Fig 1

Fig 2

  

4. An exhaust manifold with porous medium and the inlet and out let manifolds as shown below:

5. Defining the porous material to individual domains, one part as unidirectional are shown below:

6. Defining  isotropic for the other domain as shown below:

7. The Fig:3 shows how the porous medium is defined in the study 

Fig 3

By running the simulation we can obtain the inlet and outlet velocity, pressure drop, due to porous medium, depending on the size of the porous and the type of the porous there will be change in the velocity, pressure

drop, these can be captured prier using SolidWorks Flow simulation.

 

SOLIDWORKS SOLUTIONS FOR POWER AND PROCESS

Design Challenges Faced in Power and Process Industry

1. Optimizing work flow for specialized domains such as piping, tubing and welding.
2. Errors in design resulting in engineering rework and delays
3. A bottleneck appears when overlooking a entire product which was developed under various CAD Software due to various constrains
4. Unexpected Failure faced at higher pressure operation
5. The life of the product not able to predict, due to that maintenance overtime and process productivity is critical

Addressing these Challenge through SOLIDWORKS Solutions.

1. In SolidWorks we don’t need to spend our time on designing standard parts and components, where all the standard components are available in design library itself which can be obtained by simple drag and drop. For further validation of the product those standard can be directly fetched in SolidWorks Simulation.

 

Fig1: Design Library

2. SOLIDWORKS helps to eliminate the rework in design process by using design table automation, DriveworksXpress and customized integrated automation solutions.
3. Now with SOLIDWORKS you can import and export different types of cad files and neutral file formats.

Fig2:supported File Formats

4. Failure can be avoided by predicting different pressure operation at various temperatures for the given Product in the development Stage itself.

Fig3:Displacement analysis

5. The life and damage of the product would be predicted depending upon its working cycle over a period of time. Through the process, we can pre-schedule maintenance so that process productivity will be efficient.

Fig4: Fatigue analysis

Benefits of SOLIDWORKS using Power &Process industry

• Eliminate reworks and save your time.
• Reduce development cost & overall cast of the design.
• Easily automated the layout design in full plant
• The repeated documentation can be reduced.
• Validation of designs for efficiency and performance.

Customer Voice:

“We spent so much time trying to communicate design intent in 2D drawings—time that is completely eliminated when you present a realistic 3D rendering of a concept using SOLIDWORKS”

- Gary Hager 

Senior Project Manager/Engineer

 

Comparison of SolidWorks Simulation with Mathematical Calculation

Mathematical Calculation

The below shown in figure 1 which formed by two different materials AISI 1020 and Alloy Steel. The component is fixed at one end and in other side axial load is applied.

Figure 1

The compound beam as two elements and three nodes as shown in figure 2

Figure 2

SolidWorks Simulation

Simulation Procedure

• Cad Geometry
• Type of Analysis
• Type of Materials
• Fixtures
• Loads
• Meshing
• Results

Cad Geometry

Study Results

Stress Results

Displacement Results