## What is assumed mode method?

The assumed modes method is an analytical procedure to discretize an arbitrarily supported linear structure carrying lumped attachments. The method consists of assuming a deflection shape in the form of a linear combination of spatial functions multiplied by a time-varying generalized coordinates.

### What are the values of shape function?

The shape functions used to interpolate the coordinates in Eq. (7.70) are the same as those used for interpolation of the displacements. Such an element is called an isoparametric element. However, the shape functions for coordinate and displacement interpolations do not necessarily have to be the same.

#### How do you describe a shape function?

The shape function is the function which interpolates the solution between the discrete values obtained at the mesh nodes. Therefore, appropriate functions have to be used and, as already mentioned, low order polynomials are typically chosen as shape functions. In this work linear shape functions are used.

**What are the characteristics of shape function?**

Characteristic of Shape function

- Value of shape function of particular node is one and is zero to all other nodes.
- Sum of all shape function is one.
- Sum of the derivative of all the shape functions for a particular primary variable is zero.

**How do you measure natural frequencies of a cantilever beam?**

Beam is fixed from one end and the other end is free (cantilevered beam). The formula used for cantilever beam natural frequency calculations is: fn=Kn2π√EIgwl4 f n = K n 2 π E I g w l 4 . E in the formula is modulus of elasticity and I is the area moment of inertia.

## What does shape function represent *?

The shape function is the function which interpolates the solution between the discrete values obtained at the mesh nodes. Therefore, appropriate functions have to be used and, as already mentioned, low order polynomials are typically chosen as shape functions.

### What does a shape function depend on?

The number of shape functions will depend upon the number of nodes and the number of variables per node. The shape functions can therefore be viewed as functions, which denote the contribution of each nodal value at internal points of the element.

#### What conditions must a typical shape function satisfy?

Explanation: In general shape functions need to satisfy that, first derivatives must be finite within element. Shape functions are interpolation functions. First derivatives are finite within element because for easy calculations.

**How does mass affect frequency of oscillation?**

If one were to increase the mass on an oscillating spring system with a given k, the increased mass will provide more inertia, causing the acceleration due to the restoring force F to decrease (recall Newton’s Second Law: F=ma ). This will lengthen the oscillation period and decrease the frequency.