Posted On :

(Dynamic Response/Time-History Analysis) Structure response to arbitrary, time-dependent loading.

**TRANSIENT RESPONSE ANALYSIS**

*(Dynamic Response/Time-History Analysis)*

Structure response to *arbitrary, time-dependent loading*.

Compute responses by integrating through time:

*B. Modal Method*

First, do the transformation of the dynamic equations using the modal matrix before the time marching:

Then, solve the uncoupled equations using an integration method. Can use, e.g., 10%, of the total modes (m= n/10).

Uncoupled system, Fewer equations,

No inverse of matrices,

More efficient for large problems.

**1Cautions in Dynamic Analysis**

*Symmetry*: It should not be used in the dynamic analysis (normal modes, etc.)* *because symmetric structures can have antisymmetric modes.

Mechanism, rigid body motion means = 0. Can use this to check FEA models to see if they are properly connected and/or supported.

Input for FEA: loading *F(t)* or *F( )* can be very complicated in real applications and often needs to be filtered first before used as input for FEA.

*Examples*

Impact, drop test, etc.

**PROBLEM**

In the spring structure shown k1 = 10 lb./in., k2 = 15 lb./in., k3 = 20 lb./in., P= 5 lb. Determine the deflection at nodes 2 and 3.

**Solution:**

Again apply the three steps outlined previously.

*Step 1: Find the Element Stiffness Equations*

*Element 1:*

*Step 2: Find the Global stiffness matrix*

Now the global structural equation can be written as above.

*Step 3: Solve for Deflections*

The known boundary conditions are: u1 = u4 = 0, F3 = P = 3lb. Thus, rows and columns 1 and 4 will drop out, resulting in t following matrix equation,

Solving, we get u2 = 0.0692 & u3 = 0.1154

**PROBLEM **

In the spring structure shown, k1 = 10 N/mm, k2 = 15 N/mm, k3 = 20 N/mm, k4 = 25 N/mm, k5 = 30 N/mm, k6 = 35 N/mm. F2 = 100 N. Find the deflections in all springs.

**Solution:**

Here again, we follow the three-step approach described earlier, without specifically mentioning at each step.

Now, apply the boundary conditions, u1 = u4 = 0, F2 = 100 N. This is carried out by deleting the rows 1 and 4, columns 1 and 4, and replacing F2 by 100N. The final matrix equation is,

Deflections:

Spring 1: u4 – u1 = 0

Spring 2: u2 – u1 = 1.54590

Spring 3: u3 – u2 = -0.6763

Spring 4: u3 – u2 = -0.6763

Spring 5: u4 – u2 = -1.5459

Spring 6: u4 – u3 = -0.8696

Tags : Mechanical - Finite Element Analysis - Dynamic Analysis Using Element Method

Last 30 days 57 views
Related words : ### What is Transient Response Analysis Define Transient Response Analysis Definition of Transient Response Analysis where how
meaning of Transient Response Analysis
lecturing notes for Transient Response Analysis lecture notes question and answer for Transient Response Analysis answer
Transient Response Analysis study material Transient Response Analysis assignment Transient Response Analysis reference description of Transient Response Analysis
explanation of Transient Response Analysis brief detail of Transient Response Analysis easy explanation solution Transient Response Analysis wiki
Transient Response Analysis wikipedia how why is who were when is when did where did Transient Response Analysis list of Transient Response Analysis school assignment college assignment
Transient Response Analysis college notes school notes kids with diagram or figure or image difference between Transient Response Analysis www.readorrefer.in - Read Or Refer

Recent New Topics :