Wanting to use Micro SD Shield with an Arduino "Micro Board, is it possible?

Hi all,
Yep, another one of those noobs here but have been getting my feet wet daily by trial and error and haven’t fried anything yet.
I am an EE but this is my first attempt at using Arduino) as apposed to the older PLC I/O systems.

I developed a unique vibration sensor using a slide type 10K Pot. The body of the Pot is stationary while the rod with wiper slides through the body, it has a brass weight on each end with a light spring tensioner between the brass weight and the body on each end, it works very well.

I come up with a sketch that uses some smoothing and is adjustable (depending on the frequency being tested). It uses a parallel (16 pin) 16x2 LCD as on-board the monitor. I would have used a serial LCD but I just happened to have a parallel one laying around collecting dust.
It works great as it is as long as I can see the LCD screen but there are cases where I need to test vibrations and will need to record the results so I can view them after the test. I really like the “Micro Arduino Board” because of it’s size. It uses an ATmega32u4 with a 16MHz crystal oscillator.
I really need to keep the size and weight to a minimum if possible.
I guess if I had to, I could program the Atmega328, then just use the micro controller on a on a project board (along with other necessary hardware like the 16MHz crystal, etc.) I have mine setup for elapsed runtime in minutes since last reset.

I’m sure the code could easily be improved and there are probably some mistakes but it’s the best I could do on my own for the moment and it does work. I did double check the output results using my Agilent Oscilloscope.
I just need to be able to record the data from (A,0) input onto a Micro SD card.

const int numReadings = 10;

int readings[numReadings];      // the readings from the analog input
int index = 0;                  // the index of the current reading
int total = 0;                  // the running total
int average = 0;                // the average

int inputPin = A0;
   #include <LiquidCrystal.h>

   // initialize the library with the numbers of the interface pins
   LiquidCrystal lcd(12, 11, 5, 4, 3, 2);
   
   #define RES 1043
   #define AREF 5

   void setup()
{
  Serial.begin(9600); 
    lcd.begin(16, 2);
   // initialize all the readings to 0: 
   for (int thisReading = 0; thisReading < numReadings; thisReading++)
   readings[thisReading] = 0;          
}
   void loop()
 {
    // subtract the last reading:
  total= total - readings[index];         
  // read from the sensor:  
  readings[index] = analogRead(inputPin); 
  // add the reading to the total:
  total= total + readings[index];       
  // advance to the next position in the array:  
  index = index + 1;                    

  // if we're at the end of the array...
  if (index >= numReadings)              
    // ...wrap around to the beginning: 
    index = 0;                           

  // calculate the average:
  average = total / numReadings;         
  // send it to the computer as ASCII digits
  Serial.println(average);   
  delay(1);        // delay in between reads for stability   
    
    Serial.println(valToVolt(analogRead(A0)));
    delay(250);
    lcd.setCursor(0, 0);
    lcd.print(valToVolt(analogRead(A0)));
    delay(250);
    lcd.setCursor(5, 0);
    lcd.print("VDC-Average");
    lcd.setCursor(0, 1);
    lcd.print(millis()/60000);
    lcd.print(" Min.Runtime");
 }
 
    double valToVolt(double val)
 {
    return AREF*(val/RES);
    
 }

I would greatly appreciate any help I can get!!!

I tried to find something similar to this before posting my query but all I could find was using different boards other than the Arduino Micro.
Forgive me if I’m posting a query that has already been posted!

Have a great day!!

Again, Thank you very, very much!!

BTW, I've found that using a spring loaded and weighted type slide 10K Pot works much better than a Piezo element, especially at resonance levels as well as at low and high frequencies without using a band pass filter as long as I use some programming for averaging (smoothing). Not exactly sure why at this point but it does. Thank you, again!!