pdo and like query - php

Question

I have a query and it looks like:
if (strlen($search->q)) {
$where[] = ' AND (`name` LIKE :q)';
$arr['q'] = "%" . $search->q . "%";
}
$sql = 'SELECT
*,
FROM
`shop_products`
WHERE
1=1
'.implode('', $where);
Not I'm trying to get products from DB:
$result->products = $db->query($sql, $arr, $search->limitstart, $search->limit)->fetchAll();
My query function:
public function query($sql, $params=array(), $offset = null, $limit = null){
if (!is_null($offset) && !is_null($limit)) {
$sql .= ' LIMIT :limit OFFSET :offset';
$params['limit'] = (int)$limit;
$params['offset'] = (int)$offset;
}
$stmt = $this->database->prepare($sql);
if (!empty($params)) {
foreach($params as $key => $value) {
if(is_int($value)) {
$param = PDO::PARAM_INT;
} elseif(is_bool($value)) {
$param = PDO::PARAM_BOOL;
} elseif(is_null($value)) {
$param = PDO::PARAM_NULL;
} elseif(is_string($value)) {
$param = PDO::PARAM_STR;
} else {
$param = false;
}
if($param) $stmt->bindValue(":$key", $value, $param);
}
}
$stmt->execute();
return $stmt;
}
My problem that LIKE instruction does not work. How can I solve this problem and fix my code?