How to refresh app upon shaking the device?

Here is an example code.
Put this into your activity class:

  /* put this into your activity class */
  private SensorManager mSensorManager;
  private float mAccel; // acceleration apart from gravity
  private float mAccelCurrent; // current acceleration including gravity
  private float mAccelLast; // last acceleration including gravity

  private final SensorEventListener mSensorListener = new SensorEventListener() {

    public void onSensorChanged(SensorEvent se) {
      float x = se.values[0];
      float y = se.values[1];
      float z = se.values[2];
      mAccelLast = mAccelCurrent;
      mAccelCurrent = (float) Math.sqrt((double) (x*x + y*y + z*z));
      float delta = mAccelCurrent - mAccelLast;
      mAccel = mAccel * 0.9f + delta; // perform low-cut filter
    }

    public void onAccuracyChanged(Sensor sensor, int accuracy) {
    }
  };

  @Override
  protected void onResume() {
    super.onResume();
    mSensorManager.registerListener(mSensorListener, mSensorManager.getDefaultSensor(Sensor.TYPE_ACCELEROMETER), SensorManager.SENSOR_DELAY_NORMAL);
  }

  @Override
  protected void onPause() {
    mSensorManager.unregisterListener(mSensorListener);
    super.onPause();
  }

And add this to your onCreate method:

    /* do this in onCreate */
    mSensorManager = (SensorManager) getSystemService(Context.SENSOR_SERVICE);
    mSensorManager.registerListener(mSensorListener, mSensorManager.getDefaultSensor(Sensor.TYPE_ACCELEROMETER), SensorManager.SENSOR_DELAY_NORMAL);
    mAccel = 0.00f;
    mAccelCurrent = SensorManager.GRAVITY_EARTH;
    mAccelLast = SensorManager.GRAVITY_EARTH;

You can then ask “mAccel” wherever you want in your application for the current acceleration, independent from the axis and cleaned from static acceleration such as gravity.
It will be approx. 0 if there is no movement, and, lets say >2 if the device is shaked.

Based on the comments – to test this:

if (mAccel > 12) {
    Toast toast = Toast.makeText(getApplicationContext(), "Device has shaken.", Toast.LENGTH_LONG);
    toast.show();
}

Notes:

The accelometer should be deactivated onPause and activated onResume to save resources (CPU, Battery).
The code assumes we are on planet Earth 😉 and initializes the acceleration to earth gravity. Otherwise you would get a strong “shake” when the application starts and “hits” the ground from free-fall. However, the code gets used to the gravitation due to the low-cut filter and would work also on other planets or in free space, once it is initialized.
(you never know how long your application will be in use…;-)